WEBVTT Kind: captions Language: en 00:00:00.800 --> 00:00:02.470 align:start position:0% Hello<00:00:00.960> everybody.<00:00:01.480> I'm<00:00:01.640> Alexa<00:00:02.000> Proball,<00:00:02.360> the 00:00:02.470 --> 00:00:02.480 align:start position:0% Hello everybody. I'm Alexa Proball, the 00:00:02.480 --> 00:00:04.950 align:start position:0% Hello everybody. I'm Alexa Proball, the head<00:00:02.640> of<00:00:02.760> commutate<00:00:03.160> Lake<00:00:03.400> sale<00:00:03.960> and<00:00:04.520> here<00:00:04.760> we 00:00:04.950 --> 00:00:04.960 align:start position:0% head of commutate Lake sale and here we 00:00:04.960 --> 00:00:08.030 align:start position:0% head of commutate Lake sale and here we are<00:00:05.400> at<00:00:05.520> the<00:00:05.640> Go<00:00:05.960> Sim<00:00:06.240> Paris<00:00:07.320> and<00:00:07.600> with<00:00:07.800> us<00:00:07.960> we 00:00:08.030 --> 00:00:08.040 align:start position:0% are at the Go Sim Paris and with us we 00:00:08.040 --> 00:00:10.430 align:start position:0% are at the Go Sim Paris and with us we have<00:00:08.440> Sir<00:00:08.680> Timothy<00:00:09.040> Gowers<00:00:10.040> who<00:00:10.240> is<00:00:10.400> a 00:00:10.430 --> 00:00:10.440 align:start position:0% have Sir Timothy Gowers who is a 00:00:10.440 --> 00:00:12.150 align:start position:0% have Sir Timothy Gowers who is a professor<00:00:10.880> at<00:00:10.960> College<00:00:11.280> de<00:00:11.360> France<00:00:11.920> and 00:00:12.150 --> 00:00:12.160 align:start position:0% professor at College de France and 00:00:12.160 --> 00:00:15.190 align:start position:0% professor at College de France and University<00:00:12.560> of<00:00:12.640> Cambridge<00:00:13.640> and<00:00:14.520> he<00:00:14.680> can<00:00:14.880> order 00:00:15.190 --> 00:00:15.200 align:start position:0% University of Cambridge and he can order 00:00:15.200 --> 00:00:17.710 align:start position:0% University of Cambridge and he can order this<00:00:15.400> conference<00:00:15.960> and<00:00:16.200> he's<00:00:16.520> a<00:00:17.080> field<00:00:17.360> medal 00:00:17.710 --> 00:00:17.720 align:start position:0% this conference and he's a field medal 00:00:17.720 --> 00:00:18.830 align:start position:0% this conference and he's a field medal winner 00:00:18.830 --> 00:00:18.840 align:start position:0% winner 00:00:18.840 --> 00:00:21.830 align:start position:0% winner in<00:00:19.200> mathematics<00:00:19.840> and<00:00:20.080> in<00:00:20.200> combinatorics 00:00:21.830 --> 00:00:21.840 align:start position:0% in mathematics and in combinatorics 00:00:21.840 --> 00:00:23.390 align:start position:0% in mathematics and in combinatorics and 00:00:23.390 --> 00:00:23.400 align:start position:0% and 00:00:23.400 --> 00:00:25.110 align:start position:0% and it's<00:00:23.600> really<00:00:23.800> exciting.<00:00:24.400> I<00:00:24.520> went<00:00:24.760> to<00:00:24.840> math 00:00:25.110 --> 00:00:25.120 align:start position:0% it's really exciting. I went to math 00:00:25.120 --> 00:00:26.590 align:start position:0% it's really exciting. I went to math school<00:00:25.480> in 00:00:26.590 --> 00:00:26.600 align:start position:0% school in 00:00:26.600 --> 00:00:28.990 align:start position:0% school in Moscow.<00:00:27.720> One<00:00:27.880> of<00:00:27.960> my<00:00:28.040> classmates<00:00:28.520> Igor<00:00:28.720> Park 00:00:28.990 --> 00:00:29.000 align:start position:0% Moscow. One of my classmates Igor Park 00:00:29.000 --> 00:00:31.110 align:start position:0% Moscow. One of my classmates Igor Park is<00:00:29.200> a<00:00:29.440> well-known<00:00:29.760> combinatorics<00:00:30.320> scientist. 00:00:31.110 --> 00:00:31.120 align:start position:0% is a well-known combinatorics scientist. 00:00:31.120 --> 00:00:32.510 align:start position:0% is a well-known combinatorics scientist. So<00:00:31.560> I 00:00:32.510 --> 00:00:32.520 align:start position:0% So I 00:00:32.520 --> 00:00:34.310 align:start position:0% So I you<00:00:32.599> know,<00:00:33.080> I'm<00:00:33.200> not<00:00:33.560> you<00:00:33.600> know,<00:00:33.880> I<00:00:34.000> love 00:00:34.310 --> 00:00:34.320 align:start position:0% you know, I'm not you know, I love 00:00:34.320 --> 00:00:35.990 align:start position:0% you know, I'm not you know, I love mathematics<00:00:34.800> but<00:00:34.960> never<00:00:35.360> you<00:00:35.440> know,<00:00:35.640> work<00:00:35.880> at 00:00:35.990 --> 00:00:36.000 align:start position:0% mathematics but never you know, work at 00:00:36.000 --> 00:00:36.950 align:start position:0% mathematics but never you know, work at this 00:00:36.950 --> 00:00:36.960 align:start position:0% this 00:00:36.960 --> 00:00:38.950 align:start position:0% this amazing<00:00:37.640> levels.<00:00:37.960> It's<00:00:38.080> really<00:00:38.240> exciting<00:00:38.760> and 00:00:38.950 --> 00:00:38.960 align:start position:0% amazing levels. It's really exciting and 00:00:38.960 --> 00:00:40.750 align:start position:0% amazing levels. It's really exciting and all<00:00:39.360> all<00:00:39.520> the<00:00:39.680> eyes<00:00:39.880> math,<00:00:40.280> right?<00:00:40.520> It's<00:00:40.680> all 00:00:40.750 --> 00:00:40.760 align:start position:0% all all the eyes math, right? It's all 00:00:40.760 --> 00:00:42.430 align:start position:0% all all the eyes math, right? It's all matrices<00:00:41.800> all<00:00:41.920> the<00:00:42.000> way<00:00:42.080> down.<00:00:42.280> So<00:00:42.360> it's 00:00:42.430 --> 00:00:42.440 align:start position:0% matrices all the way down. So it's 00:00:42.440 --> 00:00:44.710 align:start position:0% matrices all the way down. So it's really<00:00:42.600> exciting<00:00:43.360> to<00:00:43.520> have 00:00:44.710 --> 00:00:44.720 align:start position:0% really exciting to have 00:00:44.720 --> 00:00:46.790 align:start position:0% really exciting to have Timothy<00:00:45.120> with<00:00:45.360> us<00:00:45.720> and<00:00:46.280> can<00:00:46.440> you<00:00:46.480> tell<00:00:46.640> us<00:00:46.760> a 00:00:46.790 --> 00:00:46.800 align:start position:0% Timothy with us and can you tell us a 00:00:46.800 --> 00:00:49.350 align:start position:0% Timothy with us and can you tell us a little<00:00:47.080> bit<00:00:47.360> about<00:00:48.120> how<00:00:48.320> you<00:00:48.440> came<00:00:48.680> here<00:00:49.200> and 00:00:49.350 --> 00:00:49.360 align:start position:0% little bit about how you came here and 00:00:49.360 --> 00:00:52.750 align:start position:0% little bit about how you came here and what<00:00:49.480> you<00:00:49.600> talked<00:00:49.840> about<00:00:50.240> in<00:00:50.360> your<00:00:50.560> keynote? 00:00:52.750 --> 00:00:52.760 align:start position:0% what you talked about in your keynote? 00:00:52.760 --> 00:00:55.390 align:start position:0% what you talked about in your keynote? Yes,<00:00:52.960> I<00:00:53.000> mean<00:00:53.160> I<00:00:53.240> came<00:00:53.480> here<00:00:53.640> because<00:00:54.720> uh 00:00:55.390 --> 00:00:55.400 align:start position:0% Yes, I mean I came here because uh 00:00:55.400 --> 00:00:58.550 align:start position:0% Yes, I mean I came here because uh I've<00:00:55.680> got<00:00:55.880> an<00:00:55.960> invitation<00:00:56.680> and<00:00:57.520> uh 00:00:58.550 --> 00:00:58.560 align:start position:0% I've got an invitation and uh 00:00:58.560 --> 00:01:00.110 align:start position:0% I've got an invitation and uh I'm<00:00:59.040> although<00:00:59.240> I'm<00:00:59.360> a<00:00:59.400> mathematician,<00:01:00.000> I'm 00:01:00.110 --> 00:01:00.120 align:start position:0% I'm although I'm a mathematician, I'm 00:01:00.120 --> 00:01:01.830 align:start position:0% I'm although I'm a mathematician, I'm also<00:01:00.440> very<00:01:00.680> interested<00:01:01.080> in<00:01:01.360> automatic 00:01:01.830 --> 00:01:01.840 align:start position:0% also very interested in automatic 00:01:01.840 --> 00:01:03.310 align:start position:0% also very interested in automatic theorem<00:01:02.160> proving<00:01:02.480> and<00:01:02.600> I<00:01:02.680> have<00:01:02.800> a<00:01:02.880> group<00:01:03.160> in 00:01:03.310 --> 00:01:03.320 align:start position:0% theorem proving and I have a group in 00:01:03.320 --> 00:01:03.990 align:start position:0% theorem proving and I have a group in Cambridge 00:01:03.990 --> 00:01:04.000 align:start position:0% Cambridge 00:01:04.000 --> 00:01:05.750 align:start position:0% Cambridge >> Mhm.<00:01:04.559> devoted<00:01:04.920> to<00:01:05.040> automatic<00:01:05.519> theorem 00:01:05.750 --> 00:01:05.760 align:start position:0% >> Mhm. devoted to automatic theorem 00:01:05.760 --> 00:01:07.590 align:start position:0% >> Mhm. devoted to automatic theorem proving.<00:01:06.120> That's<00:01:06.360> to<00:01:06.480> say<00:01:07.000> um 00:01:07.590 --> 00:01:07.600 align:start position:0% proving. That's to say um 00:01:07.600 --> 00:01:08.910 align:start position:0% proving. That's to say um just<00:01:07.840> trying<00:01:08.040> to<00:01:08.120> get<00:01:08.280> computers<00:01:08.680> to<00:01:08.760> do 00:01:08.910 --> 00:01:08.920 align:start position:0% just trying to get computers to do 00:01:08.920 --> 00:01:10.350 align:start position:0% just trying to get computers to do mathematics. 00:01:10.350 --> 00:01:10.360 align:start position:0% mathematics. 00:01:10.360 --> 00:01:12.070 align:start position:0% mathematics. But<00:01:11.000> uh<00:01:11.080> our<00:01:11.200> focus<00:01:11.600> is<00:01:11.720> a<00:01:11.760> little<00:01:11.960> bit 00:01:12.070 --> 00:01:12.080 align:start position:0% But uh our focus is a little bit 00:01:12.080 --> 00:01:13.670 align:start position:0% But uh our focus is a little bit different<00:01:12.520> from<00:01:13.080> um 00:01:13.670 --> 00:01:13.680 align:start position:0% different from um 00:01:13.680 --> 00:01:15.310 align:start position:0% different from um a<00:01:13.720> lot<00:01:13.920> of<00:01:14.040> what's<00:01:14.200> going<00:01:14.440> on<00:01:14.600> in<00:01:14.680> that<00:01:15.240> uh 00:01:15.310 --> 00:01:15.320 align:start position:0% a lot of what's going on in that uh 00:01:15.320 --> 00:01:18.110 align:start position:0% a lot of what's going on in that uh domain.<00:01:15.800> So<00:01:16.000> a<00:01:16.040> lot<00:01:16.200> of<00:01:16.280> what's<00:01:16.400> happening<00:01:16.760> is 00:01:18.110 --> 00:01:18.120 align:start position:0% domain. So a lot of what's happening is 00:01:18.120 --> 00:01:19.550 align:start position:0% domain. So a lot of what's happening is what<00:01:18.280> you<00:01:18.320> might<00:01:18.480> just<00:01:18.640> call<00:01:19.240> prompt 00:01:19.550 --> 00:01:19.560 align:start position:0% what you might just call prompt 00:01:19.560 --> 00:01:21.590 align:start position:0% what you might just call prompt engineering.<00:01:20.360> You're<00:01:20.440> just<00:01:20.880> you're<00:01:21.040> giving 00:01:21.590 --> 00:01:21.600 align:start position:0% engineering. You're just you're giving 00:01:21.600 --> 00:01:23.710 align:start position:0% engineering. You're just you're giving problems<00:01:22.160> to<00:01:23.000> uh 00:01:23.710 --> 00:01:23.720 align:start position:0% problems to uh 00:01:23.720 --> 00:01:25.830 align:start position:0% problems to uh language<00:01:24.080> models<00:01:24.400> to<00:01:24.520> solve<00:01:25.080> and<00:01:25.480> if<00:01:25.600> you<00:01:25.720> get 00:01:25.830 --> 00:01:25.840 align:start position:0% language models to solve and if you get 00:01:25.840 --> 00:01:27.150 align:start position:0% language models to solve and if you get the<00:01:25.920> prompts<00:01:26.280> right,<00:01:26.680> they're<00:01:26.920> getting 00:01:27.150 --> 00:01:27.160 align:start position:0% the prompts right, they're getting 00:01:27.160 --> 00:01:29.150 align:start position:0% the prompts right, they're getting better<00:01:27.400> and<00:01:27.520> better<00:01:27.760> at<00:01:27.880> solving<00:01:28.240> them.<00:01:29.000> But 00:01:29.150 --> 00:01:29.160 align:start position:0% better and better at solving them. But 00:01:29.160 --> 00:01:30.150 align:start position:0% better and better at solving them. But we<00:01:29.280> are<00:01:29.400> interested<00:01:29.760> in<00:01:29.960> really 00:01:30.150 --> 00:01:30.160 align:start position:0% we are interested in really 00:01:30.160 --> 00:01:33.030 align:start position:0% we are interested in really understanding<00:01:30.880> in<00:01:30.960> a<00:01:31.040> more<00:01:31.200> fundamental<00:01:31.760> way 00:01:33.030 --> 00:01:33.040 align:start position:0% understanding in a more fundamental way 00:01:33.040 --> 00:01:34.790 align:start position:0% understanding in a more fundamental way how 00:01:34.790 --> 00:01:34.800 align:start position:0% how 00:01:34.800 --> 00:01:36.310 align:start position:0% how human<00:01:35.120> beings<00:01:35.400> solve<00:01:35.680> problems.<00:01:36.040> It's<00:01:36.120> a<00:01:36.160> very 00:01:36.310 --> 00:01:36.320 align:start position:0% human beings solve problems. It's a very 00:01:36.320 --> 00:01:37.830 align:start position:0% human beings solve problems. It's a very mysterious 00:01:37.830 --> 00:01:37.840 align:start position:0% mysterious 00:01:37.840 --> 00:01:40.270 align:start position:0% mysterious uh<00:01:37.920> question<00:01:38.400> because<00:01:39.240> um 00:01:40.270 --> 00:01:40.280 align:start position:0% uh question because um 00:01:40.280 --> 00:01:42.350 align:start position:0% uh question because um we<00:01:40.440> know<00:01:40.640> that<00:01:41.400> uh 00:01:42.350 --> 00:01:42.360 align:start position:0% we know that uh 00:01:42.360 --> 00:01:43.710 align:start position:0% we know that uh it<00:01:42.600> shouldn't<00:01:42.920> in<00:01:43.040> some<00:01:43.240> sense<00:01:43.400> it<00:01:43.520> shouldn't 00:01:43.710 --> 00:01:43.720 align:start position:0% it shouldn't in some sense it shouldn't 00:01:43.720 --> 00:01:45.030 align:start position:0% it shouldn't in some sense it shouldn't be<00:01:43.840> possible.<00:01:44.200> If<00:01:44.320> you<00:01:44.360> have<00:01:44.480> a<00:01:44.520> general 00:01:45.030 --> 00:01:45.040 align:start position:0% be possible. If you have a general 00:01:45.040 --> 00:01:47.710 align:start position:0% be possible. If you have a general mathematical<00:01:45.600> statement<00:01:46.320> Mhm.<00:01:46.960> and<00:01:47.520> uh<00:01:47.560> you 00:01:47.710 --> 00:01:47.720 align:start position:0% mathematical statement Mhm. and uh you 00:01:47.720 --> 00:01:50.150 align:start position:0% mathematical statement Mhm. and uh you ask<00:01:48.160> does<00:01:48.360> this<00:01:48.520> statement<00:01:48.840> have<00:01:48.960> a<00:01:49.040> proof? 00:01:50.150 --> 00:01:50.160 align:start position:0% ask does this statement have a proof? 00:01:50.160 --> 00:01:52.550 align:start position:0% ask does this statement have a proof? That's<00:01:50.400> actually<00:01:51.480> uh<00:01:51.840> halting<00:01:52.240> complete. 00:01:52.550 --> 00:01:52.560 align:start position:0% That's actually uh halting complete. 00:01:52.560 --> 00:01:53.990 align:start position:0% That's actually uh halting complete. There's<00:01:52.720> no<00:01:52.920> algorithm<00:01:53.440> that<00:01:53.560> can<00:01:53.720> tell 00:01:53.990 --> 00:01:54.000 align:start position:0% There's no algorithm that can tell 00:01:54.000 --> 00:01:55.310 align:start position:0% There's no algorithm that can tell whether<00:01:54.280> a 00:01:55.310 --> 00:01:55.320 align:start position:0% whether a 00:01:55.320 --> 00:01:56.510 align:start position:0% whether a in<00:01:55.440> a<00:01:55.480> sense<00:01:55.680> there's<00:01:55.800> no<00:01:55.960> algorithm<00:01:56.320> that<00:01:56.400> can 00:01:56.510 --> 00:01:56.520 align:start position:0% in a sense there's no algorithm that can 00:01:56.520 --> 00:01:58.870 align:start position:0% in a sense there's no algorithm that can do<00:01:56.640> mathematics<00:01:57.120> in<00:01:57.240> general.<00:01:57.840> Mhm. 00:01:58.870 --> 00:01:58.880 align:start position:0% do mathematics in general. Mhm. 00:01:58.880 --> 00:02:00.830 align:start position:0% do mathematics in general. Mhm. But,<00:01:59.600> uh<00:01:59.680> we<00:01:59.840> can<00:02:00.040> do<00:02:00.160> mathematics,<00:02:00.760> and 00:02:00.830 --> 00:02:00.840 align:start position:0% But, uh we can do mathematics, and 00:02:00.840 --> 00:02:02.310 align:start position:0% But, uh we can do mathematics, and that's<00:02:01.000> because<00:02:01.320> we<00:02:01.400> don't<00:02:01.760> do<00:02:02.000> general 00:02:02.310 --> 00:02:02.320 align:start position:0% that's because we don't do general 00:02:02.320 --> 00:02:04.230 align:start position:0% that's because we don't do general mathematics,<00:02:02.800> we<00:02:02.880> do<00:02:03.080> sort<00:02:03.320> of<00:02:03.600> interesting 00:02:04.230 --> 00:02:04.240 align:start position:0% mathematics, we do sort of interesting 00:02:04.240 --> 00:02:04.990 align:start position:0% mathematics, we do sort of interesting mathematics. 00:02:04.990 --> 00:02:05.000 align:start position:0% mathematics. 00:02:05.000 --> 00:02:06.270 align:start position:0% mathematics. >> Right. 00:02:06.270 --> 00:02:06.280 align:start position:0% >> Right. 00:02:06.280 --> 00:02:07.550 align:start position:0% >> Right. So,<00:02:06.440> we're<00:02:06.600> trying<00:02:06.800> to<00:02:06.880> understand<00:02:07.320> what<00:02:07.440> it 00:02:07.550 --> 00:02:07.560 align:start position:0% So, we're trying to understand what it 00:02:07.560 --> 00:02:08.830 align:start position:0% So, we're trying to understand what it is<00:02:07.840> that<00:02:08.080> about<00:02:08.399> the<00:02:08.479> interesting 00:02:08.830 --> 00:02:08.840 align:start position:0% is that about the interesting 00:02:08.840 --> 00:02:11.270 align:start position:0% is that about the interesting mathematics<00:02:09.360> that<00:02:09.479> makes<00:02:09.759> it<00:02:10.520> possible<00:02:11.040> for 00:02:11.270 --> 00:02:11.280 align:start position:0% mathematics that makes it possible for 00:02:11.280 --> 00:02:12.830 align:start position:0% mathematics that makes it possible for human<00:02:11.600> mathematicians<00:02:12.240> with<00:02:12.360> their<00:02:12.600> rather 00:02:12.830 --> 00:02:12.840 align:start position:0% human mathematicians with their rather 00:02:12.840 --> 00:02:14.630 align:start position:0% human mathematicians with their rather limited<00:02:13.240> resources 00:02:14.630 --> 00:02:14.640 align:start position:0% limited resources 00:02:14.640 --> 00:02:16.110 align:start position:0% limited resources to<00:02:14.720> be<00:02:14.800> able<00:02:15.000> to<00:02:15.080> come<00:02:15.240> up<00:02:15.400> with<00:02:15.560> complicated 00:02:16.110 --> 00:02:16.120 align:start position:0% to be able to come up with complicated 00:02:16.120 --> 00:02:18.190 align:start position:0% to be able to come up with complicated proofs.<00:02:16.920> Right.<00:02:17.320> And<00:02:17.680> we<00:02:17.800> hope<00:02:17.959> that<00:02:18.080> by 00:02:18.190 --> 00:02:18.200 align:start position:0% proofs. Right. And we hope that by 00:02:18.200 --> 00:02:20.190 align:start position:0% proofs. Right. And we hope that by understanding<00:02:18.800> that,<00:02:19.200> we'll<00:02:19.400> be<00:02:19.520> able<00:02:19.720> to 00:02:20.190 --> 00:02:20.200 align:start position:0% understanding that, we'll be able to 00:02:20.200 --> 00:02:22.070 align:start position:0% understanding that, we'll be able to teach 00:02:22.070 --> 00:02:22.080 align:start position:0% teach 00:02:22.080 --> 00:02:25.350 align:start position:0% teach AI<00:02:22.440> to<00:02:22.520> do<00:02:22.680> it<00:02:22.800> better.<00:02:23.520> Right.<00:02:24.160> And<00:02:24.360> so, 00:02:25.350 --> 00:02:25.360 align:start position:0% AI to do it better. Right. And so, 00:02:25.360 --> 00:02:27.830 align:start position:0% AI to do it better. Right. And so, as<00:02:25.520> a<00:02:25.560> result<00:02:25.880> of<00:02:25.959> that,<00:02:26.160> I<00:02:26.240> have 00:02:27.830 --> 00:02:27.840 align:start position:0% as a result of that, I have 00:02:27.840 --> 00:02:29.670 align:start position:0% as a result of that, I have an<00:02:27.959> interest<00:02:28.360> in<00:02:28.480> what's<00:02:28.680> going<00:02:28.959> on<00:02:29.080> in<00:02:29.240> AI, 00:02:29.670 --> 00:02:29.680 align:start position:0% an interest in what's going on in AI, 00:02:29.680 --> 00:02:31.150 align:start position:0% an interest in what's going on in AI, and<00:02:29.880> so<00:02:30.040> coming<00:02:30.320> to<00:02:30.400> somewhere<00:02:30.680> like<00:02:30.880> Ghost 00:02:31.150 --> 00:02:31.160 align:start position:0% and so coming to somewhere like Ghost 00:02:31.160 --> 00:02:33.870 align:start position:0% and so coming to somewhere like Ghost Server<00:02:31.400> is<00:02:31.520> a<00:02:31.600> good<00:02:31.800> way<00:02:32.040> to 00:02:33.870 --> 00:02:33.880 align:start position:0% Server is a good way to 00:02:33.880 --> 00:02:35.830 align:start position:0% Server is a good way to meet<00:02:34.120> people<00:02:34.640> and<00:02:34.920> find<00:02:35.240> out<00:02:35.480> what<00:02:35.680> other 00:02:35.830 --> 00:02:35.840 align:start position:0% meet people and find out what other 00:02:35.840 --> 00:02:37.630 align:start position:0% meet people and find out what other people<00:02:36.040> are<00:02:36.120> thinking<00:02:36.440> about<00:02:36.760> in<00:02:36.880> the 00:02:37.630 --> 00:02:37.640 align:start position:0% people are thinking about in the 00:02:37.640 --> 00:02:40.070 align:start position:0% people are thinking about in the more<00:02:38.000> AI<00:02:38.240> domain,<00:02:38.680> so. 00:02:40.070 --> 00:02:40.080 align:start position:0% more AI domain, so. 00:02:40.080 --> 00:02:42.390 align:start position:0% more AI domain, so. Thank<00:02:40.320> you.<00:02:40.520> I<00:02:40.720> I<00:02:40.840> mean,<00:02:41.640> it<00:02:41.840> really<00:02:42.080> struck 00:02:42.390 --> 00:02:42.400 align:start position:0% Thank you. I I mean, it really struck 00:02:42.400 --> 00:02:43.910 align:start position:0% Thank you. I I mean, it really struck me.<00:02:42.480> One<00:02:42.680> thing<00:02:42.880> in<00:02:43.000> your<00:02:43.120> keynote,<00:02:43.680> right? 00:02:43.910 --> 00:02:43.920 align:start position:0% me. One thing in your keynote, right? 00:02:43.920 --> 00:02:46.990 align:start position:0% me. One thing in your keynote, right? So,<00:02:44.520> I<00:02:44.680> went<00:02:45.000> to<00:02:45.240> this<00:02:45.440> best<00:02:45.959> math<00:02:46.200> school<00:02:46.520> in 00:02:46.990 --> 00:02:47.000 align:start position:0% So, I went to this best math school in 00:02:47.000 --> 00:02:49.550 align:start position:0% So, I went to this best math school in Soviet<00:02:47.320> Union<00:02:48.120> because<00:02:48.959> and<00:02:49.160> I<00:02:49.240> should<00:02:49.480> have 00:02:49.550 --> 00:02:49.560 align:start position:0% Soviet Union because and I should have 00:02:49.560 --> 00:02:50.870 align:start position:0% Soviet Union because and I should have studied<00:02:49.800> history.<00:02:50.120> I<00:02:50.160> like<00:02:50.320> history.<00:02:50.720> I 00:02:50.870 --> 00:02:50.880 align:start position:0% studied history. I like history. I 00:02:50.880 --> 00:02:52.190 align:start position:0% studied history. I like history. I really<00:02:51.080> like<00:02:51.200> humanities.<00:02:51.680> I'm<00:02:51.800> not<00:02:51.959> very 00:02:52.190 --> 00:02:52.200 align:start position:0% really like humanities. I'm not very 00:02:52.200 --> 00:02:54.430 align:start position:0% really like humanities. I'm not very good<00:02:52.560> at<00:02:53.240> math. 00:02:54.430 --> 00:02:54.440 align:start position:0% good at math. 00:02:54.440 --> 00:02:56.310 align:start position:0% good at math. I'm<00:02:54.640> okay<00:02:55.000> at<00:02:55.080> math,<00:02:55.560> but<00:02:55.760> now<00:02:55.920> I'm<00:02:56.080> a<00:02:56.120> better 00:02:56.310 --> 00:02:56.320 align:start position:0% I'm okay at math, but now I'm a better 00:02:56.320 --> 00:02:58.870 align:start position:0% I'm okay at math, but now I'm a better programmer.<00:02:57.160> So,<00:02:57.880> but<00:02:58.080> there<00:02:58.160> was<00:02:58.320> no<00:02:58.640> other 00:02:58.870 --> 00:02:58.880 align:start position:0% programmer. So, but there was no other 00:02:58.880 --> 00:03:01.910 align:start position:0% programmer. So, but there was no other path<00:02:59.840> for<00:03:00.000> people<00:03:00.480> to<00:03:00.840> do<00:03:01.320> something<00:03:01.720> real 00:03:01.910 --> 00:03:01.920 align:start position:0% path for people to do something real 00:03:01.920 --> 00:03:03.150 align:start position:0% path for people to do something real because,<00:03:02.200> you<00:03:02.280> know,<00:03:02.480> all<00:03:02.640> the<00:03:02.800> humanities 00:03:03.150 --> 00:03:03.160 align:start position:0% because, you know, all the humanities 00:03:03.160 --> 00:03:04.750 align:start position:0% because, you know, all the humanities were<00:03:03.239> Marxist-Leninist. 00:03:04.750 --> 00:03:04.760 align:start position:0% were Marxist-Leninist. 00:03:04.760 --> 00:03:05.870 align:start position:0% were Marxist-Leninist. So, 00:03:05.870 --> 00:03:05.880 align:start position:0% So, 00:03:05.880 --> 00:03:08.150 align:start position:0% So, and<00:03:06.280> I<00:03:06.400> thought<00:03:06.840> that<00:03:07.120> math<00:03:07.640> is<00:03:07.880> very 00:03:08.150 --> 00:03:08.160 align:start position:0% and I thought that math is very 00:03:08.160 --> 00:03:10.949 align:start position:0% and I thought that math is very antisocial.<00:03:09.280> When<00:03:09.560> I<00:03:09.600> read<00:03:09.880> math<00:03:10.160> books,<00:03:10.840> they 00:03:10.949 --> 00:03:10.959 align:start position:0% antisocial. When I read math books, they 00:03:10.959 --> 00:03:12.790 align:start position:0% antisocial. When I read math books, they rubbed<00:03:11.160> me<00:03:11.239> the<00:03:11.360> wrong<00:03:11.640> way<00:03:12.200> because, 00:03:12.790 --> 00:03:12.800 align:start position:0% rubbed me the wrong way because, 00:03:12.800 --> 00:03:15.990 align:start position:0% rubbed me the wrong way because, effectively,<00:03:13.800> they<00:03:14.519> they<00:03:14.959> provide<00:03:15.320> very<00:03:15.640> like 00:03:15.990 --> 00:03:16.000 align:start position:0% effectively, they they provide very like 00:03:16.000 --> 00:03:17.990 align:start position:0% effectively, they they provide very like very<00:03:16.280> dense<00:03:16.880> statements,<00:03:17.519> and<00:03:17.640> then<00:03:17.760> there<00:03:17.880> is 00:03:17.990 --> 00:03:18.000 align:start position:0% very dense statements, and then there is 00:03:18.000 --> 00:03:19.630 align:start position:0% very dense statements, and then there is an<00:03:18.120> answer,<00:03:18.880> and<00:03:19.000> in<00:03:19.080> between<00:03:19.400> there<00:03:19.519> is<00:03:19.600> a 00:03:19.630 --> 00:03:19.640 align:start position:0% an answer, and in between there is a 00:03:19.640 --> 00:03:21.590 align:start position:0% an answer, and in between there is a phrase<00:03:19.880> like<00:03:20.680> as<00:03:20.760> an<00:03:20.880> exercise<00:03:21.360> to<00:03:21.440> the 00:03:21.590 --> 00:03:21.600 align:start position:0% phrase like as an exercise to the 00:03:21.600 --> 00:03:23.710 align:start position:0% phrase like as an exercise to the reader.<00:03:22.160> Yeah,<00:03:22.360> yeah,<00:03:22.519> yeah.<00:03:22.680> Or<00:03:23.120> it<00:03:23.400> easily 00:03:23.710 --> 00:03:23.720 align:start position:0% reader. Yeah, yeah, yeah. Or it easily 00:03:23.720 --> 00:03:26.790 align:start position:0% reader. Yeah, yeah, yeah. Or it easily follows<00:03:24.440> that<00:03:24.800> and<00:03:24.920> there<00:03:25.040> is<00:03:25.320> nothing<00:03:25.880> like 00:03:26.790 --> 00:03:26.800 align:start position:0% follows that and there is nothing like 00:03:26.800 --> 00:03:28.790 align:start position:0% follows that and there is nothing like like<00:03:26.920> it's<00:03:27.120> followed<00:03:27.480> easily,<00:03:28.000> right?<00:03:28.680> And 00:03:28.790 --> 00:03:28.800 align:start position:0% like it's followed easily, right? And 00:03:28.800 --> 00:03:30.670 align:start position:0% like it's followed easily, right? And so,<00:03:29.000> I<00:03:29.080> thought<00:03:29.680> that<00:03:29.880> I'm<00:03:30.040> dumb.<00:03:30.400> I<00:03:30.440> don't 00:03:30.670 --> 00:03:30.680 align:start position:0% so, I thought that I'm dumb. I don't 00:03:30.680 --> 00:03:32.990 align:start position:0% so, I thought that I'm dumb. I don't understand<00:03:31.040> it.<00:03:31.160> But<00:03:31.320> then<00:03:31.560> you<00:03:31.680> said<00:03:32.600> that 00:03:32.990 --> 00:03:33.000 align:start position:0% understand it. But then you said that 00:03:33.000 --> 00:03:34.150 align:start position:0% understand it. But then you said that this<00:03:33.280> is 00:03:34.150 --> 00:03:34.160 align:start position:0% this is 00:03:34.160 --> 00:03:36.790 align:start position:0% this is basically<00:03:35.400> a<00:03:35.480> wrong<00:03:35.840> way<00:03:36.239> for<00:03:36.440> people<00:03:36.720> to 00:03:36.790 --> 00:03:36.800 align:start position:0% basically a wrong way for people to 00:03:36.800 --> 00:03:40.070 align:start position:0% basically a wrong way for people to understand<00:03:37.120> math,<00:03:37.560> and<00:03:38.040> you<00:03:38.239> said<00:03:38.560> that<00:03:38.800> LLMs 00:03:40.070 --> 00:03:40.080 align:start position:0% understand math, and you said that LLMs 00:03:40.080 --> 00:03:41.830 align:start position:0% understand math, and you said that LLMs they<00:03:40.239> should<00:03:40.400> do<00:03:40.560> math 00:03:41.830 --> 00:03:41.840 align:start position:0% they should do math 00:03:41.840 --> 00:03:44.030 align:start position:0% they should do math basically<00:03:42.200> became<00:03:42.480> antisocial<00:03:43.400> and<00:03:43.560> mean 00:03:44.030 --> 00:03:44.040 align:start position:0% basically became antisocial and mean 00:03:44.040 --> 00:03:46.550 align:start position:0% basically became antisocial and mean this<00:03:44.320> way<00:03:44.560> because<00:03:45.040> mathematicians<00:03:45.760> write 00:03:46.550 --> 00:03:46.560 align:start position:0% this way because mathematicians write 00:03:46.560 --> 00:03:48.310 align:start position:0% this way because mathematicians write books<00:03:46.880> this<00:03:47.120> way<00:03:47.360> from<00:03:47.600> which<00:03:47.840> we<00:03:47.959> shall<00:03:48.160> learn 00:03:48.310 --> 00:03:48.320 align:start position:0% books this way from which we shall learn 00:03:48.320 --> 00:03:50.229 align:start position:0% books this way from which we shall learn to<00:03:48.440> read.<00:03:48.880> And<00:03:49.000> so,<00:03:49.440> suddenly<00:03:49.840> it<00:03:49.920> just 00:03:50.229 --> 00:03:50.239 align:start position:0% to read. And so, suddenly it just 00:03:50.239 --> 00:03:52.270 align:start position:0% to read. And so, suddenly it just occurred<00:03:50.560> to<00:03:50.640> me<00:03:50.800> that<00:03:51.400> math<00:03:51.680> could<00:03:52.080> could 00:03:52.270 --> 00:03:52.280 align:start position:0% occurred to me that math could could 00:03:52.280 --> 00:03:54.190 align:start position:0% occurred to me that math could could have<00:03:52.400> been<00:03:52.520> different.<00:03:53.200> It<00:03:53.520> could<00:03:53.720> have<00:03:54.000> been 00:03:54.190 --> 00:03:54.200 align:start position:0% have been different. It could have been 00:03:54.200 --> 00:03:56.310 align:start position:0% have been different. It could have been more<00:03:54.360> convenient.<00:03:55.240> And<00:03:55.440> the<00:03:55.560> And<00:03:55.800> you<00:03:55.960> also 00:03:56.310 --> 00:03:56.320 align:start position:0% more convenient. And the And you also 00:03:56.320 --> 00:03:58.710 align:start position:0% more convenient. And the And you also said<00:03:56.600> that<00:03:56.800> you're<00:03:57.040> interested<00:03:57.640> not<00:03:57.960> in<00:03:58.080> the 00:03:58.710 --> 00:03:58.720 align:start position:0% said that you're interested not in the 00:03:58.720 --> 00:04:00.310 align:start position:0% said that you're interested not in the achieving<00:03:59.120> the<00:03:59.200> result,<00:03:59.640> but<00:03:59.840> you<00:04:00.000> want<00:04:00.200> to 00:04:00.310 --> 00:04:00.320 align:start position:0% achieving the result, but you want to 00:04:00.320 --> 00:04:03.150 align:start position:0% achieving the result, but you want to see<00:04:00.480> how<00:04:01.200> a<00:04:01.280> mathematician<00:04:02.400> arrived<00:04:02.840> at<00:04:02.960> that 00:04:03.150 --> 00:04:03.160 align:start position:0% see how a mathematician arrived at that 00:04:03.160 --> 00:04:05.870 align:start position:0% see how a mathematician arrived at that result.<00:04:04.000> This<00:04:04.920> was<00:04:05.120> very<00:04:05.360> interesting<00:04:05.680> to<00:04:05.800> me. 00:04:05.870 --> 00:04:05.880 align:start position:0% result. This was very interesting to me. 00:04:05.880 --> 00:04:07.590 align:start position:0% result. This was very interesting to me. Can<00:04:06.000> you<00:04:06.080> explain<00:04:06.400> a<00:04:06.440> little<00:04:06.600> bit<00:04:06.760> like<00:04:07.240> how<00:04:07.480> do 00:04:07.590 --> 00:04:07.600 align:start position:0% Can you explain a little bit like how do 00:04:07.600 --> 00:04:09.390 align:start position:0% Can you explain a little bit like how do you<00:04:07.680> go<00:04:07.800> about<00:04:08.080> it? 00:04:09.390 --> 00:04:09.400 align:start position:0% you go about it? 00:04:09.400 --> 00:04:10.790 align:start position:0% you go about it? Yes,<00:04:09.520> I<00:04:09.560> mean<00:04:09.680> just<00:04:09.840> before<00:04:10.160> I 00:04:10.790 --> 00:04:10.800 align:start position:0% Yes, I mean just before I 00:04:10.800 --> 00:04:13.830 align:start position:0% Yes, I mean just before I get<00:04:10.959> on<00:04:11.080> to<00:04:11.160> that,<00:04:11.400> I<00:04:11.440> mean<00:04:11.880> I<00:04:12.000> think<00:04:12.360> something 00:04:13.830 --> 00:04:13.840 align:start position:0% get on to that, I mean I think something 00:04:13.840 --> 00:04:15.030 align:start position:0% get on to that, I mean I think something very<00:04:13.959> important<00:04:14.360> happened<00:04:14.600> in<00:04:14.680> the<00:04:14.720> beginning 00:04:15.030 --> 00:04:15.040 align:start position:0% very important happened in the beginning 00:04:15.040 --> 00:04:17.190 align:start position:0% very important happened in the beginning of<00:04:15.120> the<00:04:15.200> 20th<00:04:15.560> century,<00:04:15.959> which<00:04:16.200> was<00:04:16.920> putting 00:04:17.190 --> 00:04:17.200 align:start position:0% of the 20th century, which was putting 00:04:17.200 --> 00:04:19.069 align:start position:0% of the 20th century, which was putting mathematics<00:04:17.640> on<00:04:17.760> a<00:04:17.799> rigorous<00:04:18.239> footing, 00:04:19.069 --> 00:04:19.079 align:start position:0% mathematics on a rigorous footing, 00:04:19.079 --> 00:04:20.630 align:start position:0% mathematics on a rigorous footing, developing<00:04:19.560> the<00:04:19.680> axioms 00:04:20.630 --> 00:04:20.640 align:start position:0% developing the axioms 00:04:20.640 --> 00:04:23.030 align:start position:0% developing the axioms uh<00:04:20.720> ZF<00:04:21.359> axioms<00:04:21.959> and 00:04:23.030 --> 00:04:23.040 align:start position:0% uh ZF axioms and 00:04:23.040 --> 00:04:24.790 align:start position:0% uh ZF axioms and uh 00:04:24.790 --> 00:04:24.800 align:start position:0% uh 00:04:24.800 --> 00:04:27.510 align:start position:0% uh formalizing<00:04:25.760> what<00:04:25.919> we<00:04:26.000> meant<00:04:26.320> by 00:04:27.510 --> 00:04:27.520 align:start position:0% formalizing what we meant by 00:04:27.520 --> 00:04:28.470 align:start position:0% formalizing what we meant by rigorously<00:04:27.919> what<00:04:28.040> we<00:04:28.120> meant<00:04:28.320> by<00:04:28.440> a 00:04:28.470 --> 00:04:28.480 align:start position:0% rigorously what we meant by a 00:04:28.480 --> 00:04:30.030 align:start position:0% rigorously what we meant by a mathematical<00:04:29.040> proof 00:04:30.030 --> 00:04:30.040 align:start position:0% mathematical proof 00:04:30.040 --> 00:04:31.550 align:start position:0% mathematical proof and<00:04:30.120> so<00:04:30.320> on.<00:04:30.720> But<00:04:30.840> unfortunately,<00:04:31.360> I<00:04:31.400> think 00:04:31.550 --> 00:04:31.560 align:start position:0% and so on. But unfortunately, I think 00:04:31.560 --> 00:04:33.510 align:start position:0% and so on. But unfortunately, I think that<00:04:31.880> development,<00:04:32.400> though<00:04:33.000> extremely 00:04:33.510 --> 00:04:33.520 align:start position:0% that development, though extremely 00:04:33.520 --> 00:04:34.870 align:start position:0% that development, though extremely important<00:04:33.880> for<00:04:34.000> mathematics<00:04:34.480> and<00:04:34.640> very 00:04:34.870 --> 00:04:34.880 align:start position:0% important for mathematics and very 00:04:34.880 --> 00:04:37.470 align:start position:0% important for mathematics and very positive<00:04:35.240> development<00:04:35.680> in<00:04:35.760> many<00:04:36.000> ways, 00:04:37.470 --> 00:04:37.480 align:start position:0% positive development in many ways, 00:04:37.480 --> 00:04:39.430 align:start position:0% positive development in many ways, had<00:04:37.640> a<00:04:37.720> slightly<00:04:38.040> unfortunate<00:04:38.800> stylistic 00:04:39.430 --> 00:04:39.440 align:start position:0% had a slightly unfortunate stylistic 00:04:39.440 --> 00:04:41.070 align:start position:0% had a slightly unfortunate stylistic consequence<00:04:40.000> that<00:04:40.120> people<00:04:40.440> then<00:04:40.640> tried<00:04:40.919> to 00:04:41.070 --> 00:04:41.080 align:start position:0% consequence that people then tried to 00:04:41.080 --> 00:04:42.950 align:start position:0% consequence that people then tried to write<00:04:41.400> in<00:04:41.560> this<00:04:41.800> kind<00:04:42.080> of 00:04:42.950 --> 00:04:42.960 align:start position:0% write in this kind of 00:04:42.960 --> 00:04:43.990 align:start position:0% write in this kind of formal<00:04:43.360> logical<00:04:43.800> style. 00:04:43.990 --> 00:04:44.000 align:start position:0% formal logical style. 00:04:44.000 --> 00:04:47.830 align:start position:0% formal logical style. >> Dry.<00:04:45.040> Yeah,<00:04:45.200> which<00:04:45.880> um 00:04:47.830 --> 00:04:47.840 align:start position:0% >> Dry. Yeah, which um 00:04:47.840 --> 00:04:50.230 align:start position:0% >> Dry. Yeah, which um sort<00:04:48.080> of<00:04:48.440> lost 00:04:50.230 --> 00:04:50.240 align:start position:0% sort of lost 00:04:50.240 --> 00:04:51.830 align:start position:0% sort of lost Something<00:04:50.520> was<00:04:50.680> lost<00:04:51.000> in<00:04:51.080> that<00:04:51.320> process<00:04:51.720> or 00:04:51.830 --> 00:04:51.840 align:start position:0% Something was lost in that process or 00:04:51.840 --> 00:04:53.270 align:start position:0% Something was lost in that process or something<00:04:52.120> to<00:04:52.200> do<00:04:52.280> with<00:04:52.400> the<00:04:52.480> human<00:04:52.840> presence. 00:04:53.270 --> 00:04:53.280 align:start position:0% something to do with the human presence. 00:04:53.280 --> 00:04:54.710 align:start position:0% something to do with the human presence. They<00:04:53.320> look<00:04:53.480> like<00:04:53.600> computers.<00:04:54.200> They<00:04:54.440> They<00:04:54.560> want 00:04:54.710 --> 00:04:54.720 align:start position:0% They look like computers. They They want 00:04:54.720 --> 00:04:55.950 align:start position:0% They look like computers. They They want to<00:04:55.240> be<00:04:55.360> machines. 00:04:55.950 --> 00:04:55.960 align:start position:0% to be machines. 00:04:55.960 --> 00:04:57.230 align:start position:0% to be machines. >> Yeah,<00:04:56.080> exactly. 00:04:57.230 --> 00:04:57.240 align:start position:0% >> Yeah, exactly. 00:04:57.240 --> 00:04:59.230 align:start position:0% >> Yeah, exactly. Um 00:04:59.230 --> 00:04:59.240 align:start position:0% Um 00:04:59.240 --> 00:05:01.110 align:start position:0% Um So,<00:04:59.919> how<00:05:00.040> does<00:05:00.200> one<00:05:00.320> counteract<00:05:00.880> that?<00:05:01.080> I 00:05:01.110 --> 00:05:01.120 align:start position:0% So, how does one counteract that? I 00:05:01.120 --> 00:05:02.310 align:start position:0% So, how does one counteract that? I mean,<00:05:01.360> actually<00:05:01.720> I've<00:05:01.840> been<00:05:02.000> trying<00:05:02.200> to 00:05:02.310 --> 00:05:02.320 align:start position:0% mean, actually I've been trying to 00:05:02.320 --> 00:05:04.630 align:start position:0% mean, actually I've been trying to counteract<00:05:02.840> that<00:05:03.000> throughout<00:05:03.360> my<00:05:03.520> career, 00:05:04.630 --> 00:05:04.640 align:start position:0% counteract that throughout my career, 00:05:04.640 --> 00:05:08.470 align:start position:0% counteract that throughout my career, uh<00:05:05.320> long<00:05:05.560> before<00:05:06.160> anything<00:05:06.480> to<00:05:06.560> do<00:05:06.680> with<00:05:06.840> AI<00:05:07.280> or 00:05:08.470 --> 00:05:08.480 align:start position:0% uh long before anything to do with AI or 00:05:08.480 --> 00:05:10.470 align:start position:0% uh long before anything to do with AI or automatic<00:05:08.919> theorem<00:05:09.160> proving, 00:05:10.470 --> 00:05:10.480 align:start position:0% automatic theorem proving, 00:05:10.480 --> 00:05:11.790 align:start position:0% automatic theorem proving, just<00:05:10.760> by 00:05:11.790 --> 00:05:11.800 align:start position:0% just by 00:05:11.800 --> 00:05:15.470 align:start position:0% just by really<00:05:12.040> examining<00:05:13.280> carefully<00:05:13.840> how 00:05:15.470 --> 00:05:15.480 align:start position:0% really examining carefully how 00:05:15.480 --> 00:05:17.909 align:start position:0% really examining carefully how I<00:05:15.600> myself<00:05:16.080> come<00:05:16.240> up<00:05:16.400> with<00:05:16.560> proofs<00:05:17.000> or<00:05:17.600> thinking 00:05:17.909 --> 00:05:17.919 align:start position:0% I myself come up with proofs or thinking 00:05:17.919 --> 00:05:19.470 align:start position:0% I myself come up with proofs or thinking about<00:05:18.160> things<00:05:18.440> that<00:05:18.560> I<00:05:18.680> was<00:05:18.880> taught<00:05:19.200> when<00:05:19.360> I 00:05:19.470 --> 00:05:19.480 align:start position:0% about things that I was taught when I 00:05:19.480 --> 00:05:21.870 align:start position:0% about things that I was taught when I was<00:05:19.600> a<00:05:19.680> student.<00:05:20.440> Mhm.<00:05:21.000> Um<00:05:21.480> that<00:05:21.640> I<00:05:21.680> just 00:05:21.870 --> 00:05:21.880 align:start position:0% was a student. Mhm. Um that I just 00:05:21.880 --> 00:05:23.710 align:start position:0% was a student. Mhm. Um that I just accepted 00:05:23.710 --> 00:05:23.720 align:start position:0% accepted 00:05:23.720 --> 00:05:24.870 align:start position:0% accepted the<00:05:23.800> proofs<00:05:24.160> of<00:05:24.240> them.<00:05:24.400> So,<00:05:24.520> I<00:05:24.560> would<00:05:24.680> think, 00:05:24.870 --> 00:05:24.880 align:start position:0% the proofs of them. So, I would think, 00:05:24.880 --> 00:05:25.909 align:start position:0% the proofs of them. So, I would think, "Actually,<00:05:25.160> how<00:05:25.280> could<00:05:25.480> somebody<00:05:25.800> have 00:05:25.909 --> 00:05:25.919 align:start position:0% "Actually, how could somebody have 00:05:25.919 --> 00:05:27.790 align:start position:0% "Actually, how could somebody have thought<00:05:26.160> of<00:05:26.240> that<00:05:26.440> argument?"<00:05:26.919> And 00:05:27.790 --> 00:05:27.800 align:start position:0% thought of that argument?" And 00:05:27.800 --> 00:05:29.150 align:start position:0% thought of that argument?" And sometimes<00:05:28.120> if<00:05:28.240> I<00:05:28.280> thought<00:05:28.560> hard<00:05:28.760> enough<00:05:28.919> about 00:05:29.150 --> 00:05:29.160 align:start position:0% sometimes if I thought hard enough about 00:05:29.160 --> 00:05:30.710 align:start position:0% sometimes if I thought hard enough about it,<00:05:29.240> I<00:05:29.320> realized<00:05:29.760> actually<00:05:30.080> often<00:05:30.440> after 00:05:30.710 --> 00:05:30.720 align:start position:0% it, I realized actually often after 00:05:30.720 --> 00:05:32.790 align:start position:0% it, I realized actually often after teaching<00:05:31.040> it<00:05:31.160> myself,<00:05:31.919> Mhm.<00:05:32.640> I<00:05:32.680> would 00:05:32.790 --> 00:05:32.800 align:start position:0% teaching it myself, Mhm. I would 00:05:32.800 --> 00:05:34.630 align:start position:0% teaching it myself, Mhm. I would suddenly<00:05:33.160> see<00:05:33.360> something<00:05:33.800> that<00:05:33.960> would<00:05:34.480> make 00:05:34.630 --> 00:05:34.640 align:start position:0% suddenly see something that would make 00:05:34.640 --> 00:05:36.030 align:start position:0% suddenly see something that would make me<00:05:34.720> realize,<00:05:35.000> "Ah,<00:05:35.160> yes,<00:05:35.360> that's<00:05:35.560> how<00:05:35.680> to<00:05:35.800> have 00:05:36.030 --> 00:05:36.040 align:start position:0% me realize, "Ah, yes, that's how to have 00:05:36.040 --> 00:05:37.790 align:start position:0% me realize, "Ah, yes, that's how to have probably<00:05:36.480> how<00:05:36.600> that<00:05:36.800> was<00:05:37.080> or<00:05:37.240> how<00:05:37.400> could<00:05:37.640> that 00:05:37.790 --> 00:05:37.800 align:start position:0% probably how that was or how could that 00:05:37.800 --> 00:05:39.230 align:start position:0% probably how that was or how could that have<00:05:38.240> that<00:05:38.400> how<00:05:38.520> how<00:05:38.680> that<00:05:38.840> could<00:05:39.000> have<00:05:39.080> been 00:05:39.230 --> 00:05:39.240 align:start position:0% have that how how that could have been 00:05:39.240 --> 00:05:40.990 align:start position:0% have that how how that could have been discovered." 00:05:40.990 --> 00:05:41.000 align:start position:0% discovered." 00:05:41.000 --> 00:05:42.430 align:start position:0% discovered." Um 00:05:42.430 --> 00:05:42.440 align:start position:0% Um 00:05:42.440 --> 00:05:44.830 align:start position:0% Um and<00:05:43.560> so 00:05:44.830 --> 00:05:44.840 align:start position:0% and so 00:05:44.840 --> 00:05:45.910 align:start position:0% and so for<00:05:44.880> me<00:05:45.000> there's<00:05:45.200> always<00:05:45.400> been<00:05:45.600> quite<00:05:45.880> a 00:05:45.910 --> 00:05:45.920 align:start position:0% for me there's always been quite a 00:05:45.920 --> 00:05:47.550 align:start position:0% for me there's always been quite a strong<00:05:46.320> link 00:05:47.550 --> 00:05:47.560 align:start position:0% strong link 00:05:47.560 --> 00:05:50.070 align:start position:0% strong link between 00:05:50.070 --> 00:05:50.080 align:start position:0% between 00:05:50.080 --> 00:05:51.390 align:start position:0% between a<00:05:50.160> really<00:05:50.360> good<00:05:50.560> way<00:05:50.720> of<00:05:50.840> explaining 00:05:51.390 --> 00:05:51.400 align:start position:0% a really good way of explaining 00:05:51.400 --> 00:05:53.470 align:start position:0% a really good way of explaining mathematics<00:05:51.880> to<00:05:51.960> humans<00:05:52.800> Mhm.<00:05:53.200> and<00:05:53.240> a<00:05:53.280> really 00:05:53.470 --> 00:05:53.480 align:start position:0% mathematics to humans Mhm. and a really 00:05:53.480 --> 00:05:54.630 align:start position:0% mathematics to humans Mhm. and a really good<00:05:53.600> way<00:05:53.680> of<00:05:53.760> explaining<00:05:54.120> mathematics<00:05:54.560> to 00:05:54.630 --> 00:05:54.640 align:start position:0% good way of explaining mathematics to 00:05:54.640 --> 00:05:58.110 align:start position:0% good way of explaining mathematics to computers.<00:05:55.400> Mhm.<00:05:56.280> Um 00:05:58.110 --> 00:05:58.120 align:start position:0% computers. Mhm. Um 00:05:58.120 --> 00:06:01.430 align:start position:0% computers. Mhm. Um and<00:05:58.760> um<00:05:59.200> what<00:05:59.400> I<00:05:59.480> hope<00:05:59.800> is<00:06:00.120> that<00:06:00.840> uh 00:06:01.430 --> 00:06:01.440 align:start position:0% and um what I hope is that uh 00:06:01.440 --> 00:06:02.350 align:start position:0% and um what I hope is that uh Well,<00:06:01.520> I<00:06:01.560> don't<00:06:01.720> think<00:06:01.840> we<00:06:01.920> have<00:06:02.080> this<00:06:02.200> at<00:06:02.320> the 00:06:02.350 --> 00:06:02.360 align:start position:0% Well, I don't think we have this at the 00:06:02.360 --> 00:06:04.030 align:start position:0% Well, I don't think we have this at the moment,<00:06:02.640> but<00:06:02.760> I'm<00:06:02.840> hoping<00:06:03.120> that 00:06:04.030 --> 00:06:04.040 align:start position:0% moment, but I'm hoping that 00:06:04.040 --> 00:06:05.750 align:start position:0% moment, but I'm hoping that sometime<00:06:04.440> in<00:06:04.520> the<00:06:04.600> future 00:06:05.750 --> 00:06:05.760 align:start position:0% sometime in the future 00:06:05.760 --> 00:06:08.710 align:start position:0% sometime in the future we<00:06:05.880> will<00:06:06.760> be<00:06:06.840> able<00:06:07.040> to<00:06:07.160> teach<00:06:07.440> computers 00:06:08.710 --> 00:06:08.720 align:start position:0% we will be able to teach computers 00:06:08.720 --> 00:06:10.070 align:start position:0% we will be able to teach computers to<00:06:08.800> think<00:06:09.040> about<00:06:09.240> mathematics<00:06:09.720> in<00:06:09.800> a<00:06:09.880> more 00:06:10.070 --> 00:06:10.080 align:start position:0% to think about mathematics in a more 00:06:10.080 --> 00:06:12.110 align:start position:0% to think about mathematics in a more human<00:06:10.440> way<00:06:11.000> Mhm.<00:06:11.400> so<00:06:11.480> that<00:06:11.600> they<00:06:11.760> will<00:06:11.840> then<00:06:12.000> be 00:06:12.110 --> 00:06:12.120 align:start position:0% human way Mhm. so that they will then be 00:06:12.120 --> 00:06:15.310 align:start position:0% human way Mhm. so that they will then be able<00:06:12.280> to<00:06:12.360> explain<00:06:12.800> to<00:06:12.960> us<00:06:13.680> in<00:06:13.800> a<00:06:13.880> better<00:06:14.160> way 00:06:15.310 --> 00:06:15.320 align:start position:0% able to explain to us in a better way 00:06:15.320 --> 00:06:16.670 align:start position:0% able to explain to us in a better way uh<00:06:15.560> what<00:06:15.720> they've<00:06:15.920> been<00:06:16.080> doing.<00:06:16.440> So,<00:06:16.560> at<00:06:16.640> the 00:06:16.670 --> 00:06:16.680 align:start position:0% uh what they've been doing. So, at the 00:06:16.680 --> 00:06:17.870 align:start position:0% uh what they've been doing. So, at the moment,<00:06:16.960> you<00:06:17.040> know,<00:06:17.120> they<00:06:17.200> they've<00:06:17.480> copied 00:06:17.870 --> 00:06:17.880 align:start position:0% moment, you know, they they've copied 00:06:17.880 --> 00:06:19.630 align:start position:0% moment, you know, they they've copied the<00:06:17.960> style<00:06:18.400> that<00:06:18.560> they<00:06:18.720> see<00:06:19.000> in<00:06:19.120> textbooks. 00:06:19.630 --> 00:06:19.640 align:start position:0% the style that they see in textbooks. 00:06:19.640 --> 00:06:21.430 align:start position:0% the style that they see in textbooks. They<00:06:19.720> just<00:06:19.960> give<00:06:20.160> us 00:06:21.430 --> 00:06:21.440 align:start position:0% They just give us 00:06:21.440 --> 00:06:22.830 align:start position:0% They just give us give<00:06:21.560> us<00:06:21.720> the<00:06:21.880> answers,<00:06:22.360> basically. 00:06:22.830 --> 00:06:22.840 align:start position:0% give us the answers, basically. 00:06:22.840 --> 00:06:25.150 align:start position:0% give us the answers, basically. >> Right.<00:06:23.160> And<00:06:23.400> uh 00:06:25.150 --> 00:06:25.160 align:start position:0% >> Right. And uh 00:06:25.160 --> 00:06:26.350 align:start position:0% >> Right. And uh sometimes<00:06:25.520> that's<00:06:25.640> not<00:06:25.800> what<00:06:25.960> you<00:06:26.040> want. 00:06:26.350 --> 00:06:26.360 align:start position:0% sometimes that's not what you want. 00:06:26.360 --> 00:06:27.950 align:start position:0% sometimes that's not what you want. Sometimes<00:06:26.760> you<00:06:26.840> want<00:06:27.040> This<00:06:27.200> is<00:06:27.320> fascinating, 00:06:27.950 --> 00:06:27.960 align:start position:0% Sometimes you want This is fascinating, 00:06:27.960 --> 00:06:30.110 align:start position:0% Sometimes you want This is fascinating, right?<00:06:28.120> Because<00:06:28.560> I<00:06:28.760> I<00:06:28.880> vividly<00:06:29.280> remember<00:06:29.960> So, 00:06:30.110 --> 00:06:30.120 align:start position:0% right? Because I I vividly remember So, 00:06:30.120 --> 00:06:32.990 align:start position:0% right? Because I I vividly remember So, when<00:06:30.400> I<00:06:30.880> uh<00:06:31.120> you<00:06:31.200> know,<00:06:31.440> went<00:06:31.640> to<00:06:31.720> school<00:06:31.919> 57, 00:06:32.990 --> 00:06:33.000 align:start position:0% when I uh you know, went to school 57, 00:06:33.000 --> 00:06:34.430 align:start position:0% when I uh you know, went to school 57, which<00:06:33.160> is<00:06:33.240> the<00:06:33.320> most<00:06:33.560> famous<00:06:33.919> math<00:06:34.120> school<00:06:34.360> in 00:06:34.430 --> 00:06:34.440 align:start position:0% which is the most famous math school in 00:06:34.440 --> 00:06:35.950 align:start position:0% which is the most famous math school in Soviet<00:06:34.680> Union.<00:06:34.919> So,<00:06:35.000> a<00:06:35.040> lot<00:06:35.240> of<00:06:35.320> our<00:06:35.480> graduates 00:06:35.950 --> 00:06:35.960 align:start position:0% Soviet Union. So, a lot of our graduates 00:06:35.960 --> 00:06:37.310 align:start position:0% Soviet Union. So, a lot of our graduates basically,<00:06:36.320> like<00:06:36.480> Igor,<00:06:37.080> like<00:06:37.240> the 00:06:37.310 --> 00:06:37.320 align:start position:0% basically, like Igor, like the 00:06:37.320 --> 00:06:39.510 align:start position:0% basically, like Igor, like the professors<00:06:37.919> of<00:06:38.080> math<00:06:38.440> in<00:06:38.720> in<00:06:38.880> famous<00:06:39.160> places. 00:06:39.510 --> 00:06:39.520 align:start position:0% professors of math in in famous places. 00:06:39.520 --> 00:06:41.270 align:start position:0% professors of math in in famous places. And<00:06:39.880> the<00:06:39.960> other<00:06:40.120> half<00:06:40.280> became<00:06:40.560> oligarchs<00:06:41.160> and 00:06:41.270 --> 00:06:41.280 align:start position:0% And the other half became oligarchs and 00:06:41.280 --> 00:06:42.830 align:start position:0% And the other half became oligarchs and they're<00:06:41.400> all<00:06:41.600> retired.<00:06:42.440> Uh<00:06:42.520> because<00:06:42.760> they're 00:06:42.830 --> 00:06:42.840 align:start position:0% they're all retired. Uh because they're 00:06:42.840 --> 00:06:45.430 align:start position:0% they're all retired. Uh because they're very<00:06:43.040> good<00:06:43.240> at<00:06:43.520> computers.<00:06:44.480> Uh<00:06:44.560> but<00:06:44.840> you<00:06:44.919> know, 00:06:45.430 --> 00:06:45.440 align:start position:0% very good at computers. Uh but you know, 00:06:45.440 --> 00:06:47.110 align:start position:0% very good at computers. Uh but you know, So,<00:06:45.640> we<00:06:45.760> have<00:06:45.880> this<00:06:46.040> series<00:06:46.320> of<00:06:46.440> exams.<00:06:46.880> So, 00:06:47.110 --> 00:06:47.120 align:start position:0% So, we have this series of exams. So, 00:06:47.120 --> 00:06:49.150 align:start position:0% So, we have this series of exams. So, basically,<00:06:47.480> the<00:06:47.720> the<00:06:47.840> class 00:06:49.150 --> 00:06:49.160 align:start position:0% basically, the the class 00:06:49.160 --> 00:06:50.510 align:start position:0% basically, the the class of<00:06:49.280> the<00:06:49.400> math<00:06:49.640> class<00:06:50.000> was<00:06:50.160> filled 00:06:50.510 --> 00:06:50.520 align:start position:0% of the math class was filled 00:06:50.520 --> 00:06:51.950 align:start position:0% of the math class was filled progressively.<00:06:51.120> First,<00:06:51.440> the<00:06:51.520> half<00:06:51.800> of<00:06:51.880> the 00:06:51.950 --> 00:06:51.960 align:start position:0% progressively. First, the half of the 00:06:51.960 --> 00:06:54.790 align:start position:0% progressively. First, the half of the people<00:06:52.360> who<00:06:52.640> attended<00:06:53.120> the<00:06:53.600> evening<00:06:53.919> courses, 00:06:54.790 --> 00:06:54.800 align:start position:0% people who attended the evening courses, 00:06:54.800 --> 00:06:56.670 align:start position:0% people who attended the evening courses, and<00:06:54.919> then<00:06:55.200> a<00:06:55.280> quarter,<00:06:55.800> and<00:06:55.960> then<00:06:56.360> and<00:06:56.440> so,<00:06:56.560> you 00:06:56.670 --> 00:06:56.680 align:start position:0% and then a quarter, and then and so, you 00:06:56.680 --> 00:06:59.430 align:start position:0% and then a quarter, and then and so, you have<00:06:56.800> to<00:06:56.880> pass<00:06:57.200> exams.<00:06:57.680> So,<00:06:58.240> and<00:06:58.760> um<00:06:59.200> right? 00:06:59.430 --> 00:06:59.440 align:start position:0% have to pass exams. So, and um right? 00:06:59.440 --> 00:07:00.630 align:start position:0% have to pass exams. So, and um right? And<00:06:59.560> so, 00:07:00.630 --> 00:07:00.640 align:start position:0% And so, 00:07:00.640 --> 00:07:02.990 align:start position:0% And so, uh<00:07:00.880> and<00:07:01.080> I<00:07:01.160> remember<00:07:01.919> that 00:07:02.990 --> 00:07:03.000 align:start position:0% uh and I remember that 00:07:03.000 --> 00:07:04.750 align:start position:0% uh and I remember that uh<00:07:03.480> So,<00:07:03.640> I<00:07:03.720> read<00:07:03.880> some<00:07:04.040> book<00:07:04.280> on<00:07:04.360> the<00:07:04.480> number 00:07:04.750 --> 00:07:04.760 align:start position:0% uh So, I read some book on the number 00:07:04.760 --> 00:07:05.790 align:start position:0% uh So, I read some book on the number theory.<00:07:05.000> So,<00:07:05.160> Soviet<00:07:05.440> Union<00:07:05.560> had<00:07:05.680> these 00:07:05.790 --> 00:07:05.800 align:start position:0% theory. So, Soviet Union had these 00:07:05.800 --> 00:07:08.070 align:start position:0% theory. So, Soviet Union had these amazing<00:07:06.680> math<00:07:07.000> books,<00:07:07.320> right?<00:07:07.560> And<00:07:07.960> so, 00:07:08.070 --> 00:07:08.080 align:start position:0% amazing math books, right? And so, 00:07:08.080 --> 00:07:09.070 align:start position:0% amazing math books, right? And so, basically,<00:07:08.320> I<00:07:08.360> was<00:07:08.440> supposed<00:07:08.720> to<00:07:08.760> explain 00:07:09.070 --> 00:07:09.080 align:start position:0% basically, I was supposed to explain 00:07:09.080 --> 00:07:10.870 align:start position:0% basically, I was supposed to explain something,<00:07:09.440> and<00:07:09.640> I<00:07:09.680> thought<00:07:09.919> that<00:07:10.160> I<00:07:10.200> know<00:07:10.800> I 00:07:10.870 --> 00:07:10.880 align:start position:0% something, and I thought that I know I 00:07:10.880 --> 00:07:12.390 align:start position:0% something, and I thought that I know I kind<00:07:11.000> of<00:07:11.080> mechanically<00:07:11.560> memorized<00:07:12.040> a<00:07:12.080> lot<00:07:12.280> of 00:07:12.390 --> 00:07:12.400 align:start position:0% kind of mechanically memorized a lot of 00:07:12.400 --> 00:07:15.270 align:start position:0% kind of mechanically memorized a lot of mathematical<00:07:12.880> formulas.<00:07:13.919> And<00:07:14.040> so,<00:07:14.400> the<00:07:14.520> guy 00:07:15.270 --> 00:07:15.280 align:start position:0% mathematical formulas. And so, the guy 00:07:15.280 --> 00:07:17.270 align:start position:0% mathematical formulas. And so, the guy uh<00:07:15.680> was<00:07:15.840> looking<00:07:16.080> at<00:07:16.200> me.<00:07:16.800> Uh<00:07:17.040> I<00:07:17.120> was 00:07:17.270 --> 00:07:17.280 align:start position:0% uh was looking at me. Uh I was 00:07:17.280 --> 00:07:19.110 align:start position:0% uh was looking at me. Uh I was explaining<00:07:17.680> some<00:07:17.919> some<00:07:18.160> inference,<00:07:18.880> but<00:07:19.080> I 00:07:19.110 --> 00:07:19.120 align:start position:0% explaining some some inference, but I 00:07:19.120 --> 00:07:20.430 align:start position:0% explaining some some inference, but I mechanically<00:07:19.560> memorized<00:07:20.040> it.<00:07:20.160> I<00:07:20.200> didn't 00:07:20.430 --> 00:07:20.440 align:start position:0% mechanically memorized it. I didn't 00:07:20.440 --> 00:07:22.390 align:start position:0% mechanically memorized it. I didn't understand<00:07:20.880> the<00:07:20.919> underlying<00:07:21.360> math.<00:07:22.120> I<00:07:22.160> just 00:07:22.390 --> 00:07:22.400 align:start position:0% understand the underlying math. I just 00:07:22.400 --> 00:07:24.230 align:start position:0% understand the underlying math. I just kind<00:07:22.560> of<00:07:22.680> memorized<00:07:23.400> how<00:07:23.680> the<00:07:23.919> the<00:07:24.040> proof 00:07:24.230 --> 00:07:24.240 align:start position:0% kind of memorized how the the proof 00:07:24.240 --> 00:07:27.590 align:start position:0% kind of memorized how the the proof goes.<00:07:25.000> And<00:07:25.160> then,<00:07:25.480> I<00:07:25.560> forgot<00:07:26.000> midway.<00:07:27.040> Uh 00:07:27.590 --> 00:07:27.600 align:start position:0% goes. And then, I forgot midway. Uh 00:07:27.600 --> 00:07:29.710 align:start position:0% goes. And then, I forgot midway. Uh and<00:07:28.040> and<00:07:28.520> basically,<00:07:29.080> I<00:07:29.120> did<00:07:29.320> all<00:07:29.400> the<00:07:29.480> steps 00:07:29.710 --> 00:07:29.720 align:start position:0% and and basically, I did all the steps 00:07:29.720 --> 00:07:31.430 align:start position:0% and and basically, I did all the steps except<00:07:30.000> the<00:07:30.080> final<00:07:30.320> step.<00:07:30.919> And<00:07:31.040> then,<00:07:31.120> the<00:07:31.200> guy 00:07:31.430 --> 00:07:31.440 align:start position:0% except the final step. And then, the guy 00:07:31.440 --> 00:07:33.230 align:start position:0% except the final step. And then, the guy looked<00:07:31.640> at<00:07:31.760> me<00:07:31.840> smiling<00:07:32.440> as<00:07:32.600> like<00:07:32.800> expecting 00:07:33.230 --> 00:07:33.240 align:start position:0% looked at me smiling as like expecting 00:07:33.240 --> 00:07:35.630 align:start position:0% looked at me smiling as like expecting me<00:07:33.360> to<00:07:33.520> just<00:07:34.280> normally<00:07:35.120> explain<00:07:35.480> what 00:07:35.630 --> 00:07:35.640 align:start position:0% me to just normally explain what 00:07:35.640 --> 00:07:36.710 align:start position:0% me to just normally explain what follows.<00:07:35.960> So,<00:07:36.000> because<00:07:36.320> I<00:07:36.400> followed 00:07:36.710 --> 00:07:36.720 align:start position:0% follows. So, because I followed 00:07:36.720 --> 00:07:38.510 align:start position:0% follows. So, because I followed mechanically,<00:07:37.880> I<00:07:37.960> looked<00:07:38.200> at<00:07:38.280> him<00:07:38.400> with 00:07:38.510 --> 00:07:38.520 align:start position:0% mechanically, I looked at him with 00:07:38.520 --> 00:07:40.909 align:start position:0% mechanically, I looked at him with horror,<00:07:39.040> and<00:07:39.160> like<00:07:39.360> I<00:07:39.400> realized<00:07:40.640> that<00:07:40.840> I 00:07:40.909 --> 00:07:40.919 align:start position:0% horror, and like I realized that I 00:07:40.919 --> 00:07:42.870 align:start position:0% horror, and like I realized that I forgot<00:07:41.600> the<00:07:41.680> next<00:07:41.960> step.<00:07:42.320> And<00:07:42.480> then<00:07:42.600> because<00:07:42.840> I 00:07:42.870 --> 00:07:42.880 align:start position:0% forgot the next step. And then because I 00:07:42.880 --> 00:07:45.310 align:start position:0% forgot the next step. And then because I never<00:07:43.120> understood<00:07:43.640> the<00:07:43.720> whole<00:07:43.960> thing,<00:07:44.920> uh<00:07:45.240> I 00:07:45.310 --> 00:07:45.320 align:start position:0% never understood the whole thing, uh I 00:07:45.320 --> 00:07:46.590 align:start position:0% never understood the whole thing, uh I couldn't<00:07:45.560> do<00:07:45.640> it.<00:07:45.760> And<00:07:45.880> so<00:07:46.040> they<00:07:46.320> it<00:07:46.400> just 00:07:46.590 --> 00:07:46.600 align:start position:0% couldn't do it. And so they it just 00:07:46.600 --> 00:07:48.550 align:start position:0% couldn't do it. And so they it just struck<00:07:46.960> me<00:07:47.200> that,<00:07:47.800> you<00:07:47.880> know,<00:07:48.080> some<00:07:48.280> people 00:07:48.550 --> 00:07:48.560 align:start position:0% struck me that, you know, some people 00:07:48.560 --> 00:07:50.190 align:start position:0% struck me that, you know, some people really<00:07:48.760> understand<00:07:49.280> it,<00:07:49.640> and<00:07:49.760> some<00:07:49.960> people 00:07:50.190 --> 00:07:50.200 align:start position:0% really understand it, and some people 00:07:50.200 --> 00:07:52.350 align:start position:0% really understand it, and some people mechanically<00:07:50.760> follow<00:07:51.080> this,<00:07:51.880> and<00:07:52.040> I<00:07:52.120> couldn't 00:07:52.350 --> 00:07:52.360 align:start position:0% mechanically follow this, and I couldn't 00:07:52.360 --> 00:07:54.350 align:start position:0% mechanically follow this, and I couldn't do<00:07:52.520> it.<00:07:52.760> And<00:07:52.960> so<00:07:53.400> and<00:07:53.560> then<00:07:53.720> basically<00:07:54.080> it<00:07:54.160> made 00:07:54.350 --> 00:07:54.360 align:start position:0% do it. And so and then basically it made 00:07:54.360 --> 00:07:56.230 align:start position:0% do it. And so and then basically it made me<00:07:54.440> think<00:07:54.680> like<00:07:54.840> I'm<00:07:55.000> not<00:07:55.240> really<00:07:55.880> I<00:07:55.960> don't 00:07:56.230 --> 00:07:56.240 align:start position:0% me think like I'm not really I don't 00:07:56.240 --> 00:07:57.950 align:start position:0% me think like I'm not really I don't really<00:07:56.400> get<00:07:56.600> mathematics,<00:07:57.160> but<00:07:57.720> that's 00:07:57.950 --> 00:07:57.960 align:start position:0% really get mathematics, but that's 00:07:57.960 --> 00:07:59.630 align:start position:0% really get mathematics, but that's probably<00:07:58.320> because<00:07:58.800> the<00:07:59.120> the<00:07:59.240> way<00:07:59.400> it<00:07:59.520> was 00:07:59.630 --> 00:07:59.640 align:start position:0% probably because the the way it was 00:07:59.640 --> 00:08:02.230 align:start position:0% probably because the the way it was explained<00:08:00.520> was<00:08:00.720> very<00:08:01.000> mechanical<00:08:01.760> and<00:08:02.040> not 00:08:02.230 --> 00:08:02.240 align:start position:0% explained was very mechanical and not 00:08:02.240 --> 00:08:04.310 align:start position:0% explained was very mechanical and not explaining<00:08:02.760> it<00:08:02.880> to<00:08:03.000> me<00:08:03.160> myself.<00:08:04.080> Yeah,<00:08:04.200> it's 00:08:04.310 --> 00:08:04.320 align:start position:0% explaining it to me myself. Yeah, it's 00:08:04.320 --> 00:08:06.110 align:start position:0% explaining it to me myself. Yeah, it's an<00:08:04.400> interesting<00:08:04.840> measure<00:08:05.320> of 00:08:06.110 --> 00:08:06.120 align:start position:0% an interesting measure of 00:08:06.120 --> 00:08:08.110 align:start position:0% an interesting measure of the<00:08:06.200> level<00:08:06.480> of<00:08:06.600> understanding<00:08:07.200> of<00:08:07.480> say<00:08:07.800> a<00:08:08.040> a 00:08:08.110 --> 00:08:08.120 align:start position:0% the level of understanding of say a a 00:08:08.120 --> 00:08:09.270 align:start position:0% the level of understanding of say a a proof<00:08:08.480> in<00:08:08.560> mathematics. 00:08:09.270 --> 00:08:09.280 align:start position:0% proof in mathematics. 00:08:09.280 --> 00:08:11.310 align:start position:0% proof in mathematics. >> Mhm.<00:08:10.000> How<00:08:10.080> much<00:08:10.360> you<00:08:10.440> can<00:08:10.600> actually<00:08:10.840> compress 00:08:11.310 --> 00:08:11.320 align:start position:0% >> Mhm. How much you can actually compress 00:08:11.320 --> 00:08:11.590 align:start position:0% >> Mhm. How much you can actually compress it. 00:08:11.590 --> 00:08:11.600 align:start position:0% it. 00:08:11.600 --> 00:08:14.270 align:start position:0% it. >> Yes.<00:08:12.320> So<00:08:13.080> uh 00:08:14.270 --> 00:08:14.280 align:start position:0% >> Yes. So uh 00:08:14.280 --> 00:08:15.590 align:start position:0% >> Yes. So uh the<00:08:14.320> lowest<00:08:14.680> level<00:08:14.880> of<00:08:14.960> understanding,<00:08:15.520> you 00:08:15.590 --> 00:08:15.600 align:start position:0% the lowest level of understanding, you 00:08:15.600 --> 00:08:17.470 align:start position:0% the lowest level of understanding, you just<00:08:15.800> have<00:08:15.919> to<00:08:16.080> learn<00:08:16.520> each<00:08:16.760> line<00:08:17.120> and<00:08:17.280> how 00:08:17.470 --> 00:08:17.480 align:start position:0% just have to learn each line and how 00:08:17.480 --> 00:08:19.070 align:start position:0% just have to learn each line and how what<00:08:17.680> comes<00:08:18.000> in 00:08:19.070 --> 00:08:19.080 align:start position:0% what comes in 00:08:19.080 --> 00:08:20.710 align:start position:0% what comes in But<00:08:19.200> if<00:08:19.640> if<00:08:19.760> you<00:08:19.800> have<00:08:19.919> a<00:08:19.960> better<00:08:20.440> level<00:08:20.600> of 00:08:20.710 --> 00:08:20.720 align:start position:0% But if if you have a better level of 00:08:20.720 --> 00:08:21.909 align:start position:0% But if if you have a better level of understanding,<00:08:21.200> you<00:08:21.280> might<00:08:21.480> have<00:08:21.600> sort<00:08:21.800> of 00:08:21.909 --> 00:08:21.919 align:start position:0% understanding, you might have sort of 00:08:21.919 --> 00:08:25.150 align:start position:0% understanding, you might have sort of five<00:08:22.320> ideas<00:08:22.880> that<00:08:23.120> if<00:08:23.240> you<00:08:23.400> first<00:08:23.680> you<00:08:23.760> do<00:08:23.919> this 00:08:25.150 --> 00:08:25.160 align:start position:0% five ideas that if you first you do this 00:08:25.160 --> 00:08:26.550 align:start position:0% five ideas that if you first you do this and<00:08:25.240> getting<00:08:25.480> to<00:08:25.560> that<00:08:25.760> idea<00:08:26.120> is<00:08:26.240> a<00:08:26.320> fairly 00:08:26.550 --> 00:08:26.560 align:start position:0% and getting to that idea is a fairly 00:08:26.560 --> 00:08:28.030 align:start position:0% and getting to that idea is a fairly standard<00:08:26.919> calculation,<00:08:27.560> and<00:08:27.640> then<00:08:27.800> you<00:08:27.880> get 00:08:28.030 --> 00:08:28.040 align:start position:0% standard calculation, and then you get 00:08:28.040 --> 00:08:29.710 align:start position:0% standard calculation, and then you get to<00:08:28.160> this<00:08:29.040> by<00:08:29.120> a<00:08:29.200> fairly<00:08:29.440> standard 00:08:29.710 --> 00:08:29.720 align:start position:0% to this by a fairly standard 00:08:29.720 --> 00:08:31.150 align:start position:0% to this by a fairly standard calculation.<00:08:30.680> But<00:08:30.800> then<00:08:30.919> you<00:08:31.000> have<00:08:31.120> to 00:08:31.150 --> 00:08:31.160 align:start position:0% calculation. But then you have to 00:08:31.160 --> 00:08:32.990 align:start position:0% calculation. But then you have to remember<00:08:31.400> those<00:08:31.560> five<00:08:31.840> ideas.<00:08:32.400> Yes.<00:08:32.919> And 00:08:32.990 --> 00:08:33.000 align:start position:0% remember those five ideas. Yes. And 00:08:33.000 --> 00:08:34.270 align:start position:0% remember those five ideas. Yes. And maybe<00:08:33.200> you<00:08:33.280> understand<00:08:33.599> it<00:08:33.719> better<00:08:34.039> than<00:08:34.200> you 00:08:34.270 --> 00:08:34.280 align:start position:0% maybe you understand it better than you 00:08:34.280 --> 00:08:35.870 align:start position:0% maybe you understand it better than you actually<00:08:34.599> see<00:08:34.760> there's<00:08:34.960> only<00:08:35.159> one<00:08:35.400> idea,<00:08:35.800> and 00:08:35.870 --> 00:08:35.880 align:start position:0% actually see there's only one idea, and 00:08:35.880 --> 00:08:38.029 align:start position:0% actually see there's only one idea, and those<00:08:36.080> five<00:08:36.360> ideas<00:08:36.719> were<00:08:36.840> natural. 00:08:38.029 --> 00:08:38.039 align:start position:0% those five ideas were natural. 00:08:38.039 --> 00:08:39.670 align:start position:0% those five ideas were natural. Yes.<00:08:38.560> And<00:08:38.640> then<00:08:38.719> maybe<00:08:38.919> at<00:08:39.080> some<00:08:39.280> point<00:08:39.599> you 00:08:39.670 --> 00:08:39.680 align:start position:0% Yes. And then maybe at some point you 00:08:39.680 --> 00:08:41.390 align:start position:0% Yes. And then maybe at some point you reach<00:08:39.919> the<00:08:40.000> point<00:08:40.280> where 00:08:41.390 --> 00:08:41.400 align:start position:0% reach the point where 00:08:41.400 --> 00:08:43.230 align:start position:0% reach the point where just<00:08:41.560> the<00:08:41.640> whole<00:08:41.840> thing<00:08:42.200> just<00:08:42.719> you're<00:08:42.880> doing 00:08:43.230 --> 00:08:43.240 align:start position:0% just the whole thing just you're doing 00:08:43.240 --> 00:08:44.630 align:start position:0% just the whole thing just you're doing what<00:08:43.440> feels<00:08:43.680> like<00:08:43.840> the<00:08:44.000> obvious<00:08:44.320> thing,<00:08:44.560> and 00:08:44.630 --> 00:08:44.640 align:start position:0% what feels like the obvious thing, and 00:08:44.640 --> 00:08:45.710 align:start position:0% what feels like the obvious thing, and that's<00:08:44.800> when<00:08:44.920> you've<00:08:45.080> reached<00:08:45.360> the<00:08:45.440> sort<00:08:45.600> of 00:08:45.710 --> 00:08:45.720 align:start position:0% that's when you've reached the sort of 00:08:45.720 --> 00:08:47.190 align:start position:0% that's when you've reached the sort of ultimate<00:08:46.160> understanding<00:08:46.760> of<00:08:46.839> the<00:08:46.880> proof. 00:08:47.190 --> 00:08:47.200 align:start position:0% ultimate understanding of the proof. 00:08:47.200 --> 00:08:49.310 align:start position:0% ultimate understanding of the proof. >> Right.<00:08:47.640> But<00:08:47.960> but<00:08:48.400> to<00:08:48.520> me<00:08:48.680> it<00:08:48.800> was,<00:08:49.040> you<00:08:49.120> know,<00:08:49.280> a 00:08:49.310 --> 00:08:49.320 align:start position:0% >> Right. But but to me it was, you know, a 00:08:49.320 --> 00:08:50.590 align:start position:0% >> Right. But but to me it was, you know, a lot<00:08:49.520> of<00:08:49.680> it<00:08:49.880> is<00:08:50.080> like<00:08:50.280> when<00:08:50.400> you<00:08:50.480> do 00:08:50.590 --> 00:08:50.600 align:start position:0% lot of it is like when you do 00:08:50.600 --> 00:08:52.150 align:start position:0% lot of it is like when you do integration,<00:08:51.240> a<00:08:51.280> lot<00:08:51.440> of<00:08:51.520> it<00:08:51.600> is<00:08:51.680> mechanical 00:08:52.150 --> 00:08:52.160 align:start position:0% integration, a lot of it is mechanical 00:08:52.160 --> 00:08:54.510 align:start position:0% integration, a lot of it is mechanical moving<00:08:52.440> of<00:08:52.600> parts<00:08:52.880> of<00:08:53.120> of<00:08:53.320> formulas<00:08:53.760> around. 00:08:54.510 --> 00:08:54.520 align:start position:0% moving of parts of of formulas around. 00:08:54.520 --> 00:08:56.190 align:start position:0% moving of parts of of formulas around. And<00:08:54.640> so<00:08:54.760> you<00:08:54.880> can<00:08:55.040> remember<00:08:55.520> the<00:08:55.640> mechanics<00:08:56.120> of 00:08:56.190 --> 00:08:56.200 align:start position:0% And so you can remember the mechanics of 00:08:56.200 --> 00:08:57.750 align:start position:0% And so you can remember the mechanics of doing<00:08:56.440> it,<00:08:56.839> but<00:08:57.000> not<00:08:57.240> the<00:08:57.280> underlying 00:08:57.750 --> 00:08:57.760 align:start position:0% doing it, but not the underlying 00:08:57.760 --> 00:08:59.630 align:start position:0% doing it, but not the underlying principle.<00:08:58.600> And<00:08:58.720> so<00:08:58.960> I<00:08:59.040> think<00:08:59.320> a<00:08:59.360> lot<00:08:59.560> of 00:08:59.630 --> 00:08:59.640 align:start position:0% principle. And so I think a lot of 00:08:59.640 --> 00:09:00.710 align:start position:0% principle. And so I think a lot of people<00:08:59.960> will<00:09:00.080> do<00:09:00.200> mathematical 00:09:00.710 --> 00:09:00.720 align:start position:0% people will do mathematical 00:09:00.720 --> 00:09:02.110 align:start position:0% people will do mathematical transformations<00:09:01.400> as<00:09:01.520> just<00:09:01.720> some<00:09:01.880> kind<00:09:02.040> of 00:09:02.110 --> 00:09:02.120 align:start position:0% transformations as just some kind of 00:09:02.120 --> 00:09:03.950 align:start position:0% transformations as just some kind of mechanical<00:09:02.600> movements,<00:09:03.400> right?<00:09:03.720> And<00:09:03.839> they 00:09:03.950 --> 00:09:03.960 align:start position:0% mechanical movements, right? And they 00:09:03.960 --> 00:09:05.150 align:start position:0% mechanical movements, right? And they will<00:09:04.080> not<00:09:04.360> And<00:09:04.480> I<00:09:04.560> think<00:09:04.720> a<00:09:04.760> lot<00:09:04.920> of<00:09:05.000> school 00:09:05.150 --> 00:09:05.160 align:start position:0% will not And I think a lot of school 00:09:05.160 --> 00:09:06.870 align:start position:0% will not And I think a lot of school children<00:09:05.440> do<00:09:05.560> this.<00:09:06.040> Yeah,<00:09:06.200> I've<00:09:06.520> seen<00:09:06.760> that 00:09:06.870 --> 00:09:06.880 align:start position:0% children do this. Yeah, I've seen that 00:09:06.880 --> 00:09:09.590 align:start position:0% children do this. Yeah, I've seen that with<00:09:07.000> my<00:09:07.160> own<00:09:07.320> children,<00:09:07.680> actually.<00:09:08.000> Uh-huh. 00:09:09.590 --> 00:09:09.600 align:start position:0% with my own children, actually. Uh-huh. 00:09:09.600 --> 00:09:10.910 align:start position:0% with my own children, actually. Uh-huh. Everything<00:09:09.920> seems<00:09:10.200> to<00:09:10.280> be<00:09:10.400> fine,<00:09:10.720> and<00:09:10.800> then 00:09:10.910 --> 00:09:10.920 align:start position:0% Everything seems to be fine, and then 00:09:10.920 --> 00:09:12.590 align:start position:0% Everything seems to be fine, and then they<00:09:11.000> suddenly<00:09:11.320> make<00:09:11.520> some<00:09:11.720> bizarre<00:09:12.080> mistake, 00:09:12.590 --> 00:09:12.600 align:start position:0% they suddenly make some bizarre mistake, 00:09:12.600 --> 00:09:14.230 align:start position:0% they suddenly make some bizarre mistake, and<00:09:12.680> then<00:09:12.800> I<00:09:12.880> realize<00:09:13.320> that<00:09:13.920> There's<00:09:14.120> no 00:09:14.230 --> 00:09:14.240 align:start position:0% and then I realize that There's no 00:09:14.240 --> 00:09:15.710 align:start position:0% and then I realize that There's no understanding.<00:09:14.960> Yeah,<00:09:15.080> that<00:09:15.240> the<00:09:15.360> reason<00:09:15.600> it 00:09:15.710 --> 00:09:15.720 align:start position:0% understanding. Yeah, that the reason it 00:09:15.720 --> 00:09:17.590 align:start position:0% understanding. Yeah, that the reason it seemed<00:09:16.000> fine<00:09:16.280> was<00:09:16.400> just<00:09:16.560> because<00:09:16.800> they'd 00:09:17.590 --> 00:09:17.600 align:start position:0% seemed fine was just because they'd 00:09:17.600 --> 00:09:20.270 align:start position:0% seemed fine was just because they'd learned<00:09:17.960> the<00:09:18.040> manipulations<00:09:18.920> very<00:09:19.200> well,<00:09:19.600> and 00:09:20.270 --> 00:09:20.280 align:start position:0% learned the manipulations very well, and 00:09:20.280 --> 00:09:21.430 align:start position:0% learned the manipulations very well, and uh 00:09:21.430 --> 00:09:21.440 align:start position:0% uh 00:09:21.440 --> 00:09:23.070 align:start position:0% uh but<00:09:22.080> uh<00:09:22.120> if<00:09:22.200> they<00:09:22.320> got<00:09:22.520> sort<00:09:22.680> of<00:09:22.839> out<00:09:23.000> of 00:09:23.070 --> 00:09:23.080 align:start position:0% but uh if they got sort of out of 00:09:23.080 --> 00:09:24.430 align:start position:0% but uh if they got sort of out of distribution,<00:09:23.680> so<00:09:23.800> to<00:09:23.920> speak, 00:09:24.430 --> 00:09:24.440 align:start position:0% distribution, so to speak, 00:09:24.440 --> 00:09:25.270 align:start position:0% distribution, so to speak, >> Right.<00:09:24.960> Right. 00:09:25.270 --> 00:09:25.280 align:start position:0% >> Right. Right. 00:09:25.280 --> 00:09:27.790 align:start position:0% >> Right. Right. >> then<00:09:25.320> suddenly<00:09:26.200> uh<00:09:26.320> it<00:09:26.480> fell<00:09:26.640> apart. 00:09:27.790 --> 00:09:27.800 align:start position:0% >> then suddenly uh it fell apart. 00:09:27.800 --> 00:09:29.630 align:start position:0% >> then suddenly uh it fell apart. I<00:09:27.880> want<00:09:28.080> to<00:09:28.120> kind<00:09:28.280> of<00:09:28.960> uh 00:09:29.630 --> 00:09:29.640 align:start position:0% I want to kind of uh 00:09:29.640 --> 00:09:31.990 align:start position:0% I want to kind of uh zoom<00:09:29.920> in<00:09:30.040> on<00:09:30.200> the<00:09:30.800> formal<00:09:31.160> methods.<00:09:31.520> So<00:09:31.760> I<00:09:31.839> had 00:09:31.990 --> 00:09:32.000 align:start position:0% zoom in on the formal methods. So I had 00:09:32.000 --> 00:09:33.670 align:start position:0% zoom in on the formal methods. So I had a<00:09:32.040> friend<00:09:32.320> who<00:09:32.440> was<00:09:32.680> in<00:09:32.839> formal<00:09:33.280> methods<00:09:33.600> in 00:09:33.670 --> 00:09:33.680 align:start position:0% a friend who was in formal methods in 00:09:33.680 --> 00:09:36.110 align:start position:0% a friend who was in formal methods in 1993<00:09:34.520> working<00:09:34.800> with<00:09:34.880> a<00:09:34.920> computer<00:09:35.240> company, 00:09:36.110 --> 00:09:36.120 align:start position:0% 1993 working with a computer company, 00:09:36.120 --> 00:09:38.750 align:start position:0% 1993 working with a computer company, right?<00:09:36.440> And<00:09:36.560> so<00:09:37.120> it<00:09:37.280> seems<00:09:37.560> like<00:09:37.720> a<00:09:37.800> very<00:09:38.320> very 00:09:38.750 --> 00:09:38.760 align:start position:0% right? And so it seems like a very very 00:09:38.760 --> 00:09:39.750 align:start position:0% right? And so it seems like a very very kind<00:09:38.960> of 00:09:39.750 --> 00:09:39.760 align:start position:0% kind of 00:09:39.760 --> 00:09:42.990 align:start position:0% kind of stagnant<00:09:40.360> little<00:09:41.000> like<00:09:41.760> academic<00:09:42.280> niche, 00:09:42.990 --> 00:09:43.000 align:start position:0% stagnant little like academic niche, 00:09:43.000 --> 00:09:44.070 align:start position:0% stagnant little like academic niche, right?<00:09:43.240> And<00:09:43.360> so,<00:09:43.480> there<00:09:43.600> were<00:09:43.680> people<00:09:43.960> they 00:09:44.070 --> 00:09:44.080 align:start position:0% right? And so, there were people they 00:09:44.080 --> 00:09:46.230 align:start position:0% right? And so, there were people they had<00:09:44.280> the<00:09:44.400> formal<00:09:44.640> method<00:09:44.920> conferences,<00:09:46.080> and 00:09:46.230 --> 00:09:46.240 align:start position:0% had the formal method conferences, and 00:09:46.240 --> 00:09:47.430 align:start position:0% had the formal method conferences, and they<00:09:46.360> went<00:09:46.560> there,<00:09:46.800> but<00:09:47.040> they<00:09:47.200> were<00:09:47.280> not 00:09:47.430 --> 00:09:47.440 align:start position:0% they went there, but they were not 00:09:47.440 --> 00:09:48.990 align:start position:0% they went there, but they were not connected<00:09:47.800> to<00:09:47.880> the<00:09:48.040> real<00:09:48.240> world,<00:09:48.640> right?<00:09:48.800> No, 00:09:48.990 --> 00:09:49.000 align:start position:0% connected to the real world, right? No, 00:09:49.000 --> 00:09:52.230 align:start position:0% connected to the real world, right? No, so<00:09:49.520> the<00:09:49.640> first<00:09:49.960> time<00:09:50.320> I've<00:09:50.520> seen<00:09:51.360> a<00:09:51.440> talk<00:09:51.760> about 00:09:52.230 --> 00:09:52.240 align:start position:0% so the first time I've seen a talk about 00:09:52.240 --> 00:09:54.310 align:start position:0% so the first time I've seen a talk about formal<00:09:52.560> methods<00:09:53.080> actually<00:09:53.680> being<00:09:53.880> practical 00:09:54.310 --> 00:09:54.320 align:start position:0% formal methods actually being practical 00:09:54.320 --> 00:09:56.270 align:start position:0% formal methods actually being practical was<00:09:54.440> Leslie<00:09:54.760> Lamport,<00:09:55.720> who<00:09:55.840> gave<00:09:55.960> a<00:09:56.040> talk<00:09:56.200> at 00:09:56.270 --> 00:09:56.280 align:start position:0% was Leslie Lamport, who gave a talk at 00:09:56.280 --> 00:09:59.230 align:start position:0% was Leslie Lamport, who gave a talk at the<00:09:56.360> computer<00:09:56.720> conference,<00:09:57.760> and<00:09:58.280> TLA+<00:09:59.000> and<00:09:59.120> he 00:09:59.230 --> 00:09:59.240 align:start position:0% the computer conference, and TLA+ and he 00:09:59.240 --> 00:10:02.230 align:start position:0% the computer conference, and TLA+ and he mentioned<00:09:59.600> how<00:09:59.800> the<00:10:00.280> Amazon<00:10:00.840> Dyna<00:10:01.560> DynamoDB 00:10:02.230 --> 00:10:02.240 align:start position:0% mentioned how the Amazon Dyna DynamoDB 00:10:02.240 --> 00:10:05.030 align:start position:0% mentioned how the Amazon Dyna DynamoDB team<00:10:02.920> used<00:10:03.240> TLA+<00:10:03.840> to<00:10:03.960> basically<00:10:04.400> formulate 00:10:05.030 --> 00:10:05.040 align:start position:0% team used TLA+ to basically formulate 00:10:05.040 --> 00:10:06.870 align:start position:0% team used TLA+ to basically formulate that<00:10:05.160> it's<00:10:05.320> a<00:10:05.400> correct<00:10:05.800> implementation, 00:10:06.870 --> 00:10:06.880 align:start position:0% that it's a correct implementation, 00:10:06.880 --> 00:10:09.110 align:start position:0% that it's a correct implementation, right?<00:10:07.160> And<00:10:07.440> and<00:10:07.640> but<00:10:07.840> now<00:10:08.200> then<00:10:08.440> I've<00:10:08.600> seen 00:10:09.110 --> 00:10:09.120 align:start position:0% right? And and but now then I've seen 00:10:09.120 --> 00:10:11.830 align:start position:0% right? And and but now then I've seen this<00:10:09.360> whole<00:10:09.600> rise<00:10:09.840> of<00:10:10.000> Lean<00:10:10.960> in<00:10:11.120> conjunction 00:10:11.830 --> 00:10:11.840 align:start position:0% this whole rise of Lean in conjunction 00:10:11.840 --> 00:10:13.510 align:start position:0% this whole rise of Lean in conjunction with<00:10:12.160> and<00:10:12.320> people<00:10:12.600> basically<00:10:12.880> want<00:10:13.040> to<00:10:13.160> model 00:10:13.510 --> 00:10:13.520 align:start position:0% with and people basically want to model 00:10:13.520 --> 00:10:16.750 align:start position:0% with and people basically want to model the<00:10:13.680> world<00:10:14.160> now<00:10:14.760> with<00:10:15.040> Lean<00:10:15.560> and<00:10:15.760> prove,<00:10:16.640> you 00:10:16.750 --> 00:10:16.760 align:start position:0% the world now with Lean and prove, you 00:10:16.760 --> 00:10:18.550 align:start position:0% the world now with Lean and prove, you know,<00:10:16.960> things<00:10:17.280> about<00:10:17.600> it<00:10:17.760> and<00:10:17.920> apparently<00:10:18.400> it 00:10:18.550 --> 00:10:18.560 align:start position:0% know, things about it and apparently it 00:10:18.560 --> 00:10:20.670 align:start position:0% know, things about it and apparently it does<00:10:18.840> work<00:10:19.040> in<00:10:19.160> math.<00:10:19.480> So,<00:10:19.920> I'm<00:10:20.040> just<00:10:20.240> curious 00:10:20.670 --> 00:10:20.680 align:start position:0% does work in math. So, I'm just curious 00:10:20.680 --> 00:10:22.590 align:start position:0% does work in math. So, I'm just curious like<00:10:21.160> do<00:10:21.320> you<00:10:21.440> see<00:10:21.720> this<00:10:22.160> is<00:10:22.320> this<00:10:22.520> a 00:10:22.590 --> 00:10:22.600 align:start position:0% like do you see this is this a 00:10:22.600 --> 00:10:26.110 align:start position:0% like do you see this is this a breakthrough<00:10:23.800> for<00:10:23.960> formal<00:10:24.320> methods?<00:10:25.400> Um<00:10:26.040> I 00:10:26.110 --> 00:10:26.120 align:start position:0% breakthrough for formal methods? Um I 00:10:26.120 --> 00:10:27.350 align:start position:0% breakthrough for formal methods? Um I think<00:10:26.320> it's<00:10:26.440> certainly<00:10:26.720> a<00:10:26.760> breakthrough<00:10:27.280> of 00:10:27.350 --> 00:10:27.360 align:start position:0% think it's certainly a breakthrough of 00:10:27.360 --> 00:10:30.150 align:start position:0% think it's certainly a breakthrough of one<00:10:27.600> kind.<00:10:27.960> I<00:10:28.000> mean,<00:10:28.240> it's<00:10:28.880> uh 00:10:30.150 --> 00:10:30.160 align:start position:0% one kind. I mean, it's uh 00:10:30.160 --> 00:10:31.990 align:start position:0% one kind. I mean, it's uh we're<00:10:30.320> seeing 00:10:31.990 --> 00:10:32.000 align:start position:0% we're seeing 00:10:32.000 --> 00:10:34.670 align:start position:0% we're seeing the<00:10:32.040> the<00:10:32.120> the<00:10:32.200> the<00:10:32.400> story<00:10:32.800> always<00:10:33.120> used<00:10:33.360> to<00:10:33.480> be 00:10:34.670 --> 00:10:34.680 align:start position:0% the the the the story always used to be 00:10:34.680 --> 00:10:35.990 align:start position:0% the the the the story always used to be that 00:10:35.990 --> 00:10:36.000 align:start position:0% that 00:10:36.000 --> 00:10:37.710 align:start position:0% that one 00:10:37.710 --> 00:10:37.720 align:start position:0% one 00:10:37.720 --> 00:10:40.750 align:start position:0% one by<00:10:37.960> and<00:10:38.160> large<00:10:38.480> mathematicians<00:10:39.200> were 00:10:40.750 --> 00:10:40.760 align:start position:0% by and large mathematicians were 00:10:40.760 --> 00:10:42.350 align:start position:0% by and large mathematicians were they<00:10:40.800> didn't<00:10:41.040> really<00:10:41.280> need<00:10:41.760> this<00:10:42.040> extra 00:10:42.350 --> 00:10:42.360 align:start position:0% they didn't really need this extra 00:10:42.360 --> 00:10:44.710 align:start position:0% they didn't really need this extra guarantee<00:10:42.880> of<00:10:43.000> correctness<00:10:43.640> because<00:10:44.600> if 00:10:44.710 --> 00:10:44.720 align:start position:0% guarantee of correctness because if 00:10:44.720 --> 00:10:46.590 align:start position:0% guarantee of correctness because if something<00:10:45.000> was<00:10:45.120> important 00:10:46.590 --> 00:10:46.600 align:start position:0% something was important 00:10:46.600 --> 00:10:49.350 align:start position:0% something was important um<00:10:47.680> it<00:10:47.800> would<00:10:47.880> be<00:10:48.000> read<00:10:48.280> by<00:10:48.400> a<00:10:48.440> lot<00:10:48.640> of<00:10:48.720> people. 00:10:49.350 --> 00:10:49.360 align:start position:0% um it would be read by a lot of people. 00:10:49.360 --> 00:10:51.270 align:start position:0% um it would be read by a lot of people. If<00:10:49.480> it<00:10:49.600> was<00:10:49.760> if<00:10:49.960> it<00:10:50.080> was 00:10:51.270 --> 00:10:51.280 align:start position:0% If it was if it was 00:10:51.280 --> 00:10:52.390 align:start position:0% If it was if it was incorrect,<00:10:51.800> you<00:10:51.880> know,<00:10:51.960> usually<00:10:52.240> there<00:10:52.320> would 00:10:52.390 --> 00:10:52.400 align:start position:0% incorrect, you know, usually there would 00:10:52.400 --> 00:10:53.630 align:start position:0% incorrect, you know, usually there would be<00:10:52.440> small<00:10:52.760> mistakes,<00:10:53.240> but<00:10:53.360> if<00:10:53.440> there<00:10:53.520> were 00:10:53.630 --> 00:10:53.640 align:start position:0% be small mistakes, but if there were 00:10:53.640 --> 00:10:55.310 align:start position:0% be small mistakes, but if there were serious<00:10:54.040> mistakes,<00:10:54.480> somebody<00:10:54.839> would<00:10:55.000> at<00:10:55.120> some 00:10:55.310 --> 00:10:55.320 align:start position:0% serious mistakes, somebody would at some 00:10:55.320 --> 00:10:57.670 align:start position:0% serious mistakes, somebody would at some point<00:10:55.600> realize<00:10:56.040> that.<00:10:56.760> Mhm. 00:10:57.670 --> 00:10:57.680 align:start position:0% point realize that. Mhm. 00:10:57.680 --> 00:10:58.870 align:start position:0% point realize that. Mhm. And<00:10:57.760> if<00:10:57.839> it<00:10:57.920> wasn't<00:10:58.160> important,<00:10:58.600> then<00:10:58.760> who 00:10:58.870 --> 00:10:58.880 align:start position:0% And if it wasn't important, then who 00:10:58.880 --> 00:11:00.230 align:start position:0% And if it wasn't important, then who cares? 00:11:00.230 --> 00:11:00.240 align:start position:0% cares? 00:11:00.240 --> 00:11:03.390 align:start position:0% cares? Um<00:11:01.200> but<00:11:01.839> two<00:11:02.000> things<00:11:02.240> have<00:11:02.360> changed.<00:11:03.000> And<00:11:03.120> also 00:11:03.390 --> 00:11:03.400 align:start position:0% Um but two things have changed. And also 00:11:03.400 --> 00:11:04.790 align:start position:0% Um but two things have changed. And also the<00:11:03.560> other<00:11:03.760> the<00:11:03.880> other<00:11:04.000> side<00:11:04.240> of<00:11:04.320> the<00:11:04.400> story 00:11:04.790 --> 00:11:04.800 align:start position:0% the other the other side of the story 00:11:04.800 --> 00:11:06.510 align:start position:0% the other the other side of the story was<00:11:05.120> that<00:11:05.680> uh 00:11:06.510 --> 00:11:06.520 align:start position:0% was that uh 00:11:06.520 --> 00:11:08.430 align:start position:0% was that uh the<00:11:06.680> effort<00:11:07.120> needed<00:11:07.720> to<00:11:07.839> write<00:11:08.080> down<00:11:08.360> a 00:11:08.430 --> 00:11:08.440 align:start position:0% the effort needed to write down a 00:11:08.440 --> 00:11:10.710 align:start position:0% the effort needed to write down a completely<00:11:08.880> formal<00:11:09.280> proof<00:11:09.560> in<00:11:09.760> a<00:11:10.480> proof 00:11:10.710 --> 00:11:10.720 align:start position:0% completely formal proof in a proof 00:11:10.720 --> 00:11:13.150 align:start position:0% completely formal proof in a proof assistant<00:11:11.200> such<00:11:11.440> as<00:11:11.600> Isabelle<00:11:12.080> or<00:11:12.240> Coq<00:11:12.720> or 00:11:13.150 --> 00:11:13.160 align:start position:0% assistant such as Isabelle or Coq or 00:11:13.160 --> 00:11:14.710 align:start position:0% assistant such as Isabelle or Coq or Mizar<00:11:13.800> or 00:11:14.710 --> 00:11:14.720 align:start position:0% Mizar or 00:11:14.720 --> 00:11:17.510 align:start position:0% Mizar or or<00:11:14.839> Lean<00:11:15.120> which<00:11:15.240> came<00:11:15.440> in<00:11:15.520> a<00:11:15.560> bit<00:11:15.720> later 00:11:17.510 --> 00:11:17.520 align:start position:0% or Lean which came in a bit later 00:11:17.520 --> 00:11:19.870 align:start position:0% or Lean which came in a bit later was<00:11:17.640> so<00:11:17.839> great<00:11:18.920> and<00:11:19.000> so<00:11:19.120> much<00:11:19.360> greater<00:11:19.720> than 00:11:19.870 --> 00:11:19.880 align:start position:0% was so great and so much greater than 00:11:19.880 --> 00:11:21.390 align:start position:0% was so great and so much greater than just<00:11:20.080> writing<00:11:20.400> out<00:11:20.560> the<00:11:20.640> usual<00:11:20.960> style<00:11:21.280> of 00:11:21.390 --> 00:11:21.400 align:start position:0% just writing out the usual style of 00:11:21.400 --> 00:11:23.750 align:start position:0% just writing out the usual style of proof<00:11:21.960> Mhm.<00:11:22.320> that<00:11:22.360> it<00:11:22.440> just<00:11:22.640> wasn't<00:11:22.920> worth<00:11:23.200> it. 00:11:23.750 --> 00:11:23.760 align:start position:0% proof Mhm. that it just wasn't worth it. 00:11:23.760 --> 00:11:25.070 align:start position:0% proof Mhm. that it just wasn't worth it. So,<00:11:23.920> two<00:11:24.120> things<00:11:24.320> have<00:11:24.440> changed,<00:11:24.800> I<00:11:24.880> think. 00:11:25.070 --> 00:11:25.080 align:start position:0% So, two things have changed, I think. 00:11:25.080 --> 00:11:26.350 align:start position:0% So, two things have changed, I think. One<00:11:25.280> is<00:11:25.440> that 00:11:26.350 --> 00:11:26.360 align:start position:0% One is that 00:11:26.360 --> 00:11:27.950 align:start position:0% One is that conventional<00:11:26.960> proofs<00:11:27.280> have<00:11:27.400> become<00:11:27.680> more<00:11:27.880> and 00:11:27.950 --> 00:11:27.960 align:start position:0% conventional proofs have become more and 00:11:27.960 --> 00:11:29.990 align:start position:0% conventional proofs have become more and more<00:11:28.120> complicated<00:11:29.120> Mhm.<00:11:29.440> to<00:11:29.440> the<00:11:29.560> point<00:11:29.880> where 00:11:29.990 --> 00:11:30.000 align:start position:0% more complicated Mhm. to the point where 00:11:30.000 --> 00:11:32.030 align:start position:0% more complicated Mhm. to the point where there<00:11:30.120> is<00:11:30.280> genuine<00:11:30.760> worry<00:11:31.080> about<00:11:31.839> their 00:11:32.030 --> 00:11:32.040 align:start position:0% there is genuine worry about their 00:11:32.040 --> 00:11:34.190 align:start position:0% there is genuine worry about their correctness<00:11:32.720> and<00:11:33.120> uh<00:11:33.480> Right.<00:11:33.920> if<00:11:33.960> the<00:11:34.040> too 00:11:34.190 --> 00:11:34.200 align:start position:0% correctness and uh Right. if the too 00:11:34.200 --> 00:11:35.150 align:start position:0% correctness and uh Right. if the too many<00:11:34.400> proofs<00:11:34.640> come<00:11:34.880> out 00:11:35.150 --> 00:11:35.160 align:start position:0% many proofs come out 00:11:35.160 --> 00:11:37.790 align:start position:0% many proofs come out >> Fermat's<00:11:35.840> theorem<00:11:36.280> it<00:11:36.360> took<00:11:36.520> a<00:11:36.560> long<00:11:36.880> time<00:11:37.160> to 00:11:37.790 --> 00:11:37.800 align:start position:0% >> Fermat's theorem it took a long time to 00:11:37.800 --> 00:11:43.350 align:start position:0% >> Fermat's theorem it took a long time to show<00:11:38.680> that<00:11:38.880> it's<00:11:39.040> correct.<00:11:39.440> So<00:11:39.600> sorry. 00:11:43.350 --> 00:11:43.360 align:start position:0% 00:11:43.360 --> 00:11:46.430 align:start position:0% And<00:11:44.160> um 00:11:46.430 --> 00:11:46.440 align:start position:0% 00:11:46.440 --> 00:11:48.390 align:start position:0% on<00:11:46.560> the<00:11:46.640> other<00:11:46.800> side 00:11:48.390 --> 00:11:48.400 align:start position:0% on the other side 00:11:48.400 --> 00:11:50.310 align:start position:0% on the other side as<00:11:48.640> Lean<00:11:48.960> has<00:11:49.120> developed 00:11:50.310 --> 00:11:50.320 align:start position:0% as Lean has developed 00:11:50.320 --> 00:11:52.910 align:start position:0% as Lean has developed um<00:11:51.160> and<00:11:51.280> people<00:11:51.560> have<00:11:51.680> built<00:11:52.360> more<00:11:52.640> and<00:11:52.720> more 00:11:52.910 --> 00:11:52.920 align:start position:0% um and people have built more and more 00:11:52.920 --> 00:11:54.790 align:start position:0% um and people have built more and more tools<00:11:53.480> and<00:11:53.680> added<00:11:53.920> more<00:11:54.120> and<00:11:54.200> more<00:11:54.400> to<00:11:54.560> math 00:11:54.790 --> 00:11:54.800 align:start position:0% tools and added more and more to math 00:11:54.800 --> 00:11:55.710 align:start position:0% tools and added more and more to math Lean 00:11:55.710 --> 00:11:55.720 align:start position:0% Lean 00:11:55.720 --> 00:11:57.350 align:start position:0% Lean that<00:11:55.840> you<00:11:55.960> can<00:11:56.080> then<00:11:56.280> use 00:11:57.350 --> 00:11:57.360 align:start position:0% that you can then use 00:11:57.360 --> 00:12:00.950 align:start position:0% that you can then use um<00:11:58.360> barrier<00:11:58.880> to<00:11:59.160> entry<00:11:59.520> to<00:12:00.200> formalizing<00:12:00.840> has 00:12:00.950 --> 00:12:00.960 align:start position:0% um barrier to entry to formalizing has 00:12:00.960 --> 00:12:02.470 align:start position:0% um barrier to entry to formalizing has perhaps<00:12:01.200> gone<00:12:01.360> down<00:12:01.560> and<00:12:01.680> down<00:12:01.880> and<00:12:02.040> we<00:12:02.160> find 00:12:02.470 --> 00:12:02.480 align:start position:0% perhaps gone down and down and we find 00:12:02.480 --> 00:12:03.670 align:start position:0% perhaps gone down and down and we find that<00:12:03.080> uh 00:12:03.670 --> 00:12:03.680 align:start position:0% that uh 00:12:03.680 --> 00:12:05.990 align:start position:0% that uh undergraduates<00:12:04.360> can<00:12:04.520> formalize<00:12:05.080> deep 00:12:05.990 --> 00:12:06.000 align:start position:0% undergraduates can formalize deep 00:12:06.000 --> 00:12:07.710 align:start position:0% undergraduates can formalize deep bits<00:12:06.240> of<00:12:06.320> mathematics<00:12:07.120> Mhm.<00:12:07.560> which<00:12:07.640> they 00:12:07.710 --> 00:12:07.720 align:start position:0% bits of mathematics Mhm. which they 00:12:07.720 --> 00:12:08.870 align:start position:0% bits of mathematics Mhm. which they don't<00:12:07.920> even<00:12:08.080> necessarily<00:12:08.640> have<00:12:08.800> to 00:12:08.870 --> 00:12:08.880 align:start position:0% don't even necessarily have to 00:12:08.880 --> 00:12:10.390 align:start position:0% don't even necessarily have to understand<00:12:09.400> very<00:12:09.640> well<00:12:09.880> as<00:12:10.000> long<00:12:10.120> as<00:12:10.200> they<00:12:10.320> can 00:12:10.390 --> 00:12:10.400 align:start position:0% understand very well as long as they can 00:12:10.400 --> 00:12:12.110 align:start position:0% understand very well as long as they can just<00:12:10.760> cover<00:12:11.120> it<00:12:11.280> line<00:12:11.520> by<00:12:11.680> line. 00:12:12.110 --> 00:12:12.120 align:start position:0% just cover it line by line. 00:12:12.120 --> 00:12:15.310 align:start position:0% just cover it line by line. >> Right.<00:12:12.960> Um<00:12:13.920> so 00:12:15.310 --> 00:12:15.320 align:start position:0% >> Right. Um so 00:12:15.320 --> 00:12:17.550 align:start position:0% >> Right. Um so things<00:12:15.480> have<00:12:15.600> changed<00:12:15.920> a<00:12:15.960> lot<00:12:16.280> and<00:12:16.800> um 00:12:17.550 --> 00:12:17.560 align:start position:0% things have changed a lot and um 00:12:17.560 --> 00:12:19.030 align:start position:0% things have changed a lot and um there's<00:12:17.720> now<00:12:17.840> a<00:12:17.920> big<00:12:18.200> sort<00:12:18.320> of<00:12:18.440> thriving<00:12:18.880> Lean 00:12:19.030 --> 00:12:19.040 align:start position:0% there's now a big sort of thriving Lean 00:12:19.040 --> 00:12:20.870 align:start position:0% there's now a big sort of thriving Lean community.<00:12:19.840> So<00:12:19.960> I<00:12:20.040> think<00:12:20.200> I<00:12:20.280> could<00:12:20.440> call<00:12:20.680> that 00:12:20.870 --> 00:12:20.880 align:start position:0% community. So I think I could call that 00:12:20.880 --> 00:12:23.030 align:start position:0% community. So I think I could call that a 00:12:23.030 --> 00:12:23.040 align:start position:0% a 00:12:23.040 --> 00:12:24.870 align:start position:0% a maybe<00:12:23.200> not<00:12:23.360> a<00:12:23.440> breakthrough<00:12:24.160> exactly<00:12:24.680> because 00:12:24.870 --> 00:12:24.880 align:start position:0% maybe not a breakthrough exactly because 00:12:24.880 --> 00:12:26.790 align:start position:0% maybe not a breakthrough exactly because it<00:12:24.920> wasn't<00:12:25.160> really<00:12:25.320> a<00:12:25.360> conceptual<00:12:26.320> change. 00:12:26.790 --> 00:12:26.800 align:start position:0% it wasn't really a conceptual change. 00:12:26.800 --> 00:12:27.950 align:start position:0% it wasn't really a conceptual change. It's<00:12:26.920> just<00:12:27.120> more<00:12:27.240> like<00:12:27.360> a<00:12:27.440> sort<00:12:27.560> of<00:12:27.640> phase 00:12:27.950 --> 00:12:27.960 align:start position:0% It's just more like a sort of phase 00:12:27.960 --> 00:12:30.790 align:start position:0% It's just more like a sort of phase transition<00:12:29.000> that's<00:12:29.120> taken<00:12:29.480> place. 00:12:30.790 --> 00:12:30.800 align:start position:0% transition that's taken place. 00:12:30.800 --> 00:12:32.790 align:start position:0% transition that's taken place. And<00:12:31.600> um 00:12:32.790 --> 00:12:32.800 align:start position:0% And um 00:12:32.800 --> 00:12:34.710 align:start position:0% And um a<00:12:32.920> further<00:12:33.320> phase<00:12:33.600> transition<00:12:34.120> seems<00:12:34.520> to<00:12:34.640> be 00:12:34.710 --> 00:12:34.720 align:start position:0% a further phase transition seems to be 00:12:34.720 --> 00:12:37.070 align:start position:0% a further phase transition seems to be about<00:12:35.040> to<00:12:35.120> take<00:12:35.360> place<00:12:35.680> which<00:12:35.920> will<00:12:36.080> be 00:12:37.070 --> 00:12:37.080 align:start position:0% about to take place which will be 00:12:37.080 --> 00:12:39.070 align:start position:0% about to take place which will be that<00:12:37.280> auto<00:12:37.560> formalization<00:12:38.480> will<00:12:38.640> get 00:12:39.070 --> 00:12:39.080 align:start position:0% that auto formalization will get 00:12:39.080 --> 00:12:40.710 align:start position:0% that auto formalization will get sufficiently<00:12:39.600> good 00:12:40.710 --> 00:12:40.720 align:start position:0% sufficiently good 00:12:40.720 --> 00:12:41.990 align:start position:0% sufficiently good that<00:12:40.839> people<00:12:41.080> will<00:12:41.200> be<00:12:41.320> able<00:12:41.480> to<00:12:41.560> formalize 00:12:41.990 --> 00:12:42.000 align:start position:0% that people will be able to formalize 00:12:42.000 --> 00:12:43.510 align:start position:0% that people will be able to formalize without<00:12:42.280> even<00:12:42.520> bothering<00:12:42.880> to<00:12:43.000> learn<00:12:43.280> Lean. 00:12:43.510 --> 00:12:43.520 align:start position:0% without even bothering to learn Lean. 00:12:43.520 --> 00:12:45.430 align:start position:0% without even bothering to learn Lean. They<00:12:43.600> would<00:12:43.720> just<00:12:44.160> write<00:12:44.480> formalizations<00:12:45.280> and 00:12:45.430 --> 00:12:45.440 align:start position:0% They would just write formalizations and 00:12:45.440 --> 00:12:48.230 align:start position:0% They would just write formalizations and >> Right.<00:12:45.760> Write<00:12:45.920> formalizations. 00:12:48.230 --> 00:12:48.240 align:start position:0% >> Right. Write formalizations. 00:12:48.240 --> 00:12:50.230 align:start position:0% >> Right. Write formalizations. So<00:12:48.360> that<00:12:48.560> means<00:12:48.880> that<00:12:49.240> I<00:12:49.280> mean<00:12:49.560> one<00:12:49.800> immediate 00:12:50.230 --> 00:12:50.240 align:start position:0% So that means that I mean one immediate 00:12:50.240 --> 00:12:53.990 align:start position:0% So that means that I mean one immediate change<00:12:50.600> will<00:12:50.760> be<00:12:51.000> I<00:12:51.040> think<00:12:51.360> that<00:12:52.040> uh 00:12:53.990 --> 00:12:54.000 align:start position:0% change will be I think that uh 00:12:54.000 --> 00:12:56.030 align:start position:0% change will be I think that uh instead<00:12:54.320> of<00:12:54.440> journals<00:12:55.000> sending<00:12:55.360> articles<00:12:55.880> out 00:12:56.030 --> 00:12:56.040 align:start position:0% instead of journals sending articles out 00:12:56.040 --> 00:12:58.510 align:start position:0% instead of journals sending articles out to<00:12:56.160> referees<00:12:56.760> to<00:12:56.880> check<00:12:57.200> the<00:12:57.320> proofs<00:12:58.360> we'll 00:12:58.510 --> 00:12:58.520 align:start position:0% to referees to check the proofs we'll 00:12:58.520 --> 00:13:00.950 align:start position:0% to referees to check the proofs we'll just<00:12:58.720> get<00:12:58.880> computers<00:12:59.280> to<00:12:59.400> check<00:12:59.680> proofs 00:13:00.950 --> 00:13:00.960 align:start position:0% just get computers to check proofs 00:13:00.960 --> 00:13:02.550 align:start position:0% just get computers to check proofs and<00:13:01.040> so<00:13:01.120> then<00:13:01.360> the<00:13:01.480> only<00:13:01.720> remaining<00:13:02.240> job<00:13:02.440> of 00:13:02.550 --> 00:13:02.560 align:start position:0% and so then the only remaining job of 00:13:02.560 --> 00:13:04.310 align:start position:0% and so then the only remaining job of journals<00:13:02.960> will<00:13:03.080> be 00:13:04.310 --> 00:13:04.320 align:start position:0% journals will be 00:13:04.320 --> 00:13:05.590 align:start position:0% journals will be judging<00:13:04.640> whether<00:13:04.839> something's<00:13:05.200> interesting 00:13:05.590 --> 00:13:05.600 align:start position:0% judging whether something's interesting 00:13:05.600 --> 00:13:07.350 align:start position:0% judging whether something's interesting or<00:13:05.720> not.<00:13:06.120> Do<00:13:06.240> you<00:13:06.280> think<00:13:06.480> it<00:13:06.560> will<00:13:06.680> ever<00:13:06.880> happen 00:13:07.350 --> 00:13:07.360 align:start position:0% or not. Do you think it will ever happen 00:13:07.360 --> 00:13:09.350 align:start position:0% or not. Do you think it will ever happen that<00:13:07.520> you<00:13:07.600> don't<00:13:07.839> need<00:13:07.960> a<00:13:08.040> human<00:13:08.320> in<00:13:08.440> the<00:13:08.560> loop? 00:13:09.350 --> 00:13:09.360 align:start position:0% that you don't need a human in the loop? 00:13:09.360 --> 00:13:11.470 align:start position:0% that you don't need a human in the loop? That<00:13:09.520> this<00:13:09.720> vibe<00:13:10.000> proofing<00:13:10.480> will<00:13:10.640> actually<00:13:11.280> be 00:13:11.470 --> 00:13:11.480 align:start position:0% That this vibe proofing will actually be 00:13:11.480 --> 00:13:13.870 align:start position:0% That this vibe proofing will actually be good<00:13:11.640> enough? 00:13:13.870 --> 00:13:13.880 align:start position:0% good enough? 00:13:13.880 --> 00:13:15.590 align:start position:0% good enough? I<00:13:14.040> do<00:13:14.320> think<00:13:14.520> it<00:13:14.600> will<00:13:14.760> happen.<00:13:15.320> I<00:13:15.360> don't<00:13:15.520> know 00:13:15.590 --> 00:13:15.600 align:start position:0% I do think it will happen. I don't know 00:13:15.600 --> 00:13:16.829 align:start position:0% I do think it will happen. I don't know how<00:13:15.720> long<00:13:15.880> it'll<00:13:16.040> take<00:13:16.240> but<00:13:16.360> I<00:13:16.440> think<00:13:16.600> that 00:13:16.829 --> 00:13:16.839 align:start position:0% how long it'll take but I think that 00:13:16.839 --> 00:13:17.829 align:start position:0% how long it'll take but I think that that<00:13:17.080> is<00:13:17.200> the<00:13:17.360> end 00:13:17.829 --> 00:13:17.839 align:start position:0% that is the end 00:13:17.839 --> 00:13:21.070 align:start position:0% that is the end >> automatic<00:13:18.560> proof<00:13:19.280> Yeah<00:13:19.480> yeah.<00:13:19.920> that<00:13:20.360> you<00:13:20.560> will 00:13:21.070 --> 00:13:21.080 align:start position:0% >> automatic proof Yeah yeah. that you will 00:13:21.080 --> 00:13:22.950 align:start position:0% >> automatic proof Yeah yeah. that you will be<00:13:21.240> comfortable<00:13:22.440> with. 00:13:22.950 --> 00:13:22.960 align:start position:0% be comfortable with. 00:13:22.960 --> 00:13:24.230 align:start position:0% be comfortable with. >> Oh<00:13:23.040> that's<00:13:23.280> slightly<00:13:23.600> different<00:13:23.880> question 00:13:24.230 --> 00:13:24.240 align:start position:0% >> Oh that's slightly different question 00:13:24.240 --> 00:13:26.430 align:start position:0% >> Oh that's slightly different question whether<00:13:24.440> I'm<00:13:24.560> comfortable<00:13:25.000> with<00:13:25.020> [laughter] 00:13:26.430 --> 00:13:26.440 align:start position:0% whether I'm comfortable with [laughter] 00:13:26.440 --> 00:13:28.630 align:start position:0% whether I'm comfortable with [laughter] Will<00:13:26.760> you<00:13:26.839> ever<00:13:27.040> accept<00:13:27.880> something<00:13:28.400> that 00:13:28.630 --> 00:13:28.640 align:start position:0% Will you ever accept something that 00:13:28.640 --> 00:13:31.470 align:start position:0% Will you ever accept something that computer<00:13:29.000> said<00:13:29.720> is<00:13:29.880> correct<00:13:30.440> and<00:13:30.640> then 00:13:31.470 --> 00:13:31.480 align:start position:0% computer said is correct and then 00:13:31.480 --> 00:13:32.830 align:start position:0% computer said is correct and then Yeah,<00:13:31.880> because<00:13:32.120> you<00:13:32.240> you<00:13:32.400> like<00:13:32.600> you're<00:13:32.760> an 00:13:32.830 --> 00:13:32.840 align:start position:0% Yeah, because you you like you're an 00:13:32.840 --> 00:13:34.790 align:start position:0% Yeah, because you you like you're an editor<00:13:33.200> of<00:13:33.280> the<00:13:33.360> journal,<00:13:34.000> you<00:13:34.120> send<00:13:34.720> a 00:13:34.790 --> 00:13:34.800 align:start position:0% editor of the journal, you send a 00:13:34.800 --> 00:13:37.270 align:start position:0% editor of the journal, you send a submission<00:13:35.720> to<00:13:35.920> a<00:13:35.960> lean<00:13:36.200> verifier<00:13:36.960> and<00:13:37.160> it 00:13:37.270 --> 00:13:37.280 align:start position:0% submission to a lean verifier and it 00:13:37.280 --> 00:13:39.430 align:start position:0% submission to a lean verifier and it came<00:13:37.440> back<00:13:37.600> saying<00:13:37.920> this<00:13:38.120> is<00:13:38.240> correct.<00:13:39.240> Will 00:13:39.430 --> 00:13:39.440 align:start position:0% came back saying this is correct. Will 00:13:39.440 --> 00:13:42.590 align:start position:0% came back saying this is correct. Will you<00:13:39.520> be<00:13:39.680> now<00:13:40.000> comfortable<00:13:40.480> publishing<00:13:40.960> this? 00:13:42.590 --> 00:13:42.600 align:start position:0% you be now comfortable publishing this? 00:13:42.600 --> 00:13:43.950 align:start position:0% you be now comfortable publishing this? Uh<00:13:42.880> if<00:13:43.040> I<00:13:43.120> judge<00:13:43.320> it<00:13:43.400> to<00:13:43.480> be<00:13:43.600> interesting 00:13:43.950 --> 00:13:43.960 align:start position:0% Uh if I judge it to be interesting 00:13:43.960 --> 00:13:45.630 align:start position:0% Uh if I judge it to be interesting enough<00:13:44.320> then<00:13:44.920> I'd<00:13:45.040> be 00:13:45.630 --> 00:13:45.640 align:start position:0% enough then I'd be 00:13:45.640 --> 00:13:46.950 align:start position:0% enough then I'd be I<00:13:45.720> mean 00:13:46.950 --> 00:13:46.960 align:start position:0% I mean 00:13:46.960 --> 00:13:48.550 align:start position:0% I mean I'd<00:13:47.080> be<00:13:47.200> at<00:13:47.320> least<00:13:47.600> as<00:13:47.720> comfortable<00:13:48.240> in<00:13:48.320> fact 00:13:48.550 --> 00:13:48.560 align:start position:0% I'd be at least as comfortable in fact 00:13:48.560 --> 00:13:50.990 align:start position:0% I'd be at least as comfortable in fact probably<00:13:48.840> a<00:13:48.880> lot<00:13:49.080> more<00:13:49.280> comfortable 00:13:50.990 --> 00:13:51.000 align:start position:0% probably a lot more comfortable 00:13:51.000 --> 00:13:52.670 align:start position:0% probably a lot more comfortable judging<00:13:51.280> it<00:13:51.400> to<00:13:51.480> be<00:13:51.600> correct 00:13:52.670 --> 00:13:52.680 align:start position:0% judging it to be correct 00:13:52.680 --> 00:13:54.510 align:start position:0% judging it to be correct if<00:13:52.800> it<00:13:52.880> had<00:13:52.960> been<00:13:53.120> verified<00:13:53.560> in<00:13:53.720> lean.<00:13:54.080> Yes. 00:13:54.510 --> 00:13:54.520 align:start position:0% if it had been verified in lean. Yes. 00:13:54.520 --> 00:13:56.070 align:start position:0% if it had been verified in lean. Yes. Than<00:13:54.640> if<00:13:54.760> I<00:13:54.840> just<00:13:55.040> sent<00:13:55.240> it<00:13:55.360> out<00:13:55.480> to<00:13:55.560> a<00:13:55.600> referee 00:13:56.070 --> 00:13:56.080 align:start position:0% Than if I just sent it out to a referee 00:13:56.080 --> 00:13:57.270 align:start position:0% Than if I just sent it out to a referee who<00:13:56.200> probably<00:13:56.480> didn't<00:13:56.760> read<00:13:56.960> it<00:13:57.080> very 00:13:57.270 --> 00:13:57.280 align:start position:0% who probably didn't read it very 00:13:57.280 --> 00:13:57.590 align:start position:0% who probably didn't read it very carefully. 00:13:57.590 --> 00:13:57.600 align:start position:0% carefully. 00:13:57.600 --> 00:13:59.190 align:start position:0% carefully. >> Right,<00:13:57.680> that's<00:13:58.080> right.<00:13:58.280> I<00:13:58.320> mean<00:13:58.840> what<00:13:58.960> we<00:13:59.040> have 00:13:59.190 --> 00:13:59.200 align:start position:0% >> Right, that's right. I mean what we have 00:13:59.200 --> 00:14:00.790 align:start position:0% >> Right, that's right. I mean what we have the<00:13:59.280> system<00:13:59.600> and<00:13:59.960> one<00:14:00.080> has<00:14:00.280> to<00:14:00.360> remember<00:14:00.680> that 00:14:00.790 --> 00:14:00.800 align:start position:0% the system and one has to remember that 00:14:00.800 --> 00:14:02.950 align:start position:0% the system and one has to remember that the<00:14:00.880> system<00:14:01.160> we<00:14:01.280> have<00:14:01.480> now 00:14:02.950 --> 00:14:02.960 align:start position:0% the system we have now 00:14:02.960 --> 00:14:05.230 align:start position:0% the system we have now is<00:14:03.120> very<00:14:03.400> far<00:14:03.640> from<00:14:03.840> perfect.<00:14:04.480> Right,<00:14:05.000> right, 00:14:05.230 --> 00:14:05.240 align:start position:0% is very far from perfect. Right, right, 00:14:05.240 --> 00:14:07.070 align:start position:0% is very far from perfect. Right, right, right.<00:14:05.800> Unless<00:14:06.080> you<00:14:06.200> know<00:14:06.480> and<00:14:06.600> trust<00:14:06.960> the 00:14:07.070 --> 00:14:07.080 align:start position:0% right. Unless you know and trust the 00:14:07.080 --> 00:14:08.630 align:start position:0% right. Unless you know and trust the referee<00:14:07.720> to<00:14:07.800> do<00:14:07.920> a<00:14:08.000> good<00:14:08.120> job. 00:14:08.630 --> 00:14:08.640 align:start position:0% referee to do a good job. 00:14:08.640 --> 00:14:10.550 align:start position:0% referee to do a good job. >> a<00:14:08.720> lot<00:14:09.040> on<00:14:09.160> those<00:14:09.360> sort<00:14:09.520> of 00:14:10.550 --> 00:14:10.560 align:start position:0% >> a lot on those sort of 00:14:10.560 --> 00:14:13.230 align:start position:0% >> a lot on those sort of webs<00:14:10.960> of 00:14:13.230 --> 00:14:13.240 align:start position:0% webs of 00:14:13.240 --> 00:14:16.070 align:start position:0% webs of trust<00:14:13.680> and<00:14:14.520> acquaintance<00:14:15.120> with<00:14:15.240> people<00:14:15.800> and 00:14:16.070 --> 00:14:16.080 align:start position:0% trust and acquaintance with people and 00:14:16.080 --> 00:14:17.390 align:start position:0% trust and acquaintance with people and so<00:14:16.320> on.<00:14:16.520> So 00:14:17.390 --> 00:14:17.400 align:start position:0% so on. So 00:14:17.400 --> 00:14:19.350 align:start position:0% so on. So So<00:14:17.480> I'm<00:14:17.560> not<00:14:17.720> thinking<00:14:18.360> what<00:14:18.520> you<00:14:18.640> described 00:14:19.350 --> 00:14:19.360 align:start position:0% So I'm not thinking what you described 00:14:19.360 --> 00:14:20.990 align:start position:0% So I'm not thinking what you described is<00:14:19.520> very<00:14:19.760> interesting<00:14:20.160> because<00:14:20.760> and<00:14:20.920> you 00:14:20.990 --> 00:14:21.000 align:start position:0% is very interesting because and you 00:14:21.000 --> 00:14:23.350 align:start position:0% is very interesting because and you basically<00:14:21.440> mentioned<00:14:21.760> in<00:14:21.880> the<00:14:21.960> keynote<00:14:22.400> that 00:14:23.350 --> 00:14:23.360 align:start position:0% basically mentioned in the keynote that 00:14:23.360 --> 00:14:25.150 align:start position:0% basically mentioned in the keynote that the<00:14:23.520> models<00:14:23.880> in<00:14:24.000> the<00:14:24.080> recent<00:14:24.360> months<00:14:24.720> got<00:14:24.960> so 00:14:25.150 --> 00:14:25.160 align:start position:0% the models in the recent months got so 00:14:25.160 --> 00:14:27.990 align:start position:0% the models in the recent months got so good<00:14:25.800> that<00:14:26.320> the<00:14:26.960> best<00:14:27.200> models<00:14:27.480> operated<00:14:27.920> at 00:14:27.990 --> 00:14:28.000 align:start position:0% good that the best models operated at 00:14:28.000 --> 00:14:30.070 align:start position:0% good that the best models operated at the<00:14:28.120> level<00:14:28.440> of<00:14:28.520> graduate<00:14:28.840> students,<00:14:29.760> right? 00:14:30.070 --> 00:14:30.080 align:start position:0% the level of graduate students, right? 00:14:30.080 --> 00:14:31.910 align:start position:0% the level of graduate students, right? At<00:14:30.200> the<00:14:30.280> graduate<00:14:30.560> student<00:14:31.160> PhD<00:14:31.440> candidate. 00:14:31.910 --> 00:14:31.920 align:start position:0% At the graduate student PhD candidate. 00:14:31.920 --> 00:14:34.110 align:start position:0% At the graduate student PhD candidate. >> I<00:14:32.040> may<00:14:32.160> have<00:14:32.280> to<00:14:32.360> qualify<00:14:32.760> that<00:14:32.880> but<00:14:33.040> at<00:14:33.160> least 00:14:34.110 --> 00:14:34.120 align:start position:0% >> I may have to qualify that but at least 00:14:34.120 --> 00:14:35.430 align:start position:0% >> I may have to qualify that but at least uh 00:14:35.430 --> 00:14:35.440 align:start position:0% uh 00:14:35.440 --> 00:14:36.990 align:start position:0% uh some<00:14:35.680> of<00:14:35.800> the<00:14:35.920> time.<00:14:36.320> Some<00:14:36.520> of<00:14:36.600> the<00:14:36.720> some<00:14:36.920> of 00:14:36.990 --> 00:14:37.000 align:start position:0% some of the time. Some of the some of 00:14:37.000 --> 00:14:37.190 align:start position:0% some of the time. Some of the some of the<00:14:37.080> time. 00:14:37.190 --> 00:14:37.200 align:start position:0% the time. 00:14:37.200 --> 00:14:38.150 align:start position:0% the time. >> And<00:14:37.280> I<00:14:37.320> think<00:14:37.480> there<00:14:37.560> may<00:14:37.680> be<00:14:37.800> parts<00:14:38.080> of 00:14:38.150 --> 00:14:38.160 align:start position:0% >> And I think there may be parts of 00:14:38.160 --> 00:14:39.350 align:start position:0% >> And I think there may be parts of mathematics<00:14:38.640> where<00:14:38.720> they<00:14:38.839> haven't<00:14:39.120> reached 00:14:39.350 --> 00:14:39.360 align:start position:0% mathematics where they haven't reached 00:14:39.360 --> 00:14:41.470 align:start position:0% mathematics where they haven't reached that<00:14:39.520> level<00:14:39.880> but<00:14:40.240> Right. 00:14:41.470 --> 00:14:41.480 align:start position:0% that level but Right. 00:14:41.480 --> 00:14:42.350 align:start position:0% that level but Right. Um 00:14:42.350 --> 00:14:42.360 align:start position:0% Um 00:14:42.360 --> 00:14:43.910 align:start position:0% Um and<00:14:42.520> there<00:14:42.600> will<00:14:42.680> be<00:14:42.920> plenty<00:14:43.240> of<00:14:43.360> problems 00:14:43.910 --> 00:14:43.920 align:start position:0% and there will be plenty of problems 00:14:43.920 --> 00:14:47.150 align:start position:0% and there will be plenty of problems where<00:14:44.839> yeah,<00:14:45.280> but 00:14:47.150 --> 00:14:47.160 align:start position:0% where yeah, but 00:14:47.160 --> 00:14:48.710 align:start position:0% where yeah, but they<00:14:47.240> can<00:14:47.400> operate<00:14:47.760> at<00:14:47.839> that<00:14:48.000> level<00:14:48.480> if<00:14:48.640> you 00:14:48.710 --> 00:14:48.720 align:start position:0% they can operate at that level if you 00:14:48.720 --> 00:14:50.070 align:start position:0% they can operate at that level if you give<00:14:48.880> them<00:14:49.000> the<00:14:49.120> right 00:14:50.070 --> 00:14:50.080 align:start position:0% give them the right 00:14:50.080 --> 00:14:52.630 align:start position:0% give them the right questions<00:14:50.600> to<00:14:50.720> do<00:14:51.120> right<00:14:51.360> at<00:14:51.480> least.<00:14:52.040> And<00:14:52.360> and 00:14:52.630 --> 00:14:52.640 align:start position:0% questions to do right at least. And and 00:14:52.640 --> 00:14:55.150 align:start position:0% questions to do right at least. And and and<00:14:52.839> basically<00:14:53.200> you<00:14:53.280> said<00:14:53.640> that<00:14:54.360> um 00:14:55.150 --> 00:14:55.160 align:start position:0% and basically you said that um 00:14:55.160 --> 00:14:57.470 align:start position:0% and basically you said that um a<00:14:55.200> lot<00:14:55.480> of<00:14:55.800> so<00:14:55.960> you're<00:14:56.080> concerned<00:14:56.839> that<00:14:57.080> a<00:14:57.160> lot 00:14:57.470 --> 00:14:57.480 align:start position:0% a lot of so you're concerned that a lot 00:14:57.480 --> 00:15:00.630 align:start position:0% a lot of so you're concerned that a lot of<00:14:57.720> low-level<00:14:58.280> work<00:14:59.200> uh<00:14:59.480> will<00:15:00.120> you<00:15:00.240> know, 00:15:00.630 --> 00:15:00.640 align:start position:0% of low-level work uh will you know, 00:15:00.640 --> 00:15:03.350 align:start position:0% of low-level work uh will you know, students<00:15:01.040> will<00:15:01.160> now<00:15:01.760> delegate<00:15:02.280> to 00:15:03.350 --> 00:15:03.360 align:start position:0% students will now delegate to 00:15:03.360 --> 00:15:06.230 align:start position:0% students will now delegate to LLMs<00:15:04.480> instead<00:15:04.800> of<00:15:04.920> doing<00:15:05.120> this<00:15:05.280> manually, 00:15:06.230 --> 00:15:06.240 align:start position:0% LLMs instead of doing this manually, 00:15:06.240 --> 00:15:08.390 align:start position:0% LLMs instead of doing this manually, right?<00:15:06.760> Like<00:15:07.000> a<00:15:07.040> lot<00:15:07.200> of<00:15:07.320> steps<00:15:07.839> that<00:15:08.040> normally 00:15:08.390 --> 00:15:08.400 align:start position:0% right? Like a lot of steps that normally 00:15:08.400 --> 00:15:09.710 align:start position:0% right? Like a lot of steps that normally they<00:15:08.520> would<00:15:08.640> be<00:15:08.800> doing<00:15:09.000> manually,<00:15:09.480> they<00:15:09.600> would 00:15:09.710 --> 00:15:09.720 align:start position:0% they would be doing manually, they would 00:15:09.720 --> 00:15:11.110 align:start position:0% they would be doing manually, they would delegate<00:15:10.240> it 00:15:11.110 --> 00:15:11.120 align:start position:0% delegate it 00:15:11.120 --> 00:15:13.030 align:start position:0% delegate it and<00:15:11.440> and<00:15:11.920> um 00:15:13.030 --> 00:15:13.040 align:start position:0% and and um 00:15:13.040 --> 00:15:13.990 align:start position:0% and and um So 00:15:13.990 --> 00:15:14.000 align:start position:0% So 00:15:14.000 --> 00:15:15.790 align:start position:0% So you<00:15:14.240> you're<00:15:14.320> basically<00:15:14.680> worried<00:15:15.000> about<00:15:15.320> that. 00:15:15.790 --> 00:15:15.800 align:start position:0% you you're basically worried about that. 00:15:15.800 --> 00:15:17.510 align:start position:0% you you're basically worried about that. But<00:15:15.960> I'm<00:15:16.080> just<00:15:16.280> thinking<00:15:16.560> that<00:15:16.760> like<00:15:17.040> in<00:15:17.200> in<00:15:17.400> in 00:15:17.510 --> 00:15:17.520 align:start position:0% But I'm just thinking that like in in in 00:15:17.520 --> 00:15:20.470 align:start position:0% But I'm just thinking that like in in in coding<00:15:18.400> now<00:15:18.600> everybody<00:15:19.000> uses 00:15:20.470 --> 00:15:20.480 align:start position:0% coding now everybody uses 00:15:20.480 --> 00:15:22.510 align:start position:0% coding now everybody uses code<00:15:20.720> code<00:15:21.040> and<00:15:21.160> similar<00:15:21.400> tools<00:15:21.720> and<00:15:21.839> nobody 00:15:22.510 --> 00:15:22.520 align:start position:0% code code and similar tools and nobody 00:15:22.520 --> 00:15:24.030 align:start position:0% code code and similar tools and nobody There<00:15:22.720> was<00:15:22.880> a<00:15:22.920> period<00:15:23.160> of<00:15:23.280> time<00:15:23.560> in<00:15:23.680> ancient 00:15:24.030 --> 00:15:24.040 align:start position:0% There was a period of time in ancient 00:15:24.040 --> 00:15:26.230 align:start position:0% There was a period of time in ancient history<00:15:24.440> 6<00:15:24.640> months<00:15:24.840> ago<00:15:25.400> when<00:15:25.640> people 00:15:26.230 --> 00:15:26.240 align:start position:0% history 6 months ago when people 00:15:26.240 --> 00:15:28.270 align:start position:0% history 6 months ago when people questioned<00:15:26.600> that.<00:15:26.800> Now,<00:15:27.560> the<00:15:27.680> consensus<00:15:28.160> is 00:15:28.270 --> 00:15:28.280 align:start position:0% questioned that. Now, the consensus is 00:15:28.280 --> 00:15:30.830 align:start position:0% questioned that. Now, the consensus is that<00:15:28.480> the<00:15:28.560> best<00:15:28.760> developers<00:15:29.400> use<00:15:29.640> AI.<00:15:30.520> And<00:15:30.720> it 00:15:30.830 --> 00:15:30.840 align:start position:0% that the best developers use AI. And it 00:15:30.840 --> 00:15:32.430 align:start position:0% that the best developers use AI. And it just<00:15:31.120> makes<00:15:31.440> them<00:15:31.640> even<00:15:31.840> better.<00:15:32.040> The<00:15:32.120> rich 00:15:32.430 --> 00:15:32.440 align:start position:0% just makes them even better. The rich 00:15:32.440 --> 00:15:33.630 align:start position:0% just makes them even better. The rich gets<00:15:32.680> richer,<00:15:33.040> right?<00:15:33.280> Like<00:15:33.400> this<00:15:33.560> is 00:15:33.630 --> 00:15:33.640 align:start position:0% gets richer, right? Like this is 00:15:33.640 --> 00:15:35.630 align:start position:0% gets richer, right? Like this is Marxism.<00:15:34.400> So,<00:15:34.520> the<00:15:34.680> 10x<00:15:35.040> developers,<00:15:35.520> the 00:15:35.630 --> 00:15:35.640 align:start position:0% Marxism. So, the 10x developers, the 00:15:35.640 --> 00:15:37.150 align:start position:0% Marxism. So, the 10x developers, the magical<00:15:36.000> creatures<00:15:36.840> who<00:15:36.920> are<00:15:36.960> super 00:15:37.150 --> 00:15:37.160 align:start position:0% magical creatures who are super 00:15:37.160 --> 00:15:38.630 align:start position:0% magical creatures who are super productive,<00:15:37.560> become<00:15:37.840> even<00:15:38.040> more<00:15:38.200> productive, 00:15:38.630 --> 00:15:38.640 align:start position:0% productive, become even more productive, 00:15:38.640 --> 00:15:40.910 align:start position:0% productive, become even more productive, and<00:15:38.760> juniors<00:15:39.480> are<00:15:39.520> get<00:15:40.080> getting<00:15:40.320> eliminated 00:15:40.910 --> 00:15:40.920 align:start position:0% and juniors are get getting eliminated 00:15:40.920 --> 00:15:42.750 align:start position:0% and juniors are get getting eliminated because<00:15:41.200> they<00:15:41.280> cannot<00:15:41.560> compete<00:15:42.280> with<00:15:42.520> even<00:15:42.720> a 00:15:42.750 --> 00:15:42.760 align:start position:0% because they cannot compete with even a 00:15:42.760 --> 00:15:45.150 align:start position:0% because they cannot compete with even a basic<00:15:43.080> LM.<00:15:43.680> So,<00:15:44.360> uh,<00:15:44.480> so<00:15:44.600> the<00:15:44.720> question<00:15:45.040> is 00:15:45.150 --> 00:15:45.160 align:start position:0% basic LM. So, uh, so the question is 00:15:45.160 --> 00:15:48.110 align:start position:0% basic LM. So, uh, so the question is now,<00:15:45.680> I<00:15:45.760> wonder<00:15:46.440> if<00:15:46.720> if<00:15:47.040> Lean<00:15:47.400> now<00:15:47.640> becomes 00:15:48.110 --> 00:15:48.120 align:start position:0% now, I wonder if if Lean now becomes 00:15:48.120 --> 00:15:51.230 align:start position:0% now, I wonder if if Lean now becomes approachable<00:15:49.120> because<00:15:49.640> machines<00:15:50.200> can<00:15:51.000> do<00:15:51.200> a 00:15:51.230 --> 00:15:51.240 align:start position:0% approachable because machines can do a 00:15:51.240 --> 00:15:53.510 align:start position:0% approachable because machines can do a lot,<00:15:51.960> right?<00:15:52.360> Like<00:15:52.560> it<00:15:52.680> was<00:15:52.840> impractical<00:15:53.400> for 00:15:53.510 --> 00:15:53.520 align:start position:0% lot, right? Like it was impractical for 00:15:53.520 --> 00:15:55.310 align:start position:0% lot, right? Like it was impractical for people<00:15:53.760> to<00:15:53.840> do<00:15:53.920> a<00:15:53.960> lot<00:15:54.160> of<00:15:54.400> formalization. 00:15:55.310 --> 00:15:55.320 align:start position:0% people to do a lot of formalization. 00:15:55.320 --> 00:15:57.790 align:start position:0% people to do a lot of formalization. Now,<00:15:55.920> this<00:15:56.040> will<00:15:56.120> be<00:15:56.240> by<00:15:56.440> formalization.<00:15:57.560> Will 00:15:57.790 --> 00:15:57.800 align:start position:0% Now, this will be by formalization. Will 00:15:57.800 --> 00:15:59.030 align:start position:0% Now, this will be by formalization. Will it<00:15:57.920> now<00:15:58.080> become<00:15:58.360> a<00:15:58.400> tool<00:15:58.680> in<00:15:58.760> a<00:15:58.800> similar 00:15:59.030 --> 00:15:59.040 align:start position:0% it now become a tool in a similar 00:15:59.040 --> 00:16:00.190 align:start position:0% it now become a tool in a similar fashion<00:15:59.360> for<00:15:59.440> mathematicians,<00:16:00.080> for 00:16:00.190 --> 00:16:00.200 align:start position:0% fashion for mathematicians, for 00:16:00.200 --> 00:16:02.030 align:start position:0% fashion for mathematicians, for students?<00:16:00.960> So,<00:16:01.240> you<00:16:01.360> will<00:16:01.520> always<00:16:01.800> work 00:16:02.030 --> 00:16:02.040 align:start position:0% students? So, you will always work 00:16:02.040 --> 00:16:03.950 align:start position:0% students? So, you will always work alongside<00:16:02.480> Lean<00:16:03.200> or<00:16:03.280> something<00:16:03.560> like<00:16:03.720> this, 00:16:03.950 --> 00:16:03.960 align:start position:0% alongside Lean or something like this, 00:16:03.960 --> 00:16:05.910 align:start position:0% alongside Lean or something like this, right?<00:16:04.480> So,<00:16:04.680> so<00:16:04.880> it<00:16:05.000> will<00:16:05.120> not<00:16:05.320> compete<00:16:05.800> it 00:16:05.910 --> 00:16:05.920 align:start position:0% right? So, so it will not compete it 00:16:05.920 --> 00:16:07.750 align:start position:0% right? So, so it will not compete it will<00:16:06.000> be<00:16:06.080> like<00:16:06.280> a<00:16:06.560> coding<00:16:06.960> tool.<00:16:07.160> It<00:16:07.320> will<00:16:07.440> help 00:16:07.750 --> 00:16:07.760 align:start position:0% will be like a coding tool. It will help 00:16:07.760 --> 00:16:09.510 align:start position:0% will be like a coding tool. It will help you,<00:16:08.360> but<00:16:08.520> human<00:16:08.800> is<00:16:08.920> still<00:16:09.120> in<00:16:09.200> charge 00:16:09.510 --> 00:16:09.520 align:start position:0% you, but human is still in charge 00:16:09.520 --> 00:16:11.230 align:start position:0% you, but human is still in charge because<00:16:09.800> a<00:16:09.840> smart<00:16:10.320> our<00:16:10.480> computer<00:16:10.840> architect 00:16:11.230 --> 00:16:11.240 align:start position:0% because a smart our computer architect 00:16:11.240 --> 00:16:13.630 align:start position:0% because a smart our computer architect developer,<00:16:12.000> he<00:16:12.120> knows<00:16:12.440> what<00:16:12.560> to<00:16:12.680> ask,<00:16:13.520> and 00:16:13.630 --> 00:16:13.640 align:start position:0% developer, he knows what to ask, and 00:16:13.640 --> 00:16:15.350 align:start position:0% developer, he knows what to ask, and that<00:16:13.840> really<00:16:14.200> makes<00:16:14.480> a<00:16:14.520> difference.<00:16:15.280> And 00:16:15.350 --> 00:16:15.360 align:start position:0% that really makes a difference. And 00:16:15.360 --> 00:16:16.750 align:start position:0% that really makes a difference. And like,<00:16:15.600> is<00:16:15.760> this 00:16:16.750 --> 00:16:16.760 align:start position:0% like, is this 00:16:16.760 --> 00:16:18.550 align:start position:0% like, is this can<00:16:16.880> this<00:16:17.080> be<00:16:17.240> the<00:16:17.400> course<00:16:17.760> of<00:16:17.960> mathematics 00:16:18.550 --> 00:16:18.560 align:start position:0% can this be the course of mathematics 00:16:18.560 --> 00:16:20.590 align:start position:0% can this be the course of mathematics education?<00:16:19.440> So,<00:16:19.560> now<00:16:19.800> you<00:16:19.920> will<00:16:20.040> teach<00:16:20.360> with 00:16:20.590 --> 00:16:20.600 align:start position:0% education? So, now you will teach with 00:16:20.600 --> 00:16:23.790 align:start position:0% education? So, now you will teach with Lean<00:16:20.920> from<00:16:21.800> see,<00:16:22.200> you<00:16:22.280> know,<00:16:22.400> math<00:16:22.640> 101. 00:16:23.790 --> 00:16:23.800 align:start position:0% Lean from see, you know, math 101. 00:16:23.800 --> 00:16:25.150 align:start position:0% Lean from see, you know, math 101. Do<00:16:24.000> you<00:16:24.080> think<00:16:24.280> that's<00:16:24.800> that's<00:16:25.000> going<00:16:25.120> to 00:16:25.150 --> 00:16:25.160 align:start position:0% Do you think that's that's going to 00:16:25.160 --> 00:16:26.030 align:start position:0% Do you think that's that's going to happen? 00:16:26.030 --> 00:16:26.040 align:start position:0% happen? 00:16:26.040 --> 00:16:27.310 align:start position:0% happen? I<00:16:26.120> don't<00:16:26.400> know<00:16:26.560> whether<00:16:26.800> we'll<00:16:26.920> teach<00:16:27.160> with 00:16:27.310 --> 00:16:27.320 align:start position:0% I don't know whether we'll teach with 00:16:27.320 --> 00:16:28.590 align:start position:0% I don't know whether we'll teach with Lean<00:16:27.480> because<00:16:27.751> [clears throat]<00:16:27.760> I'm 00:16:28.590 --> 00:16:28.600 align:start position:0% Lean because [clears throat] I'm 00:16:28.600 --> 00:16:31.550 align:start position:0% Lean because [clears throat] I'm learning<00:16:29.200> Lean 00:16:31.550 --> 00:16:31.560 align:start position:0% learning Lean 00:16:31.560 --> 00:16:33.550 align:start position:0% learning Lean presents<00:16:31.960> an<00:16:32.040> extra<00:16:32.360> barrier<00:16:32.880> somehow.<00:16:33.400> And 00:16:33.550 --> 00:16:33.560 align:start position:0% presents an extra barrier somehow. And 00:16:33.560 --> 00:16:35.470 align:start position:0% presents an extra barrier somehow. And the<00:16:33.920> the<00:16:34.040> way<00:16:34.320> that<00:16:34.960> you<00:16:35.080> have<00:16:35.240> to<00:16:35.360> do 00:16:35.470 --> 00:16:35.480 align:start position:0% the the way that you have to do 00:16:35.480 --> 00:16:37.550 align:start position:0% the the way that you have to do mathematics<00:16:36.040> if<00:16:36.120> you<00:16:36.200> want<00:16:36.360> to<00:16:36.400> do<00:16:36.520> Lean 00:16:37.550 --> 00:16:37.560 align:start position:0% mathematics if you want to do Lean 00:16:37.560 --> 00:16:39.430 align:start position:0% mathematics if you want to do Lean is<00:16:37.640> a<00:16:37.680> little<00:16:37.880> bit<00:16:38.600> different<00:16:39.040> from<00:16:39.200> the<00:16:39.280> way 00:16:39.430 --> 00:16:39.440 align:start position:0% is a little bit different from the way 00:16:39.440 --> 00:16:40.829 align:start position:0% is a little bit different from the way you<00:16:39.520> do<00:16:39.680> normal<00:16:39.920> mathematics.<00:16:40.320> A<00:16:40.360> little<00:16:40.640> bit 00:16:40.829 --> 00:16:40.839 align:start position:0% you do normal mathematics. A little bit 00:16:40.839 --> 00:16:44.150 align:start position:0% you do normal mathematics. A little bit less<00:16:41.240> intuitive<00:16:42.080> in<00:16:42.480> various<00:16:42.839> ways.<00:16:43.360> Okay. 00:16:44.150 --> 00:16:44.160 align:start position:0% less intuitive in various ways. Okay. 00:16:44.160 --> 00:16:45.990 align:start position:0% less intuitive in various ways. Okay. Um,<00:16:44.680> or<00:16:44.800> at<00:16:44.880> least<00:16:45.000> that's<00:16:45.160> how<00:16:45.280> it<00:16:45.400> seems 00:16:45.990 --> 00:16:46.000 align:start position:0% Um, or at least that's how it seems 00:16:46.000 --> 00:16:47.750 align:start position:0% Um, or at least that's how it seems because<00:16:46.280> I've<00:16:46.880> grown<00:16:47.160> up<00:16:47.320> the<00:16:47.400> other<00:16:47.560> way 00:16:47.750 --> 00:16:47.760 align:start position:0% because I've grown up the other way 00:16:47.760 --> 00:16:48.390 align:start position:0% because I've grown up the other way maybe.<00:16:48.040> Maybe 00:16:48.390 --> 00:16:48.400 align:start position:0% maybe. Maybe 00:16:48.400 --> 00:16:49.790 align:start position:0% maybe. Maybe >> Maybe<00:16:48.520> it<00:16:48.600> will<00:16:48.720> be<00:16:48.839> some<00:16:49.320> something<00:16:49.600> better 00:16:49.790 --> 00:16:49.800 align:start position:0% >> Maybe it will be some something better 00:16:49.800 --> 00:16:51.550 align:start position:0% >> Maybe it will be some something better than<00:16:49.960> Lean.<00:16:50.440> But<00:16:50.960> something<00:16:51.320> maybe<00:16:51.520> a 00:16:51.550 --> 00:16:51.560 align:start position:0% than Lean. But something maybe a 00:16:51.560 --> 00:16:53.590 align:start position:0% than Lean. But something maybe a platform<00:16:52.000> that<00:16:52.120> has<00:16:52.280> Lean<00:16:52.560> running<00:16:53.400> in<00:16:53.520> the 00:16:53.590 --> 00:16:53.600 align:start position:0% platform that has Lean running in the 00:16:53.600 --> 00:16:54.310 align:start position:0% platform that has Lean running in the background 00:16:54.310 --> 00:16:54.320 align:start position:0% background 00:16:54.320 --> 00:16:55.950 align:start position:0% background >> Mhm.<00:16:54.600> that 00:16:55.950 --> 00:16:55.960 align:start position:0% >> Mhm. that 00:16:55.960 --> 00:16:57.870 align:start position:0% >> Mhm. that is<00:16:56.080> a<00:16:56.120> bit<00:16:56.320> more<00:16:56.560> sort<00:16:56.800> of<00:16:57.320> um, 00:16:57.870 --> 00:16:57.880 align:start position:0% is a bit more sort of um, 00:16:57.880 --> 00:16:59.750 align:start position:0% is a bit more sort of um, user-friendly<00:16:58.640> than<00:16:58.839> Lean.<00:16:59.200> Maybe<00:16:59.440> Lean<00:16:59.640> is 00:16:59.750 --> 00:16:59.760 align:start position:0% user-friendly than Lean. Maybe Lean is 00:16:59.760 --> 00:17:01.790 align:start position:0% user-friendly than Lean. Maybe Lean is integrated<00:17:00.240> into<00:17:00.480> LaTeX<00:17:00.960> and<00:17:01.200> as<00:17:01.320> you<00:17:01.480> write<00:17:01.720> a 00:17:01.790 --> 00:17:01.800 align:start position:0% integrated into LaTeX and as you write a 00:17:01.800 --> 00:17:04.030 align:start position:0% integrated into LaTeX and as you write a paper,<00:17:02.680> like<00:17:02.920> it<00:17:03.000> gets<00:17:03.240> verified.<00:17:03.960> Yeah, 00:17:04.030 --> 00:17:04.040 align:start position:0% paper, like it gets verified. Yeah, 00:17:04.040 --> 00:17:05.550 align:start position:0% paper, like it gets verified. Yeah, exactly.<00:17:04.680> I<00:17:04.720> think<00:17:04.920> if<00:17:05.040> you've<00:17:05.160> got<00:17:05.360> some 00:17:05.550 --> 00:17:05.560 align:start position:0% exactly. I think if you've got some 00:17:05.560 --> 00:17:07.030 align:start position:0% exactly. I think if you've got some interface<00:17:06.120> sort<00:17:06.319> of<00:17:06.439> a<00:17:06.520> higher<00:17:06.800> level 00:17:07.030 --> 00:17:07.040 align:start position:0% interface sort of a higher level 00:17:07.040 --> 00:17:09.550 align:start position:0% interface sort of a higher level language<00:17:07.480> that<00:17:07.640> you're<00:17:07.880> using<00:17:08.199> yourself<00:17:08.920> Mhm. 00:17:09.550 --> 00:17:09.560 align:start position:0% language that you're using yourself Mhm. 00:17:09.560 --> 00:17:11.270 align:start position:0% language that you're using yourself Mhm. but<00:17:09.760> Lean<00:17:10.040> is<00:17:10.560> um, 00:17:11.270 --> 00:17:11.280 align:start position:0% but Lean is um, 00:17:11.280 --> 00:17:13.350 align:start position:0% but Lean is um, verifying<00:17:11.760> what<00:17:11.920> you<00:17:12.000> write<00:17:12.280> as<00:17:12.439> you<00:17:12.560> write. 00:17:13.350 --> 00:17:13.360 align:start position:0% verifying what you write as you write. 00:17:13.360 --> 00:17:15.550 align:start position:0% verifying what you write as you write. Or<00:17:13.480> Lean<00:17:13.839> combined<00:17:14.319> with<00:17:15.079> uh,<00:17:15.160> automatic 00:17:15.550 --> 00:17:15.560 align:start position:0% Or Lean combined with uh, automatic 00:17:15.560 --> 00:17:17.829 align:start position:0% Or Lean combined with uh, automatic theorem<00:17:15.800> proving<00:17:16.120> tools.<00:17:16.720> Mhm.<00:17:17.439> That<00:17:17.640> could 00:17:17.829 --> 00:17:17.839 align:start position:0% theorem proving tools. Mhm. That could 00:17:17.839 --> 00:17:19.429 align:start position:0% theorem proving tools. Mhm. That could be 00:17:19.429 --> 00:17:19.439 align:start position:0% be 00:17:19.439 --> 00:17:21.110 align:start position:0% be Yeah,<00:17:19.600> I<00:17:20.120> I<00:17:20.240> think<00:17:20.439> we<00:17:20.560> will<00:17:20.720> get<00:17:20.880> to<00:17:20.920> that 00:17:21.110 --> 00:17:21.120 align:start position:0% Yeah, I I think we will get to that 00:17:21.120 --> 00:17:23.429 align:start position:0% Yeah, I I think we will get to that stage.<00:17:21.800> But<00:17:21.920> then<00:17:22.040> there's<00:17:22.160> a<00:17:22.199> sort<00:17:22.439> of<00:17:22.560> race 00:17:23.429 --> 00:17:23.439 align:start position:0% stage. But then there's a sort of race 00:17:23.439 --> 00:17:25.990 align:start position:0% stage. But then there's a sort of race between 00:17:25.990 --> 00:17:26.000 align:start position:0% between 00:17:26.000 --> 00:17:27.829 align:start position:0% between people<00:17:26.199> developing<00:17:26.680> a<00:17:26.720> platform<00:17:27.199> like<00:17:27.360> that 00:17:27.829 --> 00:17:27.839 align:start position:0% people developing a platform like that 00:17:27.839 --> 00:17:29.550 align:start position:0% people developing a platform like that and<00:17:27.959> just<00:17:28.280> AI<00:17:28.600> getting<00:17:28.880> better<00:17:29.120> and<00:17:29.200> better<00:17:29.440> at 00:17:29.550 --> 00:17:29.560 align:start position:0% and just AI getting better and better at 00:17:29.560 --> 00:17:32.270 align:start position:0% and just AI getting better and better at maths.<00:17:30.200> Right.<00:17:30.880> On<00:17:31.000> its<00:17:31.160> own. 00:17:32.270 --> 00:17:32.280 align:start position:0% maths. Right. On its own. 00:17:32.280 --> 00:17:34.950 align:start position:0% maths. Right. On its own. Um<00:17:33.080> so<00:17:33.600> I<00:17:33.680> mean<00:17:34.200> a<00:17:34.240> future<00:17:34.600> that<00:17:34.720> it<00:17:34.760> would<00:17:34.880> be 00:17:34.950 --> 00:17:34.960 align:start position:0% Um so I mean a future that it would be 00:17:34.960 --> 00:17:38.350 align:start position:0% Um so I mean a future that it would be very<00:17:35.280> I<00:17:35.320> think<00:17:35.520> very<00:17:35.800> nice<00:17:36.240> would<00:17:36.440> be<00:17:36.680> if<00:17:37.160> um 00:17:38.350 --> 00:17:38.360 align:start position:0% very I think very nice would be if um 00:17:38.360 --> 00:17:39.830 align:start position:0% very I think very nice would be if um we<00:17:38.440> had<00:17:38.640> platforms<00:17:39.200> that<00:17:39.320> made<00:17:39.520> it<00:17:39.600> really 00:17:39.830 --> 00:17:39.840 align:start position:0% we had platforms that made it really 00:17:39.840 --> 00:17:41.470 align:start position:0% we had platforms that made it really easy<00:17:40.080> to<00:17:40.200> do<00:17:40.360> mathematics<00:17:41.000> and<00:17:41.200> have<00:17:41.360> it 00:17:41.470 --> 00:17:41.480 align:start position:0% easy to do mathematics and have it 00:17:41.480 --> 00:17:44.390 align:start position:0% easy to do mathematics and have it formalized<00:17:42.040> as<00:17:42.160> you<00:17:42.280> do<00:17:42.480> it<00:17:42.800> and<00:17:43.480> uh 00:17:44.390 --> 00:17:44.400 align:start position:0% formalized as you do it and uh 00:17:44.400 --> 00:17:45.990 align:start position:0% formalized as you do it and uh um 00:17:45.990 --> 00:17:46.000 align:start position:0% um 00:17:46.000 --> 00:17:47.430 align:start position:0% um in<00:17:46.120> other<00:17:46.240> words,<00:17:46.440> sort<00:17:46.560> of<00:17:46.680> tools<00:17:47.080> that<00:17:47.240> just 00:17:47.430 --> 00:17:47.440 align:start position:0% in other words, sort of tools that just 00:17:47.440 --> 00:17:49.710 align:start position:0% in other words, sort of tools that just help<00:17:47.680> you<00:17:47.800> think<00:17:48.120> at<00:17:48.200> your<00:17:48.360> screen. 00:17:49.710 --> 00:17:49.720 align:start position:0% help you think at your screen. 00:17:49.720 --> 00:17:50.750 align:start position:0% help you think at your screen. Um 00:17:50.750 --> 00:17:50.760 align:start position:0% Um 00:17:50.760 --> 00:17:51.670 align:start position:0% Um and<00:17:50.920> I<00:17:51.040> I<00:17:51.120> know<00:17:51.200> a<00:17:51.240> lot<00:17:51.360> of<00:17:51.440> people<00:17:51.600> are 00:17:51.670 --> 00:17:51.680 align:start position:0% and I I know a lot of people are 00:17:51.680 --> 00:17:53.790 align:start position:0% and I I know a lot of people are interested<00:17:52.080> in<00:17:52.520> um<00:17:52.920> developing<00:17:53.400> such<00:17:53.600> tools, 00:17:53.790 --> 00:17:53.800 align:start position:0% interested in um developing such tools, 00:17:53.800 --> 00:17:55.030 align:start position:0% interested in um developing such tools, including<00:17:54.240> my<00:17:54.360> group<00:17:54.600> in<00:17:54.680> Cambridge, 00:17:55.030 --> 00:17:55.040 align:start position:0% including my group in Cambridge, 00:17:55.040 --> 00:17:56.190 align:start position:0% including my group in Cambridge, actually. 00:17:56.190 --> 00:17:56.200 align:start position:0% actually. 00:17:56.200 --> 00:17:57.750 align:start position:0% actually. Um 00:17:57.750 --> 00:17:57.760 align:start position:0% Um 00:17:57.760 --> 00:17:59.670 align:start position:0% Um but<00:17:58.680> uh 00:17:59.670 --> 00:17:59.680 align:start position:0% but uh 00:17:59.680 --> 00:18:00.910 align:start position:0% but uh if<00:17:59.760> you<00:17:59.840> have<00:17:59.960> a<00:18:00.040> really<00:18:00.240> good<00:18:00.400> platform<00:18:00.760> like 00:18:00.910 --> 00:18:00.920 align:start position:0% if you have a really good platform like 00:18:00.920 --> 00:18:03.790 align:start position:0% if you have a really good platform like that,<00:18:01.080> then<00:18:01.880> you<00:18:02.000> can<00:18:02.160> also<00:18:02.400> train<00:18:03.440> an<00:18:03.560> AI 00:18:03.790 --> 00:18:03.800 align:start position:0% that, then you can also train an AI 00:18:03.800 --> 00:18:07.270 align:start position:0% that, then you can also train an AI system<00:18:04.200> to<00:18:04.320> use<00:18:04.520> the<00:18:04.600> platform,<00:18:05.200> so<00:18:05.520> Right.<00:18:06.240> Uh 00:18:07.270 --> 00:18:07.280 align:start position:0% system to use the platform, so Right. Uh 00:18:07.280 --> 00:18:08.830 align:start position:0% system to use the platform, so Right. Uh So<00:18:07.400> that<00:18:07.560> will<00:18:07.680> be<00:18:07.840> our<00:18:08.040> ask<00:18:08.200> for<00:18:08.320> developers. 00:18:08.830 --> 00:18:08.840 align:start position:0% So that will be our ask for developers. 00:18:08.840 --> 00:18:10.190 align:start position:0% So that will be our ask for developers. If<00:18:08.920> you<00:18:09.000> want<00:18:09.160> to<00:18:09.240> build<00:18:09.480> such<00:18:09.680> a<00:18:09.720> platform,<00:18:10.080> it 00:18:10.190 --> 00:18:10.200 align:start position:0% If you want to build such a platform, it 00:18:10.200 --> 00:18:12.030 align:start position:0% If you want to build such a platform, it will<00:18:10.360> have<00:18:10.560> an<00:18:10.640> impact.<00:18:11.360> So<00:18:11.480> maybe,<00:18:11.800> you<00:18:11.880> know, 00:18:12.030 --> 00:18:12.040 align:start position:0% will have an impact. So maybe, you know, 00:18:12.040 --> 00:18:13.390 align:start position:0% will have an impact. So maybe, you know, I'll<00:18:12.240> close<00:18:12.640> with<00:18:12.800> the<00:18:12.880> kind<00:18:13.040> of<00:18:13.120> general 00:18:13.390 --> 00:18:13.400 align:start position:0% I'll close with the kind of general 00:18:13.400 --> 00:18:14.590 align:start position:0% I'll close with the kind of general question<00:18:13.720> because,<00:18:13.920> you<00:18:14.000> know,<00:18:14.120> I<00:18:14.200> come<00:18:14.400> from 00:18:14.590 --> 00:18:14.600 align:start position:0% question because, you know, I come from 00:18:14.600 --> 00:18:16.270 align:start position:0% question because, you know, I come from Soviet<00:18:14.960> Union,<00:18:15.280> which<00:18:15.440> had<00:18:15.560> very<00:18:15.760> strong<00:18:16.040> math 00:18:16.270 --> 00:18:16.280 align:start position:0% Soviet Union, which had very strong math 00:18:16.280 --> 00:18:18.310 align:start position:0% Soviet Union, which had very strong math and<00:18:16.400> physics,<00:18:17.160> and<00:18:17.480> a<00:18:17.560> lot<00:18:17.800> of<00:18:17.880> people<00:18:18.120> here 00:18:18.310 --> 00:18:18.320 align:start position:0% and physics, and a lot of people here 00:18:18.320 --> 00:18:20.630 align:start position:0% and physics, and a lot of people here come<00:18:18.440> from<00:18:18.600> China<00:18:19.000> or<00:18:19.120> India<00:18:19.720> or<00:18:19.800> France, 00:18:20.630 --> 00:18:20.640 align:start position:0% come from China or India or France, 00:18:20.640 --> 00:18:22.310 align:start position:0% come from China or India or France, where<00:18:20.760> they<00:18:20.840> have<00:18:21.000> very<00:18:21.240> strong<00:18:22.080> STEM 00:18:22.310 --> 00:18:22.320 align:start position:0% where they have very strong STEM 00:18:22.320 --> 00:18:24.430 align:start position:0% where they have very strong STEM education,<00:18:23.200> right?<00:18:23.480> And<00:18:23.600> so<00:18:23.800> I<00:18:23.880> think<00:18:24.160> that's 00:18:24.430 --> 00:18:24.440 align:start position:0% education, right? And so I think that's 00:18:24.440 --> 00:18:26.510 align:start position:0% education, right? And so I think that's why<00:18:25.160> uh<00:18:25.280> you<00:18:25.360> know,<00:18:25.440> for<00:18:25.600> instance,<00:18:25.920> like,<00:18:26.480> you 00:18:26.510 --> 00:18:26.520 align:start position:0% why uh you know, for instance, like, you 00:18:26.520 --> 00:18:27.550 align:start position:0% why uh you know, for instance, like, you know,<00:18:26.680> there<00:18:26.800> is<00:18:26.920> a<00:18:26.960> question,<00:18:27.400> you<00:18:27.440> know, 00:18:27.550 --> 00:18:27.560 align:start position:0% know, there is a question, you know, 00:18:27.560 --> 00:18:29.150 align:start position:0% know, there is a question, you know, women<00:18:27.880> in<00:18:28.000> tech,<00:18:28.280> women<00:18:28.600> in<00:18:28.720> science.<00:18:29.080> In 00:18:29.150 --> 00:18:29.160 align:start position:0% women in tech, women in science. In 00:18:29.160 --> 00:18:30.950 align:start position:0% women in tech, women in science. In America,<00:18:29.520> it's<00:18:29.640> very,<00:18:30.360> you<00:18:30.440> know,<00:18:30.640> much 00:18:30.950 --> 00:18:30.960 align:start position:0% America, it's very, you know, much 00:18:30.960 --> 00:18:35.870 align:start position:0% America, it's very, you know, much dramatized,<00:18:31.720> but<00:18:32.360> in<00:18:32.960> India,<00:18:33.960> Russia,<00:18:34.760> China, 00:18:35.870 --> 00:18:35.880 align:start position:0% dramatized, but in India, Russia, China, 00:18:35.880 --> 00:18:38.190 align:start position:0% dramatized, but in India, Russia, China, France,<00:18:36.600> there<00:18:36.760> is<00:18:36.880> more<00:18:37.000> balance<00:18:37.760> women<00:18:38.080> in 00:18:38.190 --> 00:18:38.200 align:start position:0% France, there is more balance women in 00:18:38.200 --> 00:18:40.750 align:start position:0% France, there is more balance women in tech<00:18:38.400> because<00:18:39.080> everybody<00:18:39.480> gets<00:18:40.440> strong 00:18:40.750 --> 00:18:40.760 align:start position:0% tech because everybody gets strong 00:18:40.760 --> 00:18:42.710 align:start position:0% tech because everybody gets strong education.<00:18:41.680> There<00:18:41.840> is<00:18:41.960> no<00:18:42.120> question,<00:18:42.640> you 00:18:42.710 --> 00:18:42.720 align:start position:0% education. There is no question, you 00:18:42.720 --> 00:18:44.390 align:start position:0% education. There is no question, you know,<00:18:42.800> of<00:18:42.880> somebody<00:18:43.240> not<00:18:43.400> getting<00:18:43.680> math.<00:18:44.200> This 00:18:44.390 --> 00:18:44.400 align:start position:0% know, of somebody not getting math. This 00:18:44.400 --> 00:18:46.270 align:start position:0% know, of somebody not getting math. This is<00:18:44.880> I<00:18:44.920> think<00:18:45.160> we're<00:18:45.280> of<00:18:45.400> the<00:18:45.480> last<00:18:45.720> generation 00:18:46.270 --> 00:18:46.280 align:start position:0% is I think we're of the last generation 00:18:46.280 --> 00:18:48.150 align:start position:0% is I think we're of the last generation which<00:18:46.440> very<00:18:46.640> educated<00:18:47.120> without<00:18:47.400> the<00:18:47.520> AI.<00:18:48.040> And 00:18:48.150 --> 00:18:48.160 align:start position:0% which very educated without the AI. And 00:18:48.160 --> 00:18:49.510 align:start position:0% which very educated without the AI. And now,<00:18:48.320> of<00:18:48.480> course,<00:18:48.840> everybody<00:18:49.240> says,<00:18:49.440> "You 00:18:49.510 --> 00:18:49.520 align:start position:0% now, of course, everybody says, "You 00:18:49.520 --> 00:18:51.270 align:start position:0% now, of course, everybody says, "You don't<00:18:49.640> need<00:18:49.800> to<00:18:49.840> know<00:18:50.000> anything.<00:18:50.480> AI<00:18:50.760> will 00:18:51.270 --> 00:18:51.280 align:start position:0% don't need to know anything. AI will 00:18:51.280 --> 00:18:52.830 align:start position:0% don't need to know anything. AI will solve<00:18:51.520> it<00:18:51.600> for<00:18:51.760> you."<00:18:51.840> So<00:18:52.000> I<00:18:52.080> wonder,<00:18:52.640> and<00:18:52.760> you 00:18:52.830 --> 00:18:52.840 align:start position:0% solve it for you." So I wonder, and you 00:18:52.840 --> 00:18:54.430 align:start position:0% solve it for you." So I wonder, and you are<00:18:52.920> at<00:18:53.040> Cambridge,<00:18:53.520> right?<00:18:53.720> Like<00:18:53.920> the 00:18:54.430 --> 00:18:54.440 align:start position:0% are at Cambridge, right? Like the 00:18:54.440 --> 00:18:58.270 align:start position:0% are at Cambridge, right? Like the citadel<00:18:54.960> of<00:18:55.680> uh<00:18:55.920> kind<00:18:56.120> of<00:18:56.440> uh<00:18:56.640> academia<00:18:57.560> and 00:18:58.270 --> 00:18:58.280 align:start position:0% citadel of uh kind of uh academia and 00:18:58.280 --> 00:19:00.350 align:start position:0% citadel of uh kind of uh academia and tradition.<00:18:58.840> And<00:18:58.960> so,<00:18:59.800> how<00:18:59.960> do<00:19:00.040> you<00:19:00.120> see<00:19:00.240> the 00:19:00.350 --> 00:19:00.360 align:start position:0% tradition. And so, how do you see the 00:19:00.360 --> 00:19:01.790 align:start position:0% tradition. And so, how do you see the role<00:19:00.560> of<00:19:00.720> math? 00:19:01.790 --> 00:19:01.800 align:start position:0% role of math? 00:19:01.800 --> 00:19:04.070 align:start position:0% role of math? Uh<00:19:02.000> so<00:19:02.200> math<00:19:02.840> uh<00:19:02.920> so<00:19:03.080> AI<00:19:03.320> is<00:19:03.480> all<00:19:03.600> math,<00:19:03.840> as<00:19:03.960> we 00:19:04.070 --> 00:19:04.080 align:start position:0% Uh so math uh so AI is all math, as we 00:19:04.080 --> 00:19:05.590 align:start position:0% Uh so math uh so AI is all math, as we know,<00:19:04.680> is<00:19:04.840> all<00:19:04.920> math.<00:19:05.120> This<00:19:05.280> is<00:19:05.360> all<00:19:05.440> the<00:19:05.520> way 00:19:05.590 --> 00:19:05.600 align:start position:0% know, is all math. This is all the way 00:19:05.600 --> 00:19:06.630 align:start position:0% know, is all math. This is all the way down,<00:19:05.760> but 00:19:06.630 --> 00:19:06.640 align:start position:0% down, but 00:19:06.640 --> 00:19:08.390 align:start position:0% down, but in<00:19:06.760> practical<00:19:07.160> application,<00:19:07.880> it's<00:19:08.000> so<00:19:08.160> much 00:19:08.390 --> 00:19:08.400 align:start position:0% in practical application, it's so much 00:19:08.400 --> 00:19:10.190 align:start position:0% in practical application, it's so much removed<00:19:08.720> now<00:19:08.920> from<00:19:09.120> math<00:19:09.680> that<00:19:09.840> very<00:19:10.040> few 00:19:10.190 --> 00:19:10.200 align:start position:0% removed now from math that very few 00:19:10.200 --> 00:19:11.990 align:start position:0% removed now from math that very few people<00:19:10.520> can<00:19:10.720> do<00:19:10.880> the<00:19:11.000> underlying<00:19:11.560> math, 00:19:11.990 --> 00:19:12.000 align:start position:0% people can do the underlying math, 00:19:12.000 --> 00:19:14.670 align:start position:0% people can do the underlying math, right?<00:19:12.280> The<00:19:12.400> actual<00:19:12.760> gradient<00:19:13.160> descent,<00:19:14.200> uh 00:19:14.670 --> 00:19:14.680 align:start position:0% right? The actual gradient descent, uh 00:19:14.680 --> 00:19:16.670 align:start position:0% right? The actual gradient descent, uh uh<00:19:14.720> uh<00:19:15.240> understanding<00:19:15.800> matrices,<00:19:16.440> it's 00:19:16.670 --> 00:19:16.680 align:start position:0% uh uh understanding matrices, it's 00:19:16.680 --> 00:19:18.710 align:start position:0% uh uh understanding matrices, it's actually<00:19:17.440> it<00:19:17.600> used<00:19:17.840> to<00:19:17.920> be<00:19:18.040> a<00:19:18.120> part<00:19:18.440> of<00:19:18.600> AI 00:19:18.710 --> 00:19:18.720 align:start position:0% actually it used to be a part of AI 00:19:18.720 --> 00:19:21.150 align:start position:0% actually it used to be a part of AI education.<00:19:19.720> Now,<00:19:20.240> nobody<00:19:20.680> really<00:19:20.920> needs 00:19:21.150 --> 00:19:21.160 align:start position:0% education. Now, nobody really needs 00:19:21.160 --> 00:19:23.990 align:start position:0% education. Now, nobody really needs this.<00:19:21.480> People<00:19:21.760> just<00:19:22.000> can<00:19:22.160> like<00:19:22.640> ask 00:19:23.990 --> 00:19:24.000 align:start position:0% this. People just can like ask 00:19:24.000 --> 00:19:25.590 align:start position:0% this. People just can like ask right?<00:19:24.560> So, 00:19:25.590 --> 00:19:25.600 align:start position:0% right? So, 00:19:25.600 --> 00:19:27.910 align:start position:0% right? So, I<00:19:25.680> think<00:19:26.080> like<00:19:26.360> every<00:19:26.640> year<00:19:27.360> more<00:19:27.680> and<00:19:27.800> more 00:19:27.910 --> 00:19:27.920 align:start position:0% I think like every year more and more 00:19:27.920 --> 00:19:30.030 align:start position:0% I think like every year more and more people<00:19:28.240> in<00:19:28.320> the<00:19:28.480> AI<00:19:28.680> have<00:19:28.960> no<00:19:29.120> idea<00:19:29.680> what<00:19:29.880> is 00:19:30.030 --> 00:19:30.040 align:start position:0% people in the AI have no idea what is 00:19:30.040 --> 00:19:32.230 align:start position:0% people in the AI have no idea what is the<00:19:30.120> underlying<00:19:30.600> math,<00:19:31.320> how<00:19:31.520> it<00:19:31.680> work<00:19:31.960> How<00:19:32.160> do 00:19:32.230 --> 00:19:32.240 align:start position:0% the underlying math, how it work How do 00:19:32.240 --> 00:19:34.350 align:start position:0% the underlying math, how it work How do you<00:19:32.360> think<00:19:33.120> like<00:19:33.360> it<00:19:33.480> becomes<00:19:33.720> specialized<00:19:34.240> to 00:19:34.350 --> 00:19:34.360 align:start position:0% you think like it becomes specialized to 00:19:34.360 --> 00:19:37.310 align:start position:0% you think like it becomes specialized to like<00:19:34.560> PyTorch<00:19:35.120> people<00:19:35.400> optimizing<00:19:36.440> for<00:19:36.600> GPUs, 00:19:37.310 --> 00:19:37.320 align:start position:0% like PyTorch people optimizing for GPUs, 00:19:37.320 --> 00:19:39.470 align:start position:0% like PyTorch people optimizing for GPUs, they<00:19:37.440> need<00:19:37.640> to<00:19:37.760> know<00:19:38.120> both<00:19:38.400> the<00:19:38.520> math<00:19:38.920> and<00:19:39.080> how 00:19:39.470 --> 00:19:39.480 align:start position:0% they need to know both the math and how 00:19:39.480 --> 00:19:41.630 align:start position:0% they need to know both the math and how the<00:19:39.600> computation<00:19:41.000> becomes<00:19:41.360> a<00:19:41.400> very 00:19:41.630 --> 00:19:41.640 align:start position:0% the computation becomes a very 00:19:41.640 --> 00:19:45.150 align:start position:0% the computation becomes a very specialized<00:19:42.200> tool.<00:19:42.960> So,<00:19:43.600> I<00:19:43.720> wonder<00:19:44.640> as<00:19:44.800> a 00:19:45.150 --> 00:19:45.160 align:start position:0% specialized tool. So, I wonder as a 00:19:45.160 --> 00:19:47.750 align:start position:0% specialized tool. So, I wonder as a professor<00:19:45.560> of<00:19:45.680> mathematics,<00:19:46.240> how<00:19:46.440> do<00:19:46.600> you<00:19:46.720> see 00:19:47.750 --> 00:19:47.760 align:start position:0% professor of mathematics, how do you see 00:19:47.760 --> 00:19:48.390 align:start position:0% professor of mathematics, how do you see uh 00:19:48.390 --> 00:19:48.400 align:start position:0% uh 00:19:48.400 --> 00:19:49.590 align:start position:0% uh math 00:19:49.590 --> 00:19:49.600 align:start position:0% math 00:19:49.600 --> 00:19:52.990 align:start position:0% math kind<00:19:49.760> of<00:19:50.000> as<00:19:50.120> a<00:19:50.640> foundation<00:19:51.000> of<00:19:51.080> science? 00:19:52.990 --> 00:19:53.000 align:start position:0% kind of as a foundation of science? 00:19:53.000 --> 00:19:54.670 align:start position:0% kind of as a foundation of science? Are<00:19:53.120> we<00:19:53.240> going<00:19:53.360> to<00:19:53.440> be<00:19:53.520> able<00:19:53.680> to<00:19:53.800> preserve<00:19:54.400> it 00:19:54.670 --> 00:19:54.680 align:start position:0% Are we going to be able to preserve it 00:19:54.680 --> 00:19:56.430 align:start position:0% Are we going to be able to preserve it that<00:19:54.960> way?<00:19:55.400> Or<00:19:55.680> is<00:19:55.800> it<00:19:55.920> going<00:19:56.040> to<00:19:56.120> become<00:19:56.400> a 00:19:56.430 --> 00:19:56.440 align:start position:0% that way? Or is it going to become a 00:19:56.440 --> 00:19:57.870 align:start position:0% that way? Or is it going to become a very<00:19:56.680> niche 00:19:57.870 --> 00:19:57.880 align:start position:0% very niche 00:19:57.880 --> 00:19:59.750 align:start position:0% very niche uh<00:19:58.040> area<00:19:58.520> or<00:19:58.720> like<00:19:59.080> how<00:19:59.240> do<00:19:59.320> you<00:19:59.400> see<00:19:59.480> the<00:19:59.600> role 00:19:59.750 --> 00:19:59.760 align:start position:0% uh area or like how do you see the role 00:19:59.760 --> 00:20:02.430 align:start position:0% uh area or like how do you see the role of<00:19:59.880> math<00:20:00.120> in<00:20:00.320> in<00:20:00.480> education,<00:20:01.440> right?<00:20:01.920> Uh<00:20:02.360> to 00:20:02.430 --> 00:20:02.440 align:start position:0% of math in in education, right? Uh to 00:20:02.440 --> 00:20:05.990 align:start position:0% of math in in education, right? Uh to make<00:20:02.640> the<00:20:02.760> people<00:20:03.040> of<00:20:03.120> tomorrow? 00:20:05.990 --> 00:20:06.000 align:start position:0% 00:20:06.000 --> 00:20:07.790 align:start position:0% I<00:20:06.080> don't<00:20:06.360> know<00:20:06.560> what's<00:20:06.760> going<00:20:06.960> to<00:20:07.080> happen.<00:20:07.440> I'm 00:20:07.790 --> 00:20:07.800 align:start position:0% I don't know what's going to happen. I'm 00:20:07.800 --> 00:20:10.070 align:start position:0% I don't know what's going to happen. I'm I'm<00:20:07.920> a<00:20:07.960> bit<00:20:08.200> worried<00:20:08.440> about<00:20:08.720> that.<00:20:09.560> Uh<00:20:09.600> as<00:20:09.720> I 00:20:10.070 --> 00:20:10.080 align:start position:0% I'm a bit worried about that. Uh as I 00:20:10.080 --> 00:20:12.350 align:start position:0% I'm a bit worried about that. Uh as I like<00:20:10.200> I<00:20:10.320> said<00:20:10.600> in<00:20:10.760> my<00:20:11.520> uh<00:20:11.600> not<00:20:11.760> in<00:20:11.840> the<00:20:11.920> keynote 00:20:12.350 --> 00:20:12.360 align:start position:0% like I said in my uh not in the keynote 00:20:12.360 --> 00:20:13.950 align:start position:0% like I said in my uh not in the keynote panel<00:20:12.760> yesterday,<00:20:13.280> there<00:20:13.360> was<00:20:13.480> a<00:20:13.520> discussion 00:20:13.950 --> 00:20:13.960 align:start position:0% panel yesterday, there was a discussion 00:20:13.960 --> 00:20:15.270 align:start position:0% panel yesterday, there was a discussion about 00:20:15.270 --> 00:20:15.280 align:start position:0% about 00:20:15.280 --> 00:20:16.470 align:start position:0% about AI<00:20:15.600> and<00:20:15.760> education. 00:20:16.470 --> 00:20:16.480 align:start position:0% AI and education. 00:20:16.480 --> 00:20:17.390 align:start position:0% AI and education. >> Right. 00:20:17.390 --> 00:20:17.400 align:start position:0% >> Right. 00:20:17.400 --> 00:20:18.990 align:start position:0% >> Right. And<00:20:17.520> I'm<00:20:17.680> worried<00:20:17.960> about<00:20:18.240> this<00:20:18.360> perception 00:20:18.990 --> 00:20:19.000 align:start position:0% And I'm worried about this perception 00:20:19.000 --> 00:20:20.390 align:start position:0% And I'm worried about this perception that<00:20:19.200> we<00:20:19.320> don't<00:20:19.520> need<00:20:19.680> to<00:20:19.800> know<00:20:20.000> anything 00:20:20.390 --> 00:20:20.400 align:start position:0% that we don't need to know anything 00:20:20.400 --> 00:20:23.470 align:start position:0% that we don't need to know anything because<00:20:20.720> we<00:20:20.840> can<00:20:21.000> outsource<00:20:22.160> all<00:20:22.400> our 00:20:23.470 --> 00:20:23.480 align:start position:0% because we can outsource all our 00:20:23.480 --> 00:20:25.110 align:start position:0% because we can outsource all our So,<00:20:23.560> there<00:20:23.680> was<00:20:23.760> somebody<00:20:24.160> uh<00:20:24.400> Bill<00:20:24.720> Wren<00:20:24.960> who 00:20:25.110 --> 00:20:25.120 align:start position:0% So, there was somebody uh Bill Wren who 00:20:25.120 --> 00:20:26.910 align:start position:0% So, there was somebody uh Bill Wren who said<00:20:25.400> that<00:20:26.080> uh 00:20:26.910 --> 00:20:26.920 align:start position:0% said that uh 00:20:26.920 --> 00:20:28.710 align:start position:0% said that uh we<00:20:27.040> can<00:20:27.200> outsource 00:20:28.710 --> 00:20:28.720 align:start position:0% we can outsource 00:20:28.720 --> 00:20:30.150 align:start position:0% we can outsource knowledge,<00:20:29.240> but<00:20:29.360> we<00:20:29.480> can't<00:20:29.760> outsource 00:20:30.150 --> 00:20:30.160 align:start position:0% knowledge, but we can't outsource 00:20:30.160 --> 00:20:31.990 align:start position:0% knowledge, but we can't outsource understanding<00:20:30.840> or<00:20:30.920> something<00:20:31.240> like<00:20:31.400> that.<00:20:31.920> I 00:20:31.990 --> 00:20:32.000 align:start position:0% understanding or something like that. I 00:20:32.000 --> 00:20:33.590 align:start position:0% understanding or something like that. I think<00:20:32.200> that's 00:20:33.590 --> 00:20:33.600 align:start position:0% think that's 00:20:33.600 --> 00:20:36.030 align:start position:0% think that's I<00:20:33.640> think<00:20:33.800> that's<00:20:34.520> quite<00:20:34.880> true<00:20:35.200> and<00:20:35.360> I<00:20:35.440> think<00:20:35.840> if 00:20:36.030 --> 00:20:36.040 align:start position:0% I think that's quite true and I think if 00:20:36.040 --> 00:20:38.270 align:start position:0% I think that's quite true and I think if we<00:20:36.200> don't<00:20:36.640> have 00:20:38.270 --> 00:20:38.280 align:start position:0% we don't have 00:20:38.280 --> 00:20:40.510 align:start position:0% we don't have um<00:20:38.760> a<00:20:38.800> significant<00:20:39.360> percentage<00:20:39.920> of<00:20:40.080> people<00:20:40.400> in 00:20:40.510 --> 00:20:40.520 align:start position:0% um a significant percentage of people in 00:20:40.520 --> 00:20:42.870 align:start position:0% um a significant percentage of people in a<00:20:40.560> society<00:20:41.160> who<00:20:41.280> really<00:20:41.520> understand 00:20:42.870 --> 00:20:42.880 align:start position:0% a society who really understand 00:20:42.880 --> 00:20:45.110 align:start position:0% a society who really understand mathematics<00:20:43.520> and<00:20:44.120> uh 00:20:45.110 --> 00:20:45.120 align:start position:0% mathematics and uh 00:20:45.120 --> 00:20:46.990 align:start position:0% mathematics and uh at<00:20:45.280> some<00:20:45.520> level, 00:20:46.990 --> 00:20:47.000 align:start position:0% at some level, 00:20:47.000 --> 00:20:48.910 align:start position:0% at some level, uh<00:20:47.400> then<00:20:47.560> we<00:20:47.680> will<00:20:47.800> operate 00:20:48.910 --> 00:20:48.920 align:start position:0% uh then we will operate 00:20:48.920 --> 00:20:50.950 align:start position:0% uh then we will operate we'll<00:20:49.040> be<00:20:49.160> somehow<00:20:49.640> under<00:20:50.000> the<00:20:50.120> control<00:20:50.720> of 00:20:50.950 --> 00:20:50.960 align:start position:0% we'll be somehow under the control of 00:20:50.960 --> 00:20:54.590 align:start position:0% we'll be somehow under the control of these<00:20:51.480> systems.<00:20:51.960> We<00:20:52.040> won't<00:20:52.280> we'll<00:20:52.440> be<00:20:52.800> passive 00:20:54.590 --> 00:20:54.600 align:start position:0% these systems. We won't we'll be passive 00:20:54.600 --> 00:20:58.310 align:start position:0% these systems. We won't we'll be passive consumers<00:20:55.200> of<00:20:55.360> them<00:20:55.600> and<00:20:56.160> um 00:20:58.310 --> 00:20:58.320 align:start position:0% 00:20:58.320 --> 00:20:59.630 align:start position:0% So,<00:20:58.440> that<00:20:58.640> worries<00:20:58.960> me<00:20:59.040> and<00:20:59.120> I<00:20:59.320> I<00:20:59.360> think<00:20:59.480> that 00:20:59.630 --> 00:20:59.640 align:start position:0% So, that worries me and I I think that 00:20:59.640 --> 00:21:01.150 align:start position:0% So, that worries me and I I think that maybe<00:20:59.880> what<00:21:00.000> happens.<00:21:00.720> On<00:21:00.800> the<00:21:00.840> other<00:21:00.960> hand,<00:21:01.080> I 00:21:01.150 --> 00:21:01.160 align:start position:0% maybe what happens. On the other hand, I 00:21:01.160 --> 00:21:04.870 align:start position:0% maybe what happens. On the other hand, I think<00:21:01.640> it<00:21:01.840> will<00:21:02.040> remain<00:21:02.400> the<00:21:02.480> case<00:21:03.160> Mhm.<00:21:03.920> that 00:21:04.870 --> 00:21:04.880 align:start position:0% think it will remain the case Mhm. that 00:21:04.880 --> 00:21:07.790 align:start position:0% think it will remain the case Mhm. that uh<00:21:05.360> people<00:21:05.720> who<00:21:06.600> do<00:21:06.760> make<00:21:07.000> the<00:21:07.120> effort<00:21:07.480> to<00:21:07.600> have 00:21:07.790 --> 00:21:07.800 align:start position:0% uh people who do make the effort to have 00:21:07.800 --> 00:21:09.990 align:start position:0% uh people who do make the effort to have a<00:21:07.840> good<00:21:08.000> understanding<00:21:08.480> of<00:21:08.560> mathematics 00:21:09.990 --> 00:21:10.000 align:start position:0% a good understanding of mathematics 00:21:10.000 --> 00:21:11.870 align:start position:0% a good understanding of mathematics will<00:21:10.200> have<00:21:10.320> a<00:21:10.360> big<00:21:10.560> advantage. 00:21:11.870 --> 00:21:11.880 align:start position:0% will have a big advantage. 00:21:11.880 --> 00:21:12.470 align:start position:0% will have a big advantage. Um 00:21:12.470 --> 00:21:12.480 align:start position:0% Um 00:21:12.480 --> 00:21:13.510 align:start position:0% Um bit<00:21:12.600> like<00:21:12.760> what<00:21:12.880> you<00:21:12.960> were<00:21:13.040> saying<00:21:13.280> earlier 00:21:13.510 --> 00:21:13.520 align:start position:0% bit like what you were saying earlier 00:21:13.520 --> 00:21:15.230 align:start position:0% bit like what you were saying earlier about<00:21:13.680> the<00:21:13.760> rich<00:21:14.000> getting<00:21:14.240> richer.<00:21:14.600> If<00:21:14.760> you 00:21:15.230 --> 00:21:15.240 align:start position:0% about the rich getting richer. If you 00:21:15.240 --> 00:21:17.430 align:start position:0% about the rich getting richer. If you Right.<00:21:15.760> If<00:21:15.920> you<00:21:16.080> know<00:21:16.280> how<00:21:16.440> to 00:21:17.430 --> 00:21:17.440 align:start position:0% Right. If you know how to 00:21:17.440 --> 00:21:18.830 align:start position:0% Right. If you know how to If<00:21:17.480> you<00:21:17.600> If<00:21:17.760> you<00:21:17.840> know<00:21:18.000> maths<00:21:18.400> well,<00:21:18.680> then 00:21:18.830 --> 00:21:18.840 align:start position:0% If you If you know maths well, then 00:21:18.840 --> 00:21:21.590 align:start position:0% If you If you know maths well, then you'll<00:21:19.000> be<00:21:19.120> able<00:21:19.320> to<00:21:19.400> you'll<00:21:19.480> be<00:21:19.560> better<00:21:19.960> at<00:21:20.360> um 00:21:21.590 --> 00:21:21.600 align:start position:0% you'll be able to you'll be better at um 00:21:21.600 --> 00:21:24.030 align:start position:0% you'll be able to you'll be better at um using<00:21:22.040> AI<00:21:22.560> and<00:21:22.760> using<00:21:23.000> it<00:21:23.120> to<00:21:23.200> do<00:21:23.360> mathematics 00:21:24.030 --> 00:21:24.040 align:start position:0% using AI and using it to do mathematics 00:21:24.040 --> 00:21:25.070 align:start position:0% using AI and using it to do mathematics and 00:21:25.070 --> 00:21:25.080 align:start position:0% and 00:21:25.080 --> 00:21:26.670 align:start position:0% and having<00:21:25.320> an<00:21:25.400> understanding<00:21:25.920> of<00:21:26.040> what<00:21:26.200> you<00:21:26.280> can 00:21:26.670 --> 00:21:26.680 align:start position:0% having an understanding of what you can 00:21:26.680 --> 00:21:28.790 align:start position:0% having an understanding of what you can what<00:21:26.920> you<00:21:27.000> can<00:21:27.160> use<00:21:27.360> the<00:21:27.440> tools<00:21:27.840> for<00:21:28.280> and<00:21:28.520> so 00:21:28.790 --> 00:21:28.800 align:start position:0% what you can use the tools for and so 00:21:28.800 --> 00:21:29.950 align:start position:0% what you can use the tools for and so on. 00:21:29.950 --> 00:21:29.960 align:start position:0% on. 00:21:29.960 --> 00:21:32.670 align:start position:0% on. Um<00:21:30.600> so<00:21:30.800> I<00:21:30.880> hope<00:21:31.160> that<00:21:31.880> uh<00:21:31.960> that<00:21:32.200> message<00:21:32.560> will 00:21:32.670 --> 00:21:32.680 align:start position:0% Um so I hope that uh that message will 00:21:32.680 --> 00:21:34.750 align:start position:0% Um so I hope that uh that message will get<00:21:32.880> through. 00:21:34.750 --> 00:21:34.760 align:start position:0% get through. 00:21:34.760 --> 00:21:36.510 align:start position:0% get through. Do<00:21:34.920> you<00:21:35.000> see<00:21:35.160> young<00:21:35.400> people,<00:21:36.120> so<00:21:36.320> you're 00:21:36.510 --> 00:21:36.520 align:start position:0% Do you see young people, so you're 00:21:36.520 --> 00:21:38.310 align:start position:0% Do you see young people, so you're teaching<00:21:36.920> in<00:21:37.160> France<00:21:37.480> and<00:21:37.600> then<00:21:38.080> in 00:21:38.310 --> 00:21:38.320 align:start position:0% teaching in France and then in 00:21:38.320 --> 00:21:40.150 align:start position:0% teaching in France and then in Cambridge.<00:21:38.720> Do<00:21:38.880> you<00:21:39.000> see 00:21:40.150 --> 00:21:40.160 align:start position:0% Cambridge. Do you see 00:21:40.160 --> 00:21:42.710 align:start position:0% Cambridge. Do you see young<00:21:40.320> people<00:21:40.560> coming<00:21:40.800> into<00:21:41.000> maths<00:21:41.960> who<00:21:42.560> will 00:21:42.710 --> 00:21:42.720 align:start position:0% young people coming into maths who will 00:21:42.720 --> 00:21:44.790 align:start position:0% young people coming into maths who will make<00:21:42.880> great<00:21:43.120> mathematicians<00:21:44.360> despite<00:21:44.720> of 00:21:44.790 --> 00:21:44.800 align:start position:0% make great mathematicians despite of 00:21:44.800 --> 00:21:47.030 align:start position:0% make great mathematicians despite of everything<00:21:45.160> else<00:21:45.800> happening? 00:21:47.030 --> 00:21:47.040 align:start position:0% everything else happening? 00:21:47.040 --> 00:21:49.470 align:start position:0% everything else happening? Like<00:21:47.240> do<00:21:47.360> you<00:21:47.480> see<00:21:47.720> like<00:21:47.960> is<00:21:48.080> there<00:21:48.280> supply<00:21:49.400> of 00:21:49.470 --> 00:21:49.480 align:start position:0% Like do you see like is there supply of 00:21:49.480 --> 00:21:50.910 align:start position:0% Like do you see like is there supply of smart<00:21:49.840> young<00:21:50.040> students<00:21:50.360> Well,<00:21:50.480> I'm<00:21:50.680> very 00:21:50.910 --> 00:21:50.920 align:start position:0% smart young students Well, I'm very 00:21:50.920 --> 00:21:53.070 align:start position:0% smart young students Well, I'm very lucky<00:21:51.200> to<00:21:51.360> be<00:21:51.880> um<00:21:52.200> at<00:21:52.320> Trinity<00:21:52.760> College, 00:21:53.070 --> 00:21:53.080 align:start position:0% lucky to be um at Trinity College, 00:21:53.080 --> 00:21:54.750 align:start position:0% lucky to be um at Trinity College, Cambridge<00:21:53.520> and<00:21:53.640> we<00:21:53.760> get<00:21:54.160> regularly 00:21:54.750 --> 00:21:54.760 align:start position:0% Cambridge and we get regularly 00:21:54.760 --> 00:21:56.190 align:start position:0% Cambridge and we get regularly incredibly<00:21:55.320> good<00:21:55.520> mathematicians<00:21:56.080> coming 00:21:56.190 --> 00:21:56.200 align:start position:0% incredibly good mathematicians coming 00:21:56.200 --> 00:21:56.230 align:start position:0% incredibly good mathematicians coming >> Mhm. 00:21:56.230 --> 00:21:56.240 align:start position:0% >> Mhm. 00:21:56.240 --> 00:21:57.710 align:start position:0% >> Mhm. >> there.<00:21:56.720> So<00:21:56.800> they're<00:21:56.960> still<00:21:57.200> being<00:21:57.400> produced 00:21:57.710 --> 00:21:57.720 align:start position:0% >> there. So they're still being produced 00:21:57.720 --> 00:22:00.630 align:start position:0% >> there. So they're still being produced somewhere<00:21:58.240> and<00:21:58.440> get<00:21:58.680> to<00:21:58.880> Trinity.<00:21:59.680> And<00:22:00.560> for 00:22:00.630 --> 00:22:00.640 align:start position:0% somewhere and get to Trinity. And for 00:22:00.640 --> 00:22:03.790 align:start position:0% somewhere and get to Trinity. And for the<00:22:00.760> moment,<00:22:01.280> I<00:22:01.360> think<00:22:01.600> they<00:22:01.840> are<00:22:01.960> still 00:22:03.790 --> 00:22:03.800 align:start position:0% the moment, I think they are still 00:22:03.800 --> 00:22:06.310 align:start position:0% the moment, I think they are still noticeably<00:22:04.560> ahead<00:22:04.840> of<00:22:05.080> what<00:22:05.360> AI<00:22:05.680> can 00:22:06.310 --> 00:22:06.320 align:start position:0% noticeably ahead of what AI can 00:22:06.320 --> 00:22:07.390 align:start position:0% noticeably ahead of what AI can Mhm. 00:22:07.390 --> 00:22:07.400 align:start position:0% Mhm. 00:22:07.400 --> 00:22:11.110 align:start position:0% Mhm. Um<00:22:08.400> the<00:22:08.480> very<00:22:08.680> best<00:22:09.040> students<00:22:09.440> anyway. 00:22:11.110 --> 00:22:11.120 align:start position:0% Um the very best students anyway. 00:22:11.120 --> 00:22:13.310 align:start position:0% Um the very best students anyway. Um 00:22:13.310 --> 00:22:13.320 align:start position:0% Um 00:22:13.320 --> 00:22:14.470 align:start position:0% Um So<00:22:13.400> there<00:22:13.520> is<00:22:13.600> hope.<00:22:13.960> There<00:22:14.080> is<00:22:14.160> hope<00:22:14.320> for<00:22:14.400> the 00:22:14.470 --> 00:22:14.480 align:start position:0% So there is hope. There is hope for the 00:22:14.480 --> 00:22:16.630 align:start position:0% So there is hope. There is hope for the future<00:22:14.720> of<00:22:14.800> maths.<00:22:15.000> Yes,<00:22:15.160> there<00:22:15.280> is. 00:22:16.630 --> 00:22:16.640 align:start position:0% future of maths. Yes, there is. 00:22:16.640 --> 00:22:18.870 align:start position:0% future of maths. Yes, there is. But<00:22:17.400> uh 00:22:18.870 --> 00:22:18.880 align:start position:0% But uh 00:22:18.880 --> 00:22:21.630 align:start position:0% But uh Yeah,<00:22:19.120> it's<00:22:19.400> it's 00:22:21.630 --> 00:22:21.640 align:start position:0% Yeah, it's it's 00:22:21.640 --> 00:22:23.550 align:start position:0% Yeah, it's it's It<00:22:21.760> could<00:22:21.920> go<00:22:22.120> either<00:22:22.320> way,<00:22:22.520> I<00:22:22.600> think.<00:22:22.840> It's 00:22:23.550 --> 00:22:23.560 align:start position:0% It could go either way, I think. It's 00:22:23.560 --> 00:22:24.710 align:start position:0% It could go either way, I think. It's We<00:22:23.680> We<00:22:23.800> really<00:22:24.000> don't<00:22:24.200> know<00:22:24.320> what's<00:22:24.480> going<00:22:24.640> to 00:22:24.710 --> 00:22:24.720 align:start position:0% We We really don't know what's going to 00:22:24.720 --> 00:22:26.430 align:start position:0% We We really don't know what's going to happen.<00:22:25.200> That's<00:22:25.360> great.<00:22:25.600> I<00:22:25.640> mean,<00:22:26.040> it's<00:22:26.200> it's 00:22:26.430 --> 00:22:26.440 align:start position:0% happen. That's great. I mean, it's it's 00:22:26.440 --> 00:22:27.950 align:start position:0% happen. That's great. I mean, it's it's it's<00:22:26.600> really<00:22:26.800> great<00:22:27.120> to<00:22:27.320> see<00:22:27.560> that<00:22:27.800> you're 00:22:27.950 --> 00:22:27.960 align:start position:0% it's really great to see that you're 00:22:27.960 --> 00:22:29.470 align:start position:0% it's really great to see that you're doing<00:22:28.400> things<00:22:28.600> with<00:22:28.760> Lean.<00:22:28.920> So<00:22:29.080> what<00:22:29.240> is<00:22:29.360> your 00:22:29.470 --> 00:22:29.480 align:start position:0% doing things with Lean. So what is your 00:22:29.480 --> 00:22:31.150 align:start position:0% doing things with Lean. So what is your goal<00:22:29.720> for<00:22:29.840> the<00:22:29.960> next<00:22:30.200> year?<00:22:30.440> So,<00:22:30.920> you<00:22:31.000> know,<00:22:31.080> if 00:22:31.150 --> 00:22:31.160 align:start position:0% goal for the next year? So, you know, if 00:22:31.160 --> 00:22:33.310 align:start position:0% goal for the next year? So, you know, if we<00:22:31.240> meet<00:22:31.400> here<00:22:31.600> next<00:22:31.960> year,<00:22:32.680> what<00:22:32.880> do<00:22:32.960> you<00:22:33.080> want 00:22:33.310 --> 00:22:33.320 align:start position:0% we meet here next year, what do you want 00:22:33.320 --> 00:22:36.510 align:start position:0% we meet here next year, what do you want to<00:22:33.440> have<00:22:33.720> achieved<00:22:35.040> by<00:22:35.600> this 00:22:36.510 --> 00:22:36.520 align:start position:0% to have achieved by this 00:22:36.520 --> 00:22:39.190 align:start position:0% to have achieved by this like<00:22:36.720> in<00:22:36.800> a<00:22:36.880> year<00:22:37.280> with<00:22:37.480> your<00:22:37.600> lab? 00:22:39.190 --> 00:22:39.200 align:start position:0% like in a year with your lab? 00:22:39.200 --> 00:22:40.230 align:start position:0% like in a year with your lab? Well, 00:22:40.230 --> 00:22:40.240 align:start position:0% Well, 00:22:40.240 --> 00:22:42.350 align:start position:0% Well, I<00:22:40.400> was<00:22:40.600> talking<00:22:40.960> in<00:22:41.080> my<00:22:41.400> keynote<00:22:41.920> a<00:22:42.000> little<00:22:42.200> bit 00:22:42.350 --> 00:22:42.360 align:start position:0% I was talking in my keynote a little bit 00:22:42.360 --> 00:22:43.910 align:start position:0% I was talking in my keynote a little bit about<00:22:42.600> a<00:22:42.640> platform<00:22:43.200> that<00:22:43.360> my<00:22:43.560> group<00:22:43.800> is 00:22:43.910 --> 00:22:43.920 align:start position:0% about a platform that my group is 00:22:43.920 --> 00:22:45.230 align:start position:0% about a platform that my group is developing 00:22:45.230 --> 00:22:45.240 align:start position:0% developing 00:22:45.240 --> 00:22:47.670 align:start position:0% developing um<00:22:45.560> Mhm.<00:22:46.040> that<00:22:46.160> would<00:22:46.320> in<00:22:46.840> sort<00:22:47.040> of<00:22:47.160> encourage 00:22:47.670 --> 00:22:47.680 align:start position:0% um Mhm. that would in sort of encourage 00:22:47.680 --> 00:22:49.070 align:start position:0% um Mhm. that would in sort of encourage people<00:22:48.000> to 00:22:49.070 --> 00:22:49.080 align:start position:0% people to 00:22:49.080 --> 00:22:51.550 align:start position:0% people to produce<00:22:49.440> not<00:22:49.680> just<00:22:49.920> proofs,<00:22:50.360> but<00:22:50.720> proofs<00:22:51.440> that 00:22:51.550 --> 00:22:51.560 align:start position:0% produce not just proofs, but proofs that 00:22:51.560 --> 00:22:53.110 align:start position:0% produce not just proofs, but proofs that are<00:22:51.640> transparent,<00:22:52.360> so<00:22:52.480> you<00:22:52.600> can<00:22:52.720> see<00:22:52.960> where 00:22:53.110 --> 00:22:53.120 align:start position:0% are transparent, so you can see where 00:22:53.120 --> 00:22:54.470 align:start position:0% are transparent, so you can see where the<00:22:53.240> ideas<00:22:53.520> come<00:22:53.680> from. 00:22:54.470 --> 00:22:54.480 align:start position:0% the ideas come from. 00:22:54.480 --> 00:22:57.830 align:start position:0% the ideas come from. So<00:22:54.640> my<00:22:55.280> sort<00:22:55.440> of<00:22:55.520> main<00:22:55.880> short-term<00:22:56.480> hope 00:22:57.830 --> 00:22:57.840 align:start position:0% So my sort of main short-term hope 00:22:57.840 --> 00:22:59.270 align:start position:0% So my sort of main short-term hope Maybe<00:22:58.000> short<00:22:58.680> What<00:22:58.840> I<00:22:58.880> think<00:22:59.120> of<00:22:59.200> as 00:22:59.270 --> 00:22:59.280 align:start position:0% Maybe short What I think of as 00:22:59.280 --> 00:23:01.470 align:start position:0% Maybe short What I think of as short-term,<00:22:59.760> but<00:22:59.880> in<00:23:00.000> this<00:23:00.240> world,<00:23:01.120> a<00:23:01.200> year 00:23:01.470 --> 00:23:01.480 align:start position:0% short-term, but in this world, a year 00:23:01.480 --> 00:23:04.190 align:start position:0% short-term, but in this world, a year feels<00:23:01.760> like<00:23:01.960> long-term<00:23:02.480> as<00:23:02.640> well. 00:23:04.190 --> 00:23:04.200 align:start position:0% feels like long-term as well. 00:23:04.200 --> 00:23:05.710 align:start position:0% feels like long-term as well. Is<00:23:04.560> just<00:23:04.760> platform<00:23:05.160> will<00:23:05.240> be<00:23:05.360> much<00:23:05.600> more 00:23:05.710 --> 00:23:05.720 align:start position:0% Is just platform will be much more 00:23:05.720 --> 00:23:06.830 align:start position:0% Is just platform will be much more developed<00:23:06.200> and<00:23:06.320> we'll<00:23:06.440> be<00:23:06.560> able<00:23:06.760> to 00:23:06.830 --> 00:23:06.840 align:start position:0% developed and we'll be able to 00:23:06.840 --> 00:23:09.150 align:start position:0% developed and we'll be able to demonstrate<00:23:07.400> that<00:23:07.520> it<00:23:07.600> really<00:23:07.840> is<00:23:08.400> uh 00:23:09.150 --> 00:23:09.160 align:start position:0% demonstrate that it really is uh 00:23:09.160 --> 00:23:10.470 align:start position:0% demonstrate that it really is uh a<00:23:09.200> good<00:23:09.440> way<00:23:09.560> of<00:23:09.680> thinking<00:23:09.920> about<00:23:10.160> how<00:23:10.240> to<00:23:10.360> do 00:23:10.470 --> 00:23:10.480 align:start position:0% a good way of thinking about how to do 00:23:10.480 --> 00:23:12.470 align:start position:0% a good way of thinking about how to do mathematics.<00:23:11.440> This<00:23:11.560> sounds<00:23:11.760> great.<00:23:12.080> So,<00:23:12.280> if 00:23:12.470 --> 00:23:12.480 align:start position:0% mathematics. This sounds great. So, if 00:23:12.480 --> 00:23:14.470 align:start position:0% mathematics. This sounds great. So, if you<00:23:12.720> are<00:23:12.920> ever<00:23:13.160> in<00:23:13.280> San<00:23:13.400> Francisco<00:23:13.760> Bay<00:23:13.880> Area, 00:23:14.470 --> 00:23:14.480 align:start position:0% you are ever in San Francisco Bay Area, 00:23:14.480 --> 00:23:16.230 align:start position:0% you are ever in San Francisco Bay Area, we're<00:23:14.720> on<00:23:15.000> the<00:23:15.120> uh<00:23:15.280> meet<00:23:15.440> up<00:23:15.560> there.<00:23:15.920> Just<00:23:16.080> come 00:23:16.230 --> 00:23:16.240 align:start position:0% we're on the uh meet up there. Just come 00:23:16.240 --> 00:23:17.670 align:start position:0% we're on the uh meet up there. Just come and<00:23:16.360> give<00:23:16.520> us<00:23:16.600> a<00:23:16.640> talk<00:23:16.840> and<00:23:17.160> do<00:23:17.280> a<00:23:17.320> demo<00:23:17.560> of<00:23:17.640> the 00:23:17.670 --> 00:23:17.680 align:start position:0% and give us a talk and do a demo of the 00:23:17.680 --> 00:23:19.350 align:start position:0% and give us a talk and do a demo of the platform.<00:23:18.360> We'd<00:23:18.440> like<00:23:18.720> We'd<00:23:18.840> like<00:23:19.040> our<00:23:19.120> center 00:23:19.350 --> 00:23:19.360 align:start position:0% platform. We'd like We'd like our center 00:23:19.360 --> 00:23:21.470 align:start position:0% platform. We'd like We'd like our center student<00:23:19.720> to<00:23:19.960> show<00:23:20.240> it.<00:23:20.840> We'd<00:23:21.000> love<00:23:21.160> to<00:23:21.280> play 00:23:21.470 --> 00:23:21.480 align:start position:0% student to show it. We'd love to play 00:23:21.480 --> 00:23:22.430 align:start position:0% student to show it. We'd love to play with<00:23:21.600> it. 00:23:22.430 --> 00:23:22.440 align:start position:0% with it. 00:23:22.440 --> 00:23:23.830 align:start position:0% with it. Well,<00:23:22.560> thank<00:23:22.760> you<00:23:22.800> so<00:23:22.920> much.<00:23:23.400> We<00:23:23.480> appreciate 00:23:23.830 --> 00:23:23.840 align:start position:0% Well, thank you so much. We appreciate 00:23:23.840 --> 00:23:27.120 align:start position:0% Well, thank you so much. We appreciate it.<00:23:24.320> Thanks<00:23:24.520> a<00:23:24.560> lot.<00:23:24.800> Yeah.