1 00:00:10,300 --> 00:00:18,550 Thank you very much. It's my great pleasure. It's an honour to do this, teach much literature lecture, as was said. 2 00:00:18,550 --> 00:00:22,600 And it's my great pleasure also to have been introduced by John Bull, 3 00:00:22,960 --> 00:00:29,800 with whom I have worked so many times over the past years about matters of policy of science. 4 00:00:30,160 --> 00:00:42,399 I'm not sure which was my last visit to Oxford, but I remember vividly giving a seminar here in 2008 on the invitation of Terry Lyons and the subject, 5 00:00:42,400 --> 00:00:47,130 which since then has grown to proportions that I thought would be impossible. 6 00:00:47,170 --> 00:00:52,299 Anyway, it's great to be back here, especially in this new, 7 00:00:52,300 --> 00:00:59,050 beautiful building and to do this exercise in which one has to address an audience 8 00:00:59,350 --> 00:01:05,620 ranging from end of high school to distinguished university professor at the same time. 9 00:01:06,370 --> 00:01:17,080 So let's go on with recalling some things about mathematics now with these kind of particular science mathematicians know it, of course, 10 00:01:17,090 --> 00:01:28,329 then mathematicians have to be aware and I like to remind of an event which was not unnoticed by some people a few years ago when the Wall 11 00:01:28,330 --> 00:01:38,530 Street Journal decided to make a ranking of all the possible jobs on the face of the earth that they could think of and what came out first. 12 00:01:38,530 --> 00:01:44,320 Of course, you may be guessing if I am quoting these statistics, it may be good news for the mathematician. 13 00:01:44,950 --> 00:01:49,870 And indeed it was mathematician number one here. 14 00:01:51,280 --> 00:02:00,729 Of course, they put the poor lumberjack class and some of you may know some lumberjacks and feel depressed. 15 00:02:00,730 --> 00:02:04,810 But don't these kind of rankings we know is total crap. 16 00:02:05,540 --> 00:02:13,360 But it's was here. The first rank, the first ranking, the first place has some truth in it for sure. 17 00:02:14,320 --> 00:02:24,459 So mathematician number one and 2014, they did it again and they put again mathematician at the first place. 18 00:02:24,460 --> 00:02:31,630 Now there are a company called Career Cars to introspection of what will be the jobs of the future and so on. 19 00:02:32,260 --> 00:02:38,350 And they have this point that mathematician is very well adapted to a very moving future 20 00:02:38,350 --> 00:02:43,690 because by definition mathematics can adapt to any kind of problem and situation, 21 00:02:44,140 --> 00:02:54,190 and also a world in which is much and much more dominated by changes of and processing of information or driven through computers, 22 00:02:54,190 --> 00:02:58,420 which is a way to bring mathematics to real life, so to speak. 23 00:02:59,530 --> 00:03:04,360 What was the definition that our colleagues from Wall Street Journal use? 24 00:03:04,690 --> 00:03:05,559 That's interesting. 25 00:03:05,560 --> 00:03:15,820 Mathematician is somebody who applies mathematical theories and formulas to teach or solve problems in a business, educational or industrial climate. 26 00:03:16,480 --> 00:03:27,070 No, that's good. In particular, the fact that they use the word solve problems because mathematics was invented to solve problems, 27 00:03:27,070 --> 00:03:35,200 was created or discovered to solve problems, and has been doing so for many, many years, for thousands of years, 28 00:03:35,200 --> 00:03:44,380 arguably and still there is something missing for the definition to be complete because of course, 29 00:03:44,530 --> 00:03:48,760 mathematician is also somebody who creates new mathematics, 30 00:03:49,180 --> 00:03:53,049 because mathematics is not just something which is given and that you apply, 31 00:03:53,050 --> 00:03:58,000 it is also something which is in constant evolution, continuous evolution. 32 00:03:58,040 --> 00:04:04,089 It's good to remind that round the earth now there are maybe a couple of hundreds 33 00:04:04,090 --> 00:04:10,930 of thousands of mathematicians and maybe as many theorems proven per year. 34 00:04:11,230 --> 00:04:19,450 It's a very rapidly evolving field, also driven by interaction with other sciences and driven by interaction with the technology. 35 00:04:19,630 --> 00:04:20,620 Or more and more. 36 00:04:22,120 --> 00:04:39,520 It has been estimated a few years ago that mathematical research was accounting for 16% of the gross value of gross value added in the UK economy. 37 00:04:39,910 --> 00:04:49,479 There was a study quantifying this. When the results arrived, many mathematicians said, Wow, this, how did they do this study? 38 00:04:49,480 --> 00:04:56,709 And so then in the end was not so bad to the the way they handled the process and so on, 39 00:04:56,710 --> 00:05:00,010 which is very complicated because we have all kind of indirect effects. 40 00:05:00,460 --> 00:05:10,960 Was not so bad actually in France we are doing the same study nowadays as usual will see the different terminology, 41 00:05:10,960 --> 00:05:14,610 different procedure and so on, make it different results. 42 00:05:14,620 --> 00:05:23,290 But one thing for sure whatever the precise result, mathematics is playing a very important role in today's economy, in today's technology. 43 00:05:23,290 --> 00:05:27,790 And this role is increasing and increasing year after year. 44 00:05:28,360 --> 00:05:34,960 And also people are getting it now, for instance, in culture, in the data industry and so on. 45 00:05:35,350 --> 00:05:40,930 I remember a few years ago a big conference in San Diego with a joint mathematical meeting. 46 00:05:41,500 --> 00:05:51,430 In one of the in one of the sessions, there was the director of research of some big studio making movies, some major. 47 00:05:51,820 --> 00:06:02,860 And he was saying to an audience of delighted mathematicians, we should pay you guys royalties for every blockbuster which is out in Hollywood, 48 00:06:03,160 --> 00:06:09,040 given the amount of mathematical research that to use all the equations, new equations, 49 00:06:09,040 --> 00:06:15,500 numerical schemes and so on, it plays a more and more important role in the movie industry also. 50 00:06:16,240 --> 00:06:21,129 Well speaking, I am noticing that the power is not here. 51 00:06:21,130 --> 00:06:27,190 So there may be. If we don't do something, it might turn off the middle of the talk. 52 00:06:29,290 --> 00:06:34,360 Hold on. It's just talking. It's just a fragile contact. 53 00:06:35,740 --> 00:06:37,900 Okay. So the technological problem. 54 00:06:40,930 --> 00:06:51,490 Yes, one important think about mathematics also, and that the reason on this slide, which I will not go through every detail, is very impressionistic. 55 00:06:51,910 --> 00:07:00,790 There are figures from the past and also figures from the distant birth past, because we also live with them. 56 00:07:00,910 --> 00:07:09,700 Every mathematician knows we are friends with the mathematician from the past using their ideas and they are still there. 57 00:07:10,630 --> 00:07:16,930 For instance, I put full year, I put during the year there is Shannon, there is LA Plus and so on. 58 00:07:17,290 --> 00:07:22,300 One of the most important theorems in mathematics is the central limit theorem. 59 00:07:22,600 --> 00:07:31,390 It says Whenever you are looking at an experiment, material is repeated a large number of times, a random experiment repeated many, many times. 60 00:07:31,840 --> 00:07:38,110 And you want to know which is the deviation of the observed statistics, respect to the theoretical statistics, 61 00:07:38,110 --> 00:07:46,569 respect to the mean this fluctuations are gushing with a large probability of being small and the small probability of being large. 62 00:07:46,570 --> 00:07:51,760 And the first proof of this was by Laplace, beginning of the 19th century. 63 00:07:52,150 --> 00:07:58,990 And this thing is still an extremely important theorem, still used in many cases, and so on. 64 00:07:58,990 --> 00:08:05,620 And conversely, every all of these things, 65 00:08:05,620 --> 00:08:13,450 all of these contributions get enriched and get new developments in the tides of current world and current technology. 66 00:08:14,620 --> 00:08:27,550 Let's take one example, just one for years, and that is so here comes full year, but the same time as the plus four. 67 00:08:27,760 --> 00:08:37,750 He worked on the full year transform and full year analysis, of which the two basic equations are the ones appearing on the left of for you here. 68 00:08:37,930 --> 00:08:47,500 It's written here in very compact form. Just suffice to know that the theory is a theory on which you can write books of hundreds of pages, 69 00:08:47,950 --> 00:09:00,069 but also which can be summarised in a very small number of equations in a very compact form, and still is extremely useful, extremely applied. 70 00:09:00,070 --> 00:09:05,440 And that's the strength of mathematics, because it is based on abstraction. 71 00:09:05,920 --> 00:09:09,700 It can be applied to a number of concrete situations. 72 00:09:10,240 --> 00:09:14,590 It also draws inspiration from a number of concrete situations. 73 00:09:15,040 --> 00:09:21,130 So we have this kind of branching the real world going in many different ways to the abstract concept. 74 00:09:21,600 --> 00:09:28,889 I considered going back in many different ways to the real world. The full technique of looking, 75 00:09:28,890 --> 00:09:38,970 which are which are the frequencies in the given signal were first applied by Fujii to study the evolution of the heat in the material. 76 00:09:39,370 --> 00:09:42,509 So you had a piece of metal, you are heating some place. 77 00:09:42,510 --> 00:09:46,950 You want to know how the heat would propagate, how it would cooled down and so on. 78 00:09:48,090 --> 00:09:57,090 And it has been used to so many different things now we use for geneticists to study the songs of birds because it's a signal, 79 00:09:57,090 --> 00:10:02,910 even though so different from the signal for you we use for geneticists, for images. 80 00:10:03,150 --> 00:10:12,750 This is famous picture of beautiful Lena used in all studies of image processing and this is the beautiful fully transform of Lena. 81 00:10:13,170 --> 00:10:17,370 And this is used as a way to benchmark, to test, 82 00:10:17,370 --> 00:10:28,440 to communicate for geneticists is used worldwide whenever there is need of analysing and that is in the variations of the signal in the image. 83 00:10:29,340 --> 00:10:36,989 And it's used also in medical devices like this when you are having a scanner are amending and 84 00:10:36,990 --> 00:10:43,709 it's basically doing a free transform of your body and that's how you get some information. 85 00:10:43,710 --> 00:10:50,910 Then you have to play the full year formulas to invert the fully transform and get back to the information here. 86 00:10:50,910 --> 00:10:54,780 How to get back from the fully transformed to Lena. That's a mathematical problem. 87 00:10:54,780 --> 00:10:59,339 How to get back from your fully transform to the images of your your organs. 88 00:10:59,340 --> 00:11:05,010 That's also a problem. And this gets mixed with all kinds of new techniques. 89 00:11:05,010 --> 00:11:13,049 Of course, at the last, the International Congress of Mathematicians in World, there was plenary talk by Immanuel Kant, 90 00:11:13,050 --> 00:11:16,950 this French mathematician working in Stanford, 91 00:11:16,950 --> 00:11:29,459 specialist of what is called as various techniques related to machine learning, artificial intelligence, so to speak. 92 00:11:29,460 --> 00:11:32,340 And the sparsity here. 93 00:11:32,760 --> 00:11:45,120 And he explain how by working with people from some hospital humanas trying to write mathematical techniques based on free transform analysis, 94 00:11:45,660 --> 00:11:49,140 he was able to divide by eight. 95 00:11:49,290 --> 00:11:57,450 The time that takes somebody to be in the scanner to get the information collected with important consequences, 96 00:11:57,780 --> 00:12:00,810 in particular when it comes to curing children. 97 00:12:01,380 --> 00:12:13,500 And this is, of course, the blending of old phooey techniques with new techniques coming in this case from mixture of statistics, 98 00:12:13,500 --> 00:12:21,550 geometry, whatever, in one of these experiments, in one of these other parts of this of his talking can, 99 00:12:21,600 --> 00:12:33,750 this was describing as results of work he had done in collaboration with 3000 other people in which from a fully transform image of some organism, 100 00:12:33,760 --> 00:12:41,700 somebody you delete 98% of the information and still able to reconstruct it to such accuracy 101 00:12:41,700 --> 00:12:47,160 that you cannot distinguish the original and the modification with your bare eyes. 102 00:12:47,700 --> 00:12:53,700 So these are techniques that show how you can blend the old and the new mathematics in this and 103 00:12:53,700 --> 00:12:59,880 also show that it is constantly renewed to adapt to new constraints and goods and technologies. 104 00:13:00,450 --> 00:13:07,290 So that's for commenting on the status of the mathematical knowledge and the mathematical science. 105 00:13:08,250 --> 00:13:16,640 Now, this so far was a kind of rosy picture, but the life of a mathematician is not so rosy. 106 00:13:17,100 --> 00:13:21,750 It is suffering every day and failure every day. 107 00:13:22,410 --> 00:13:32,010 I remember very well our our common friend thinking of John Craig Evans from Berkeley saying 108 00:13:32,010 --> 00:13:37,319 exactly these words every day is a failure because you are searching and it doesn't work. 109 00:13:37,320 --> 00:13:47,100 It doesn't work and it doesn't work. And still, in the end, when you walk, when you look back, say, ten year period of ten years, 110 00:13:47,100 --> 00:13:51,600 you're amazed to see how much has been done and how much progress has been made. 111 00:13:52,230 --> 00:13:57,060 Let's because mathematics as any science is globally cooperative. 112 00:13:57,480 --> 00:14:02,969 And so there's a lot and a lot of progress done very fast through the joint efforts of everybody. 113 00:14:02,970 --> 00:14:07,680 But then the scale of the individual, it's permanent suffering, so to speak. 114 00:14:08,700 --> 00:14:15,870 Well, still, it is quite thrilling. If you do not have the suffering, then you are not happy to win. 115 00:14:16,530 --> 00:14:21,120 So here we are in the way that the typical way of working, thinking and. 116 00:14:21,150 --> 00:14:30,240 That's finding and waiting for plane carriage to whisper some height in our ears, you know, how will this occur? 117 00:14:31,140 --> 00:14:36,630 Sometimes there are these experiments in which the solution seems to be coming. 118 00:14:36,960 --> 00:14:45,570 Who knows from where? Ramanujan used to say that there was some goddess whispering to his ear during sleep or something. 119 00:14:46,080 --> 00:14:53,760 I personally experienced a couple of wonderful, wonderful things. 120 00:14:53,940 --> 00:14:59,730 One is I said in the book that they will describe in more detail later. 121 00:15:00,180 --> 00:15:13,320 So imagine that I was it was in Princeton and there I was some evening working alone, trying to fix some proof that doesn't work. 122 00:15:13,920 --> 00:15:21,030 I had already announced the result publicly, so I was under monster pressure to fix the damn proof. 123 00:15:21,030 --> 00:15:24,059 And there was this problem. Well, this problem comes from. 124 00:15:24,060 --> 00:15:27,120 I have to fix this one. The M. 125 00:15:27,450 --> 00:15:31,410 2 a.m. Three M nothing occurs. No solution. 126 00:15:31,920 --> 00:15:35,490 I in the end gets go to bed completely desperate. 127 00:15:36,030 --> 00:15:38,400 And in the morning just wake. What is it? 128 00:15:38,410 --> 00:15:46,470 And then there is in my in my in my brain really the voicing put the second term on the other side and take for you transform. 129 00:15:46,890 --> 00:15:50,160 And that was it. That was the beginning of the solution. 130 00:15:50,730 --> 00:15:58,050 So powerful is the unconscious brain, you know, continuing to work even through your thinking you have abandoned. 131 00:15:58,830 --> 00:16:02,309 Where does this come from? That's key problem. 132 00:16:02,310 --> 00:16:05,610 And we would pay a lot to know how to trigger this. 133 00:16:06,270 --> 00:16:11,990 Now, even when you have the good idea comes another problem, which is convince your colleagues. 134 00:16:14,160 --> 00:16:20,910 Books of both history of science are full of stories, tragic stories like Galois or able, for instance, 135 00:16:20,910 --> 00:16:26,130 of scientists who did not manage to convince their peers that they were looking in the right direction. 136 00:16:26,580 --> 00:16:31,860 This one is a symbol of something even more compelling. 137 00:16:31,860 --> 00:16:40,680 This is Ignaz Zimmer was the first one to understand the importance of cleaning for medical doctors. 138 00:16:41,040 --> 00:16:45,990 And, you know, if you're a medical doctor and you are doing a dissection of a corpse, 139 00:16:46,770 --> 00:16:55,290 and just later that day you are helping some woman to give birth, it's good to wash hands in the in between. 140 00:16:56,640 --> 00:17:05,490 Well, it looks like so obvious now, but it was not that the time would be tremendous death rates in the hospitals. 141 00:17:05,970 --> 00:17:15,660 And this guy just became crazy, literally trying and not managing to convince his colleagues about this, doing experiments, whatever. 142 00:17:16,080 --> 00:17:19,890 So this is an example, of course, science in the end, 143 00:17:20,220 --> 00:17:26,400 correct the mistakes and people understood it was all this movement about bacteria, about hygiene and so on. 144 00:17:26,910 --> 00:17:38,310 But it may be longer than at the scale of an individual and scientists who practice are not so much better than other people for changing ideas. 145 00:17:38,820 --> 00:17:47,969 Science is very good at changing theory, but scientists often get used to a theory and fall in love with it and are very 146 00:17:47,970 --> 00:17:51,840 reluctant when somebody tells them no know that's not the right way anyway. 147 00:17:52,170 --> 00:17:55,380 So convincing the peers is another of these obstacles. 148 00:17:55,890 --> 00:17:59,010 And then another thing that occurs to you. 149 00:17:59,100 --> 00:18:06,330 Another you will not see plague, but disease is the problem of people asking you to tell the future. 150 00:18:07,440 --> 00:18:13,980 It can be jollies. Can you profess to villain what will be mathematics in 2015? 151 00:18:14,790 --> 00:18:21,600 Wow. What the [INAUDIBLE] do I know? I don't answer this on the on the television, but sometimes I answer with this. 152 00:18:21,750 --> 00:18:24,600 Could my point, Caryn, before I read the could by Poincaré, 153 00:18:24,600 --> 00:18:31,620 let me say that it may be annoying when you have a journalist asking you to do this predicting job, 154 00:18:31,620 --> 00:18:34,709 but it's also annoying when it's a government or institution, 155 00:18:34,710 --> 00:18:44,220 for instance, asking you to justify for the use of the money that you receive and predicting what results you can prove in one year, 156 00:18:44,220 --> 00:18:47,430 two years, three years, four years, and so on. What do we know? 157 00:18:47,760 --> 00:18:56,700 Most of the good results will rise without you forcing it by surprise, and you should never try to try and predict too much. 158 00:18:57,240 --> 00:19:08,460 So here's his point, Kerry. Somebody some journalist is asking him now we are in 1900s what is the what will be the science of the 20th century? 159 00:19:09,150 --> 00:19:17,200 And Kerry answers, Monsieur, your letter is coming to me, arriving to me after some time. 160 00:19:17,700 --> 00:19:21,060 If in 1801. Had asked to. 161 00:19:21,260 --> 00:19:25,130 Any scientist what would be science of the 19th century? 162 00:19:25,670 --> 00:19:28,700 How much nonsense he would have said good. Heaven. 163 00:19:29,630 --> 00:19:33,020 This thought forbids me to answer. 164 00:19:33,800 --> 00:19:37,430 I think that surprising results shall be obtained. 165 00:19:38,240 --> 00:19:42,410 And that's precisely the reason why I cannot say anything about them. 166 00:19:42,950 --> 00:19:48,080 Because if I could foresee them. What surprise would there remain in them? 167 00:19:48,650 --> 00:19:58,730 So please excuse my silence. So this spring, a record they said they were with used, saying that you can never predict the future of the science. 168 00:19:59,330 --> 00:20:05,030 Now if you think a bit more and that will be the subject of the talk, 169 00:20:05,570 --> 00:20:14,090 I think that surprising results shall be obtained is more than just playing with the concepts and words. 170 00:20:14,090 --> 00:20:22,400 It is also asserting belief in the fact that there will always be inventive people 171 00:20:23,360 --> 00:20:29,360 discovering new things that they are teachers their masters have not predicted. 172 00:20:29,930 --> 00:20:34,160 And that point is the fundamental problem of higher education. 173 00:20:34,700 --> 00:20:42,830 Too many people in the audience, it is obvious. But let's we are said this the important thing of education and the problem of master and student 174 00:20:43,460 --> 00:20:50,330 is to train the student in such a way that he can have new ideas that the master did not have. 175 00:20:50,960 --> 00:21:00,980 So and I put on these slides some examples of people who, with just a few ideas, 176 00:21:02,330 --> 00:21:10,610 revolutionised story of 20th century and people that Poincaré could never have imagined the contributions 177 00:21:11,150 --> 00:21:16,820 or people who are emblematic of all these things which happened in the world of ideas of 20th century. 178 00:21:17,330 --> 00:21:20,360 I also put the picture of a university here. 179 00:21:20,360 --> 00:21:29,390 I'm sorry, I should have put Oxford when coming here, but I put a picture of famous university to remind of what they just said. 180 00:21:29,840 --> 00:21:36,950 What makes the value of the University of Ohio institution of something is not the fact that students there 181 00:21:37,220 --> 00:21:44,360 are told the best science of the day is the fact that the students will one day go out and do science, 182 00:21:44,360 --> 00:21:51,980 which is better than what they were taught that the principal problem, the most important and nobody really knows how to do this, 183 00:21:52,670 --> 00:21:58,010 but still we have to solve this problem here in the right it start with him. 184 00:21:58,100 --> 00:22:02,450 Alan Turing as we know it as the Hollywood movie around him. 185 00:22:03,020 --> 00:22:12,020 And Turing is remarkable and exemplifies first power of ideas, of course. 186 00:22:12,440 --> 00:22:20,690 And as we know, one of the main fathers of computer theory, but also how much it can change history. 187 00:22:20,930 --> 00:22:24,470 We know there was his role in Second World War. 188 00:22:24,950 --> 00:22:30,500 He was involved in the deciphering of the Enigma code, in particular the one for submarines. 189 00:22:31,130 --> 00:22:36,310 And when you read days and accounts of story there, the role of Turing and so on, 190 00:22:36,320 --> 00:22:42,800 it is clear first that there would not have been an efficient solution to solve this without his particular input. 191 00:22:43,250 --> 00:22:48,600 And second, that without this, the story of Second World War could have been completely different. 192 00:22:48,620 --> 00:22:52,640 In 1944, the Normandy event would not have been possible. 193 00:22:53,060 --> 00:22:56,750 The war would have lasted probably at least two more years. 194 00:22:56,750 --> 00:23:02,960 Anything was possible. It's amazing to think that during the four last years of the of the war, 195 00:23:03,350 --> 00:23:10,429 the Allied Coalition was able to read all the messages of the Germans, and still it was so darn difficult. 196 00:23:10,430 --> 00:23:14,870 So let's imagine what it would have been without that single idea. 197 00:23:15,830 --> 00:23:22,340 The to the left of Turing is Paul Elder, the most prolific mathematician of the 20th century, 198 00:23:23,090 --> 00:23:31,850 also emblematic of the fact that ideas and creativity to such a geopolitical issue, social issue. 199 00:23:32,330 --> 00:23:44,570 And there was a tremendous event also during Second World War, a huge, huge migration of ideas of the idea ecosystem from Europe to America, 200 00:23:44,900 --> 00:23:51,980 with all these very bright Jews who were expelled and their friends and laboratories coming and so on, 201 00:23:52,370 --> 00:23:57,170 some of them extremely dedicated, some of them changing the whole of science. 202 00:23:57,590 --> 00:24:07,489 If this was one of these and as according to the facts we know of his biography, there was this guy with no home, no family, 203 00:24:07,490 --> 00:24:18,230 apart from his mother, no possessions, no car, no job, nothing but a suitcase with a few belongings and ideas, ideas, ideas. 204 00:24:18,710 --> 00:24:27,420 And there were many like this during the. Wondering to have been changing the face of the world ecosystem of ideas during the 20th century. 205 00:24:28,320 --> 00:24:34,350 To the left of FDR, she's Leo Szilard, not so well known, but the key person. 206 00:24:34,350 --> 00:24:44,010 Also, during the same period, Silla was the first human being to have the idea of a nuclear chain reaction. 207 00:24:44,520 --> 00:24:48,870 And he told how this occurred. 208 00:24:49,850 --> 00:24:59,810 This was in London. You had read the account of a lecture by Rutherford, the father of atomic physics, the father of nuclear physics. 209 00:25:00,230 --> 00:25:07,040 And Rutherford was saying something like, Yes, there is some energy in the atom, but it's so tiny. 210 00:25:07,730 --> 00:25:14,510 Anybody who would want to extract something from it would be talking moonshine. 211 00:25:15,020 --> 00:25:20,690 I'd be a dreamer and so on. And Szilard was very annoyed by this and just by contradiction spirit. 212 00:25:20,690 --> 00:25:25,190 He wanted to prove him wrong. So thinking, thinking, thinking. 213 00:25:25,190 --> 00:25:32,630 No solution, no solution. And one day crossing the street and staring at some light, whatever green light becomes red. 214 00:25:33,410 --> 00:25:37,850 He was the idea chain reaction and he had the idea of the principle. 215 00:25:37,850 --> 00:25:44,329 And so this was 1933 and see how how this could could change things. 216 00:25:44,330 --> 00:25:51,709 Just at the time he had the he had the feeling he knew that German's physics, the most advanced of the time, 217 00:25:51,710 --> 00:26:00,620 was the best position to devise this weapon and so frightened that the idea would get into the wrong. 218 00:26:02,030 --> 00:26:07,700 This is the patent which Fermi and Szilard made for nuclear reactor. 219 00:26:08,240 --> 00:26:16,220 So Szilard also was the guy who wrote the letter for Einstein, the letter which was sent to the President of the United States, 220 00:26:16,640 --> 00:26:22,640 and in the end was the start of a program that involved more than 100,000 people. 221 00:26:23,090 --> 00:26:32,629 Just one idea at the beginning, and here we see on these examples, the power of ideas can be just one brain with the right configuration, 222 00:26:32,630 --> 00:26:39,800 and then it is multiplied by the power of collaboration in technology projects and scientific projects. 223 00:26:40,670 --> 00:26:50,060 So here are some of these people were in there is this element in some of the for instance, in the Szilard story, which I also already told, 224 00:26:50,780 --> 00:26:58,939 which is the fact that it's unpredictable when the illumination will come in science and research, 225 00:26:58,940 --> 00:27:04,429 we all notice the small illuminations, the big illuminations, all rippling carrying. 226 00:27:04,430 --> 00:27:09,080 The famous text wrote about some of his illuminations for which he was famous. 227 00:27:09,740 --> 00:27:16,250 In one of these stories he says he tells about like more emitted peaceful mashup here. 228 00:27:16,250 --> 00:27:21,620 That is when he puts the foot on the stairs. That is to come back in some bus. 229 00:27:21,920 --> 00:27:31,520 Then comes the elimination. And there was nothing related to the to the problem he was striving to solve in this bus. 230 00:27:31,760 --> 00:27:36,380 But just the idea was there as he was doing something completely different. 231 00:27:37,340 --> 00:27:40,850 Here is another passage of the same point. Read text. 232 00:27:41,420 --> 00:27:49,580 Disgusted by my failure, I went to spend a few days on the seaside thinking something completely different. 233 00:27:51,120 --> 00:27:53,970 One day while walking on the cliff. 234 00:27:54,510 --> 00:28:05,549 The idea came to me always with the same features very brief, sudden and immediate certainty that arithmetic trends, 235 00:28:05,550 --> 00:28:12,810 forms of indefinite ternary quadratic forms are identical to those of non-Euclidean geometries. 236 00:28:13,980 --> 00:28:18,000 A few remarks on this. So this is part of a long text about it. 237 00:28:18,750 --> 00:28:28,830 First, even for people in the audience who don't know about quadratic forms, they see that there is nothing comparable to walking on the cliff. 238 00:28:30,420 --> 00:28:40,020 So in some popular representation, there are these ideas of the eureka moment coming, like when you have this guy Archimedes in his bath. 239 00:28:40,020 --> 00:28:44,340 And then the idea for the for the Archimedes thrust on Newton. 240 00:28:44,610 --> 00:28:47,889 The apple in this legend. And then the idea for gravitation and so on. 241 00:28:47,890 --> 00:28:52,290 And the idea being triggered by something which has some relation with the problem. 242 00:28:53,490 --> 00:28:57,470 These are usually legends. Here it is completely different. 243 00:28:57,480 --> 00:29:03,810 There is no relation whatsoever between the grief and the illumination just taking you by surprise. 244 00:29:04,000 --> 00:29:11,790 And that's often the case. The second is that Frank insists on the fact that he's further disgusted by his figure, 245 00:29:11,790 --> 00:29:19,920 which means long period of working hard on the problem, then making a break, and then the rosy illumination. 246 00:29:20,610 --> 00:29:26,849 The process described by Poincare is not pure work, not pure illumination. 247 00:29:26,850 --> 00:29:37,560 It's alternating between both. And that's also typical, I guess, by the way, I see there are some young people listening. 248 00:29:38,100 --> 00:29:49,470 If someday, you know, you have this big math exam to prepare and you need to go and meet your friends at the pub some evening, 249 00:29:49,530 --> 00:29:54,180 you can tell your parents you're playing the point. I remember to think that. 250 00:29:58,720 --> 00:30:06,230 And maybe it will work fine, especially if you say it was told to you by the French professor anyway. 251 00:30:06,850 --> 00:30:18,490 So the final remark on the text is that here, when Kerry put the big words without explanation and he says in the text, 252 00:30:18,610 --> 00:30:22,660 they will be technical words, but don't worry, you don't need to understand them. 253 00:30:22,690 --> 00:30:29,500 Only the circumstances matter. And I think that's one of the reasons why the text was successful if plan Kerry had tried to expand it. 254 00:30:29,830 --> 00:30:33,969 Okay, let's do it slowly. We'll explain to you what is required to form that. 255 00:30:33,970 --> 00:30:37,200 A ternary cratic form. What is it? Indefinite. I will explain you. 256 00:30:37,210 --> 00:30:44,890 What is the new code in geometry and so on? So much of the audience would have been lost even if Kerry was very pedagogical, 257 00:30:44,890 --> 00:30:49,870 and the important fact, which is the elimination woman, would be buried in those explanations. 258 00:30:50,260 --> 00:30:57,520 So the fact that Poincaré put the technical word without explanation, I think was important in the success of this writing. 259 00:30:58,510 --> 00:31:10,209 And I did the same in my book to identify Living Theorem before the theorem, actually, without being aware of it, is another instance of these. 260 00:31:10,210 --> 00:31:21,400 I knew the Poincare text, but while writing the book I did not realise he was applying to larger scale the same technique as Poincare. 261 00:31:21,880 --> 00:31:23,410 It looked natural to me, you know. 262 00:31:23,800 --> 00:31:31,720 We also knew this in mathematics very often that there is some guy coming and telling us, I have this great idea, let's do this and this. 263 00:31:31,720 --> 00:31:34,780 And you tell him, yes, that's what I explained to you when? 264 00:31:34,780 --> 00:31:40,810 Months ago, because you hear something and then you appropriate it to itself. 265 00:31:41,530 --> 00:31:49,960 So for the record, by the way, when I wrote the book, the my original title was this Don't You? 266 00:31:49,990 --> 00:31:55,389 Hammer and French publisher were not so happy. 267 00:31:55,390 --> 00:31:58,910 They said, it's too explicit. Let's do something bit more mysterious. 268 00:31:58,930 --> 00:32:03,760 Anyway, we had a discussion and they came out with this one and he said, That's good. 269 00:32:04,540 --> 00:32:12,129 And then it was to the English publishers, and the English publisher said, Oh, to him, you know, you know, it's a bit mysterious. 270 00:32:12,130 --> 00:32:19,530 We don't understand. And so they came back and said, Why not before the CRM? 271 00:32:19,680 --> 00:32:28,290 They said, okay, let's do it. But the subtle details are always interesting when you go in the translations. 272 00:32:28,830 --> 00:32:32,350 Anyway, in this book it's exactly the same. 273 00:32:32,350 --> 00:32:40,470 I focussed on the circumstances. Nowadays there are very fine books about explaining about mathematics. 274 00:32:40,860 --> 00:32:47,640 What is a science developed like? What's a theory, doing the history of the subject and so on. 275 00:32:48,240 --> 00:32:56,729 But here I wanted something complementary with the daily life of a mathematician in his struggle, in the emotions. 276 00:32:56,730 --> 00:33:01,170 And actually it was not my idea initially. It was because I met that other publisher. 277 00:33:01,620 --> 00:33:07,590 This was in some dinner. This was before the feed's middle. 278 00:33:07,980 --> 00:33:12,750 And the guy was saying, okay, why don't we try and publish a book together and so on. 279 00:33:13,170 --> 00:33:17,309 Okay, I have ideas. I could write a book on entropy. 280 00:33:17,310 --> 00:33:22,260 I am supposed to be one of the world experts. There are all these. It's fascinating, it's important and so on. 281 00:33:22,650 --> 00:33:29,670 He didn't care the least, and the only thing he cared was, But what is it to be a mathematician? 282 00:33:29,850 --> 00:33:36,600 What do you do? What do you seeing? How do you work? And so on. And so I was embarrassed how to describe this. 283 00:33:37,080 --> 00:33:43,860 And then I thought after we spend part of our time explaining kids and so on, that science is an adventure. 284 00:33:44,220 --> 00:33:47,070 So let's write it as a novel, as an adventure. 285 00:33:47,610 --> 00:33:55,590 So I took a theorem of mine, a theorem charged with lot of emotion, theorem, which had been a difficult story. 286 00:33:56,010 --> 00:34:01,940 And I wrote how it was the genesis of the theorem like adventure novel. 287 00:34:01,950 --> 00:34:07,559 But everything in there was true. And so that's what is behind the singularity. 288 00:34:07,560 --> 00:34:15,090 When we talk of a theorem, it's after publication and one's the theorem is ready to walk and to be used. 289 00:34:15,690 --> 00:34:22,650 But all the process that is before that the life of the researcher, the mathematician, goes behind the scenes. 290 00:34:23,010 --> 00:34:28,710 And that's a long process and how you're going to look for it. 291 00:34:29,400 --> 00:34:36,300 What will you be trying to prove? This also is important and this is part of what you learn with the experience. 292 00:34:36,810 --> 00:34:44,940 So the first chapter of the book is, I like to say, is like for conviction as a discussion between me and my former student, 293 00:34:44,940 --> 00:34:48,900 Clement Wolf, and the main collaborator at the time. 294 00:34:49,350 --> 00:34:58,739 And we are discussing about some problem and in the discussion because he remembers some conversation from two years before with somebody. 295 00:34:58,740 --> 00:35:02,280 I remember another conversation from somebody else from last year. 296 00:35:02,610 --> 00:35:07,200 We put this together and said, but this maybe has to do with the land of dumping. 297 00:35:07,290 --> 00:35:10,529 It was completely not our subject initially. 298 00:35:10,530 --> 00:35:14,009 It was not what we wanted to work on was different. 299 00:35:14,010 --> 00:35:17,250 But then we said, okay, let's try. It was coincidence. 300 00:35:17,370 --> 00:35:23,669 Let's try and go for it. And then so long story first decide which is a statement. 301 00:35:23,670 --> 00:35:28,530 We're going to prove how it's related to physics, how are we going to change it, and so on. 302 00:35:28,920 --> 00:35:31,650 Two years and a half in various places, 303 00:35:32,700 --> 00:35:42,060 large part of it why I'm in Princeton and he's in Paris and communicating by email many times in which we are making mistakes occurring many, 304 00:35:42,210 --> 00:35:49,950 several quality at several times in which there is conversation with somebody that takes us out of the predicament and so on. 305 00:35:49,950 --> 00:35:55,169 And so I told this all in impressionistic way, like this difficulty, 306 00:35:55,170 --> 00:36:01,620 the difficulty how we solved it and so on, and also with all the environment, how we do it. 307 00:36:01,620 --> 00:36:11,309 So there is a description of that night that you are spending alone with your cup of tea and working and working endless computations. 308 00:36:11,310 --> 00:36:17,100 But there's also that moment in which you are discussing with your colleague and the colleague doesn't agree with you, 309 00:36:17,100 --> 00:36:18,630 and this would give you a new idea. 310 00:36:18,990 --> 00:36:24,780 Or there is a moment in which your first attempt of publication gets rejected and you are reading the rejection letter. 311 00:36:24,780 --> 00:36:31,290 And so suicide. Or there's the moment in which you are putting everything together and you are so excited and so forth. 312 00:36:31,290 --> 00:36:37,920 That's the life that the real life of a mathematician and as the lives of all other human beings, it's full of emotions. 313 00:36:38,670 --> 00:36:43,950 Also, I put the formulas straight and as they were in the language as it is. 314 00:36:44,550 --> 00:36:52,800 So the object, which is the theorem, which is the hero of the book because we are witnessing the way it develops into something organised 315 00:36:52,980 --> 00:36:58,680 start from chaos becomes organised little by little in such a way that you can publish it in the end. 316 00:36:59,070 --> 00:37:09,540 And so we are witnessing the various stages with extracts of the paper, with scribblings, with formulas and so on, and it was a bit of a gamble. 317 00:37:10,050 --> 00:37:14,130 There is this famous quote by Hawking, Stephen Hawking saying. 318 00:37:14,760 --> 00:37:18,450 Well, actually, advice from his editor don't put any formulas. 319 00:37:18,480 --> 00:37:26,610 Each formula will divide by two the number of readers. If the rule was really true, there would not have been a single reader for the book. 320 00:37:27,570 --> 00:37:31,020 Maybe a few molecules of reader someplace. 321 00:37:31,500 --> 00:37:40,560 Given the amount of formulas which I put, some readers told me to spend as much time reading the formulas as reading the text. 322 00:37:40,710 --> 00:37:46,860 Just contemplating, by the way, that the first one of the first book I am aware of, 323 00:37:46,860 --> 00:37:53,250 which has been entirely for Bruno Jensen, 30 Typesetting in Tech, maybe a little. 324 00:37:53,790 --> 00:37:59,910 Did you write books in tech? No. So this was this was quite an experiment. 325 00:38:00,540 --> 00:38:11,340 Anyway, what is the story which I told before that let me mention that near the publication of the book, in which, as I said, the hero is the theorem. 326 00:38:11,820 --> 00:38:15,570 I became aware of this amazing book by Francis before. 327 00:38:15,630 --> 00:38:27,360 I guess he's a Cambridge scholar read plenty in which, in his own words, the hero is an idea and that ideas mathematical pontification of economy. 328 00:38:27,840 --> 00:38:34,350 And we see through it the story of the Soviet economy from the boom of the fifties to the collapse of the nineties. 329 00:38:34,350 --> 00:38:35,070 Let's see here. 330 00:38:35,400 --> 00:38:45,540 And here it is told in such a way that we see the idea interacting, the abstract idea interacting in many ways with the humans and the times. 331 00:38:45,540 --> 00:38:50,309 It works beautifully at times. It's a disaster in control of each one of my personal heroes. 332 00:38:50,310 --> 00:38:54,740 It goes to the first hero of the of the book and the hero. 333 00:38:54,750 --> 00:39:00,210 So there was this idea that there is this idea and see it's interference with the world of humans. 334 00:39:00,840 --> 00:39:04,600 No. A little bit. Just a little bit of mathematics. 335 00:39:04,620 --> 00:39:08,489 What is it that we proved, by the way, which I learned? 336 00:39:08,490 --> 00:39:13,490 Which time should I aim at stopping? Okay. 337 00:39:13,490 --> 00:39:21,740 Super. So in the book, we are working on the premise of mathematical physics and problems related to plasma physics. 338 00:39:22,400 --> 00:39:25,940 Problem is about stability. Problem is about relaxation. 339 00:39:26,390 --> 00:39:29,870 Stability is such an important property in the world. 340 00:39:30,290 --> 00:39:36,049 And we are we have every kind of stability arises around us. 341 00:39:36,050 --> 00:39:38,780 But the most important are the ones coming from friction. 342 00:39:40,460 --> 00:39:52,790 We learn in school here about the rules of Galileo that if there is a ball and you kick this ball, we go on forever straight with constant speed. 343 00:39:53,390 --> 00:39:58,550 Of course you do the experiment cross and of course the ball starts after a few metres. 344 00:39:58,910 --> 00:40:04,700 So what you are being taught in school is false? Well, it's because of the friction. 345 00:40:04,700 --> 00:40:09,050 And friction is mostly powerful force for stability. 346 00:40:09,770 --> 00:40:12,889 Friction is related to irreversible phenomena. 347 00:40:12,890 --> 00:40:19,220 Phenomena in which something is dissipated like you are hitting something in the heat is cooling down and 348 00:40:19,640 --> 00:40:26,629 all kinds of phenomena in which there is something which doesn't go very perfectly or not perfectly at all. 349 00:40:26,630 --> 00:40:31,190 Something is lost. Some information is lost. Disorder is increasing. 350 00:40:31,190 --> 00:40:38,239 Entropy is increasing. As a physicist see at all scale, there is another powerful force of stability. 351 00:40:38,240 --> 00:40:47,750 The fact that we are all feeling the extraction of the earth, keeping us down in place when by the end we saw it when there was this. 352 00:40:47,840 --> 00:40:52,490 What was it like? Landed on this asteroid some time ago. 353 00:40:52,790 --> 00:40:58,700 Almost no gravity made it so unstable, slumped at crazy distances from the asteroid. 354 00:40:59,450 --> 00:41:03,349 But now in gas, there is some analogue of the friction. 355 00:41:03,350 --> 00:41:09,770 There is this phenomena of increase of entropy in which I worked and many people worked a theoretical or practical level. 356 00:41:10,220 --> 00:41:21,290 But the plasma is like a miraculous, perfect, perfect state of matter in which there is no friction and nothing irreversible, almost nothing. 357 00:41:21,890 --> 00:41:29,840 Plasma is when you have imposed such conditions that the electrons have been ripped away from the nuclei. 358 00:41:30,350 --> 00:41:36,170 These electrons, they interact with the good old rules like they are negatively charged. 359 00:41:36,500 --> 00:41:37,720 So they repair each other. 360 00:41:37,730 --> 00:41:47,990 They are very light, so they move very quickly and it it's important, technologically speaking and theoretically to understand how plasma works. 361 00:41:48,800 --> 00:41:56,270 So it's a problem which is grounded in physics. And even though there is no entropy increase, 362 00:41:56,570 --> 00:42:06,139 Landau in the forties suggested that there was some stability mechanism there and he argued using the Vlasov equation, 363 00:42:06,140 --> 00:42:15,410 which is at the basis of plasma physics. So where a physicist can see all these beautiful different states for plasma mathematician, 364 00:42:15,410 --> 00:42:23,720 we see that primarily it's this beautiful equation and that the equation you have to work on to understand this stability. 365 00:42:24,410 --> 00:42:30,950 It's the same equation, by the way, which is used in galactic dynamics and also in certain instances of true dynamics. 366 00:42:31,370 --> 00:42:35,600 So the same problems of stability arise in these areas. 367 00:42:36,350 --> 00:42:43,250 And to convince people not to use mathematical reasoning and the good old for you transform in particular. 368 00:42:44,030 --> 00:42:49,130 And most of all he use the linear approximation equation is not linear, 369 00:42:49,550 --> 00:42:58,010 but simplify it and turn it into a so-called linear equation in which the response is always proportional to the impact, roughly speaking. 370 00:42:59,210 --> 00:43:08,150 And is it true that the Landau reasoning applies to the real world, to the real plasma? 371 00:43:08,180 --> 00:43:16,700 This was not clear. Even there were arguments to suggest that this was force and there was some debate, some fixing. 372 00:43:16,700 --> 00:43:25,880 Yes, the no mathematicians are like and this is this problem particularly that we solved with claim on showing that yes, 373 00:43:26,090 --> 00:43:31,130 the result the reasoning of Londo does work for the nonlinear equation also. 374 00:43:31,670 --> 00:43:41,329 But then this was quite more difficult in the linear than the linear case, where the linear case is couple of pages of computation. 375 00:43:41,330 --> 00:43:53,080 The nonlinear took us something like 150 page of reasoning and proofs and, and competition and most of all demanded new ideas. 376 00:43:53,120 --> 00:44:01,520 So what is it that the mathematician can do with physics problems, even with physics problems which are known experimentally to hold, 377 00:44:01,970 --> 00:44:09,020 is to suggest to new interpretation and to make connection connections between various fields. 378 00:44:09,380 --> 00:44:17,360 These are one of the most powerful things. Mathematicians can finding the abstract links and in particular and this was a great 379 00:44:17,360 --> 00:44:22,340 surprise because neither Kremen nor I had any suspicion of these connections. 380 00:44:22,730 --> 00:44:33,650 We find that the stability problem of the plasma by Londo was related to the stability problem of the solar system, 381 00:44:33,800 --> 00:44:38,210 in particular in the version suggested by Kolmogorov in the 1950s. 382 00:44:38,720 --> 00:44:44,750 And the paradox, according to which sometimes something like a solar system behaves very well, 383 00:44:45,260 --> 00:44:51,980 like planets will never collide, even though there is no physical rule to force them to behave well. 384 00:44:52,850 --> 00:45:02,120 And also was related to a famous experiment done by Muhlenberg at Al-Quds, the plasma eco beautiful experiment. 385 00:45:02,600 --> 00:45:10,670 You send some pulse electric poles in the plasma, so there will be some electric field created by the electric pulse. 386 00:45:11,180 --> 00:45:15,590 And then you let the electric field behave as it wishes. 387 00:45:16,070 --> 00:45:18,050 It will be done spontaneously, 388 00:45:18,500 --> 00:45:27,590 after which time you send the second electric pulse at a different frequency and let it behave and vanish and then do nothing. 389 00:45:27,980 --> 00:45:31,700 And you will measure a spontaneous response of the plasma one. 390 00:45:31,700 --> 00:45:35,990 It was quiet. This is true that plasmas are slightly weird objects. 391 00:45:36,500 --> 00:45:40,970 It also shows that plasma reacts with delay to some stimuli. 392 00:45:41,390 --> 00:45:46,820 And this delay, we found, was crucial to explain why it still worked in the nonlinear world. 393 00:45:47,300 --> 00:45:56,690 So the connection between these three paradoxical statements, the contributions of long, dark and forgotten man bed was a crucial insight of us. 394 00:45:57,470 --> 00:46:02,660 And I told you the story in a few minutes is plain words. 395 00:46:03,170 --> 00:46:09,110 This before that the world two years and a half of struggle and efforts and coincidences. 396 00:46:09,530 --> 00:46:11,600 The relation with Kolmogorov, by the way, 397 00:46:12,140 --> 00:46:20,330 the first one who suggested this was my colleague Images du Mehta from Lille after hearing me discussing with some 398 00:46:20,330 --> 00:46:27,860 colleague about related facts and the reason why he had this idea that there was a relation was totally wrong. 399 00:46:27,950 --> 00:46:31,279 I mean, he saw some pictures on my on the desk. 400 00:46:31,280 --> 00:46:39,440 He said, Yeah, this reminds me of the chronograph thing. But the drawing that they had done was precisely the case in which did not work. 401 00:46:40,730 --> 00:46:47,809 See these kind of coincidences. But in research it's important to be able to recognise when you have a piece of luck. 402 00:46:47,810 --> 00:46:54,560 And so I thought, okay, let's see if we can understand this took me one year to understand just the link and so on. 403 00:46:55,220 --> 00:47:00,620 Let's conclude by. Commenting on the list of the ingredients. 404 00:47:01,250 --> 00:47:05,890 Basically, everything I took so far was just the inspiration is important. 405 00:47:05,900 --> 00:47:09,230 Yes, it's that makes all the difference. But who knows how it comes? 406 00:47:09,890 --> 00:47:12,049 We don't know how the solution come to you, 407 00:47:12,050 --> 00:47:19,790 but we know the ingredients that are important and they will be seven ingredients which are so important in this job and these seven ingredients. 408 00:47:20,240 --> 00:47:25,400 We all have an important place in the tale. The first is documentation. 409 00:47:25,940 --> 00:47:30,589 Documentation can be the all libraries can be the virtual libraries and so on. 410 00:47:30,590 --> 00:47:36,740 But there is no such thing as a mathematician working from scratch without any knowledge of the past. 411 00:47:37,430 --> 00:47:47,280 I put the bonus formula here because it was detailed, but something typical of the New Deal posed by the actual information at some point in the work. 412 00:47:47,300 --> 00:47:51,590 We need a formula for accurate derivatives of the composition of functions. 413 00:47:52,100 --> 00:47:55,220 And I think, gosh, I think there's a formula. 414 00:47:55,250 --> 00:47:59,780 Maybe 15 years ago I had something like this in my studies. 415 00:48:00,200 --> 00:48:04,460 No idea what the formula was called. No idea where to look for it, whatever. 416 00:48:04,910 --> 00:48:13,700 But then with search engine in a few seconds and the right keywords get the formula, the history, the range of application, anything you want. 417 00:48:14,180 --> 00:48:21,650 So this is a new idea in the sense that getting or finding the information, when you have the idea, what you're looking for is not a problem. 418 00:48:22,010 --> 00:48:27,860 But still you need to have the right ideas and it changes the way we we live with this. 419 00:48:27,860 --> 00:48:33,740 But still, these libraries, all these results of experiments and so on are so important. 420 00:48:34,130 --> 00:48:40,070 Constructions from the first the second ingredient is probably the most important, but is the most elusive. 421 00:48:40,070 --> 00:48:44,360 It's the motivation. Nobody knows how people are motivated. 422 00:48:44,870 --> 00:48:50,330 Sometimes it's true that they have this inspiration from a book that they read when they are a child. 423 00:48:50,750 --> 00:48:53,809 Here I put a picture of Donald in Magic Land. 424 00:48:53,810 --> 00:48:57,799 I was watching this when I was a little kid. I saw it much later. 425 00:48:57,800 --> 00:49:03,980 I thought, Wow, is this naive? But still, I found it so fascinating. 426 00:49:04,040 --> 00:49:07,490 Maybe this had a great influence in me becoming mathematician later. 427 00:49:07,790 --> 00:49:15,200 Sometimes it's a teacher. It is not that all the career of Alan Turing was inspired from the book he read when he was ten years old. 428 00:49:15,320 --> 00:49:23,870 Natural Wonders Every Child Should Know. So this is the power of impressing, impregnating the brain of young children sometimes. 429 00:49:24,650 --> 00:49:33,620 And all countries in developed or developed countries currently are striving for this because they see motivation, 430 00:49:33,620 --> 00:49:37,159 lack of motivation as the main threat on science. 431 00:49:37,160 --> 00:49:43,280 Nowadays, if not enough young people do it, then who is going to make science? 432 00:49:43,640 --> 00:49:51,410 And that's why many people are working beautiful books of popularising science and also some pedagogical experiments are being conducted. 433 00:49:51,410 --> 00:50:02,750 Here's one blackout on bees done in the den in London with the with the researcher working with kids, ten year old children, 434 00:50:03,050 --> 00:50:08,990 8 to 10 year old children from school on some scientific experiment which was published 435 00:50:08,990 --> 00:50:14,059 in Biology Letters on animal behaviour showing that you can do science even when your 436 00:50:14,060 --> 00:50:19,459 nine year old principal finding we discovered that bumblebees can use a combination of 437 00:50:19,460 --> 00:50:24,320 colour and spatial relationships in deciding which colour from what to forage from. 438 00:50:24,800 --> 00:50:31,880 We also discovered that science is cool and fun because you get to do stuff that no one has ever done before is cute, right? 439 00:50:32,480 --> 00:50:39,469 Usually it is said that the principal findings should be something completely new, but on this particular example, it's a principal finding. 440 00:50:39,470 --> 00:50:44,090 It's important that people discover and rediscover and motivation. 441 00:50:44,450 --> 00:50:51,080 When you think of when you have a big achievement to make monster obstacles to solve a scientist. 442 00:50:51,090 --> 00:50:54,560 If you don't have enormous motivation, you just don't do it. 443 00:50:55,400 --> 00:50:58,280 The third is the ecosystem, the environment. 444 00:50:58,910 --> 00:51:05,620 Whenever in story of mankind, you look for the places where innovations are made and that sometime, you know, 445 00:51:05,870 --> 00:51:11,929 Persepolis, the most innovative city in the world, sometimes it's Paris, sometimes London, sometimes it's Budapest. 446 00:51:11,930 --> 00:51:15,530 Whatever the it's always an environment. 447 00:51:15,530 --> 00:51:18,979 It's not single individuals. And that's your problem. 448 00:51:18,980 --> 00:51:19,430 Also, 449 00:51:19,430 --> 00:51:29,480 when you are directing an Institute of Research I'm been director of Security Plenary for five years and have no problems to maintain the ecosystem. 450 00:51:29,690 --> 00:51:33,710 You are within an ecosystem, in this case Paris higher education ecosystem, 451 00:51:34,040 --> 00:51:41,720 but you're maintaining the small ecosystem inside so that the conversation and so on will trigger the new direction of research. 452 00:51:41,810 --> 00:51:46,940 As it triggered the start of the project I was talking about and learned out the MP. 453 00:51:48,230 --> 00:51:55,700 The next ingredient is the exchange when the birth of the new project is mainly ecosystem mixing. 454 00:51:56,270 --> 00:51:59,280 But when you are started your. Project and you are working on it. 455 00:51:59,300 --> 00:52:07,090 It may be that it's two individuals or three individuals, a small number, and then the communication between them can be a matter of vital importance. 456 00:52:07,100 --> 00:52:16,070 In my case was. Most of it was done by email as we were on the two sides of the Atlantic with emails every day. 457 00:52:16,340 --> 00:52:22,430 And in the end, it's like you have these two brains working together, and it's more than just the sum of the two. 458 00:52:22,730 --> 00:52:25,880 It's like a localised brain. 459 00:52:26,690 --> 00:52:31,339 Tim Gowers made these extraordinary experiments putting must project in which 460 00:52:31,340 --> 00:52:36,440 hundreds of mathematicians collaborate together on a single on a single problem. 461 00:52:37,010 --> 00:52:40,720 Is this a direction of research for the future? 462 00:52:40,730 --> 00:52:49,040 Future way to do research? Is it an experiment which also is interesting in itself, in the way that decision process is organised and so on? 463 00:52:49,370 --> 00:52:56,780 Who knows? But for sure it is interesting and shows new possibilities from communication by technologies. 464 00:52:57,560 --> 00:53:00,800 The next ingredient which is so important, is constraint. 465 00:53:01,370 --> 00:53:10,519 So it looks like paradoxical to see that constraints are important to creativity and research, but it soudan important in mathematics. 466 00:53:10,520 --> 00:53:19,160 We live with this constant constraint of having something totally rigorous, and if there is one mistake, some praise, the whole proof will fall down. 467 00:53:19,910 --> 00:53:24,220 And we need, of course, the rigour and so on. But it's not. 468 00:53:24,230 --> 00:53:31,070 And it's no accident that mathematics is also a feeling which creativity so extraordinarily valued and praised. 469 00:53:31,910 --> 00:53:41,180 To take an analogy, poetry is a form of art in which constraints are monster in all kinds of of cultures, 470 00:53:41,180 --> 00:53:45,440 and still in which creativity and imagination is too much valued. 471 00:53:46,010 --> 00:53:49,460 Here are two examples coming from other arts. 472 00:53:49,850 --> 00:53:57,649 One example from music in which a crazy constraint imposed on himself by Ligeti to write a short piece in which the only key, 473 00:53:57,650 --> 00:54:07,040 the only note is a path from the very last one forces him to do all kinds of variations and the rhythm and the on the strength and so on. 474 00:54:07,220 --> 00:54:16,310 You don't get bored at all. But by listening to this piece, which is only made of A's, and the other one is this famous book by of Perec, 475 00:54:16,700 --> 00:54:21,440 in which there is no each letter e has disappeared, even though this is a thick novel. 476 00:54:21,770 --> 00:54:29,300 And of course the language in there doesn't resemble that of any other book written in French language, very particular. 477 00:54:30,200 --> 00:54:35,120 And you have to find all these creative solutions to to go around the constraint. 478 00:54:35,570 --> 00:54:41,959 Next ingredient are we talked about but let's recall it explicitly is a mixture of hard work, 479 00:54:41,960 --> 00:54:47,180 systematic and elimination coming at some point which Poincaré described so well. 480 00:54:48,140 --> 00:54:55,190 And final ingredient is tenacity because it's always almost always wrong. 481 00:54:55,190 --> 00:54:58,850 And you throw your efforts in the in the dustbin. 482 00:54:59,390 --> 00:55:05,780 With tenacity comes luck. We come together and you need some luck to do the good things. 483 00:55:05,900 --> 00:55:09,770 Most importantly, to be able to recognise when you do have some luck. 484 00:55:10,460 --> 00:55:14,850 So this makes a lot of ingredients and that's why it's very precious. 485 00:55:14,890 --> 00:55:23,940 These ideas when they come into shape, it's cute this nice you maybe some people know this electronic drawing and I carrot. 486 00:55:24,740 --> 00:55:32,620 This is what you are taught at school about how things work. Well, let's make the hypothesis, experiment, conclusion, whatever. 487 00:55:33,230 --> 00:55:36,240 Think it's not the way it works in practice. 488 00:55:36,540 --> 00:55:47,180 Practice is like this and you won't always find that someone did do science instrument breaks not expect the amazing results turn out to be crap. 489 00:55:47,540 --> 00:55:50,779 What the [INAUDIBLE] is going on? Thinking yes. 490 00:55:50,780 --> 00:55:58,310 No. Yeah, that's funny. This makes sense. They figured this out 50 years ago and then realise again and again. 491 00:55:58,970 --> 00:56:08,450 So here the cartoonist made this great job of describing the experiment, the experience of one scientist. 492 00:56:08,450 --> 00:56:15,860 But to get a more accurate picture, multiply this by the number of scientists and make all kinds of intertwining 493 00:56:16,130 --> 00:56:19,910 together because these are all these stories or sort of interactions together. 494 00:56:19,910 --> 00:56:29,090 It's a very chaotic and confused process from which has to come out something very rigorous and very sound. 495 00:56:29,570 --> 00:56:37,580 That's tricky and that's the beauty of it. And two quotes to conclude about the nature of ideas, 496 00:56:37,580 --> 00:56:43,250 how precious they are and what we should regard that we should consider them first is by Jefferson. 497 00:56:43,700 --> 00:56:50,660 Jefferson is so useful because whenever you have an argument about intellectual property with some American, 498 00:56:51,740 --> 00:56:57,320 because he's a founding father, you are quoting Jefferson and he can say nothing against this. 499 00:56:58,200 --> 00:57:05,430 So what those deficiencies, if nature has made any seem less susceptible than all others of exclusive property, 500 00:57:05,940 --> 00:57:11,670 it is the action of the thinking power called an idea which an individual may exclusively possess. 501 00:57:12,090 --> 00:57:14,220 As long as he keeps it to himself. 502 00:57:14,670 --> 00:57:22,230 But the moment it is divulged, it forces itself into the position of everyone, and the receiver cannot dispossess himself of it. 503 00:57:22,800 --> 00:57:29,250 Its peculiar character, too, is that no one possesses the less because every other possesses the whole of it. 504 00:57:29,250 --> 00:57:35,280 He who we see tonight here from me receives instruction himself without listening mind, 505 00:57:35,760 --> 00:57:41,010 as he who likes his tapered mind receives light without darkening me. 506 00:57:41,700 --> 00:57:44,840 In those days, politicians did speak to their own country. 507 00:57:47,010 --> 00:57:56,790 This is for playing carried the last word. A thought is like a lightning strike in a long night. 508 00:57:56,790 --> 00:57:59,999 But it is this lightning, which is everything. 509 00:58:00,000 --> 00:58:01,980 And with this, I will conclude. Thank you.