Cedric Villani: The Hidden Beauty of Mathematics | Spring 2017 Wall Exchange

[Music] [Music] bonsoir Madame Monsieur je m'appelle slipped off tell Cecilia director the Institute is it to Devon say Peter was on a tray count on civil war surveillance e for the world exchange just to have a Caprice a mood round are no poor practice appearing soiree - orange to be stimulants keep Prabhakar love affliction good evening ladies and gentlemen my name is Philippe hotel I'm the director of the Peter wall Institute for Advanced Studies the Institute was founded 25 years ago to promote high-level interdisciplinary scholarship on questions of critical importance to society one of our main goals is to bring high-level debate and discourse into the public realm and the wall exchange lecture series was established a number of years ago to do just that and tonight I believe that you will see a wonderful example of the kind of engagement we seek to foster at the Institute I would like to thank first our sponsors for the evening the Pacific Institute of mathematical sciences PIMs the Georgia Strait and the taiyi and of course I would very much like to thank the band the straitjackets Jerry Bowie on trumpet and attack on guitar rod McDonald on bass Johnny boogies a gown drums and our very own distinguished Peter wall professor Brett Finlay on saxophone and clarinet and many other instruments that he didn't bring with him tonight the evening for tonight's presentation rather the format for tonight's presentation will be as follows Professor cédric Villani will give a 40 minute presentation and that will be followed by a question and answer period moderated by Professor Peter Klein professor cédric Villani is the director of the Institute Alvie point out here which is France's premier and oldest Institute for Research and mathematical sciences professor Valenti has received many mathematical awards including the Fields Medal in 2010 which is often considered the most prestigious award for mathematical research professor Valenti is a specialist of mathematical analysis applied to problems of statistical physics geometry and probability and his books on gas theory an optimal transport had become classics in their field beyond professor Delaney's outstanding contributions to mathematical research he has also made a huge impact on the world as the self-appointed ambassador of mathematics he speaks with eloquence passion and humor on the importance of mathematics in our everyday life and he draws inspiration from that field that he shares generalists generously with many around the world Peter Klein is an Emmy award-winning journalist and he serves as an associate professor and the director of the UBC School of Journalism he's also the founding director of the Global Reporting Center at UBC a nonprofit organization which is dedicated to researching and producing global journalism Peter Klein is also an associate of the Peter wall Institute for Advanced Studies so I'd like you all to please help me welcome professor of Lanning [Applause] thank you for the warm welcome thank you for the great introduction it's a great pleasure to be here again in Vancouver and to be a guest of the P W I a s and to see again and meet again some old and dear friends of mine tonight we will talk about mathematics in a way that may not be the most usual we will talk about art we'll talk about beauty we'll talk about why mathematics is such an artistic activity such an art this for many people will seem like a mystery but for mathematicians for my colleagues it is so obvious and natural that most of them won't even understand that there is need to talk about it it's not like obvious let us however examine this in detail and that means is that this is just one of the many paradoxes which lie in the nature of mathematical sciences for a start let me review some of these paradoxes which make mathematics so special first of all mathematics is at the same time about rigor and imagination a lot of rigor and a lot of imagination and you may wonder why I put this picture here on the left this is an allusion to a classic joke so it's a mathematicians joke so not sure that you will find it appearing and here goes the joke you have these three scientists three friends who are travelling in a distant country on a train and here is what they see by the window and one of them the biology says oh that's funny all my life I have seen white sheep but I see that in this country there is a breed of black sheep and the colleague physicist says ok let's not just do conclusions so fast maybe it's a random event maybe there is some mutation fluctuation who knows some of these heaps are black not all of them and when the mathematician looks upon his two colleagues and says my friends let us be rigorous here the only thing we can say for sure is that in his country there is at least one sheep such that at least one side is black in Oregon rigueur and of course it shows it's part of this old eBay the physicists and the mathematicians physicists will say to the mathematicians why do you want to prove everything there are some steps which are obvious or natural but uncertain know you never know sometimes in this obvious beat lies a lot on the other hand it's not the rigor that makes your career in mathematics and when you want to hire a colleague and if the recommendation letter arrives and say that this is a very rigorous mathematician it's not good for the hiring what the letter shooting system is the vision and the imagination that is how you gain the respect among colleagues you see this complicated formula it's extracted from what is arguably the most famous mathematical paper of the 21st century the final proof by Grigori Perelman of the Poincare conjecture about possible shapes of a bounded three-dimensional universe a beautiful piece of work solving a geometry problem of about one century old and when the manuscript was out when people when mathematical community could watch it and examine it what did they say they did not say all Perelman managed to be more rigorous and to perform computations which are more tricky than the rest of us though they looked at this formula and they said where the hell did he get this from what is this entropy how did he have the idea to introduce this thing where does it come from what imagination that is how you gain the respect of your fellows in mathematics by proving your imagination and your capacity to find the tools that people had not even conceived before so that's one of the paradoxes it is with the logic that we prove it is with intuition that we discover or that we invent that is what oh he Poincare a the famous French mathematician used to say a second paradox is that mathematic is at the same time abstract and universal ubiquitous when we say that something is abstract means that it's nowhere when you say that something is universal it means that it's everywhere and that is mathematics at the same time nowhere because did you ever see a theorem here but at the same time everywhere because yes we can say these these and these and that they are all related to the same theorem or the same notion you know I put an image which I love Lady of Shalott ignorant to a famous poetry by your law Tennyson and in this poem it's about an old legend in which the Lady of Shalott is kind of princess or noble lady who had been condemned by some curves to see the world only through the reflection of a mirror and that is the fate of the mathematicians unable to do experiment directly but watching and studying the world through the abstract mirror of notions formulas and equations and theorems and through this discovering some truths and some of these truths even though they are abstractions we will apply in many contexts everywhere like the famous bell-shaped distribution of errors that you will find in the fluctuations of the level of the oceans or of the cosmic back wave background or radio wave background or in the situations of the size of people or anywhere one of the most big features statements in mathematics the next paradox of mathematics is that it is at the same time very inegalitarian and very democratic you very indicate Italian because we are not equal in front of the mathematics problem and for most people a researcher in mathematics is some kind of alien you know but for us mathematicians when we study the achievements of the great mathematicians in the history we feel like they are the aliens people like a manager nor Gauss we look at what they did in all and we wonder how could they do such things even if we would spend were 1000 years working on this we would not do as great and there is inequality this but at the same time you know mathematics problems are for everybody to try you don't need an authorization you don't need funding from the government or whatever and it happens that sometimes a great problem is solved by somebody who is an outsider not the bigshot in the field it happens when a trio of indian mathematicians in 2002 found a great primality algorithm much better than what there was before for checking the primality they were not unknown researchers but not considered as the big stars in the field and even more spectacularly when just a few years ago etang xanga made an extraordinary discovery so eating Zhang was not at all recognized as a hero in the shield his career had been so difficult that at times he had to serve as a waiter in restaurants and things like this and arrived at about 50 years of age it was not at all on the radar and then he proved outstanding serum he became a superstar overnight in the mathematics world got all the award that it was possible to get this kind of things are rare but they happen and so there is this democratic element the next paradox about mathematics is that it is at the same time so ancient and so you very ancient because this is the only science in which we can still read the texts and contributions of scientists from hundreds of years ago or even thousands of years ago you know what you find in the books by Euclid is still valid and because it's based on the truth of the reasoning and it will always be true and no other science can say the same on the other hand it's changing continuously and there are all the time you to the new object which are being found here I put pictures to evoke the Ricci flow or the stochastic linear evolution which has become big stars in the past education has played a crucial role for instance in the solution of the Poincare conjecture for the Ricci fool so it is constantly renewing and another paradox which is well known to mathematicians is that it is at the same time a very solitary and very collective solitary because there are all these moments in which you are all alone in front of your sheet of paper and wondering how you will find the solution that for sure is hidden someplace in your brain but that is done difficult to get a hand on and most of the time your attempts will end up in the de in the Bema yes but on the other hand it's such a collective activity we spend so much time in conferences and lectures and meetings and gatherings around the world and actually that is one of the things that these are most striking when you compare the curriculum vitae of physicists and that of a mathematician usually the physicists will publish more but the mathematician will travel more much more conferences and lectures and we could spend our life traveling and discussing with each other because our job is about ideas and promoting ideas discussing ideas and discussion is one of the prime ways to enrich ideas next paradox mathematics is at the same time so damn simple and so damn difficult and sometimes something which should so simple will be so difficult take this example which is well known and see this is the problem of bisecting an angle dissecting an angle you have an angle which is given and you want to draw the line that will separate this angle into two halves equal it's a simple construction you find it in the Euclid's element you learn how to do it it's cool and there is with the comparison with the ruler you can do it easily ok and then the ancient Greeks asked next step we know how to divide it into two now let's divide it into three equal parts with compass and ruler how do we do what is the recipe it took more than 2,000 years before it was proven that there is no recipe it's not even that it was too difficult that we had to be more clever it was proven that there is no recipe in the world that would be able with just compassion ruler to separate an arbitrary angle into three paths now this problem looks so simple that you would have given it as an exercise to a tutu to a high school student but actually so difficult that it needed abstract developments of higher algebra Galois theory and so on to realize its impossibility and many things are like this in mathematics and final paradox mathematics is both science and art now we've been taught that science is one thing art is another thing and when you go to vatican and you watch the beautiful frescoes by a fellow there is one wall about the science is another about the art and another one about religion and moral and these are three spheres which are distinct and respectful of each other and so on but actually mathematicians will tell you our field is both science and art how can it be let's discuss about this first we can use art to talk about science in the same way as we can use art to talk about pretty much everything and because everybody relates to us it's often a good how to say it toy and horse you know to grab the attention of people and subject that they would not like otherwise I remember very well when I was a kid earng animated cartoon called Donald in Mass magic land a Walt Disney cartoon in which Donald Duck was having lots of adventures with the about mathematical concepts not deep mathematics I tell you but I found it very fascinating as a child and in there the tricks to talk about mathematics in a way that would be appealing to youngsters where classical art tricks for instance about the golden ratio appearing in the paintings in architecture and whatever and I will not see more about golden ratio because it is overrated even though I'm not dismissing that it is beautifully interesting but we've heard about it so much and people saw it so many times in every kind of possible trick that it's better not to add to this you know when mathematicians are told by their friends oh please tell us about the golden ratio with the reference no not the golden ratio again another trick which was used was about the music and this was also one of the axis developing Donald Duck animated cartoon yes and it's good that we had music first before this talk music in the times of the ancient Greek was considered as a mathematical art and this by the way is one of the reasons why in French language it is still poor mathematics and what was the idea idea was that when we want to organize the music and the sound we have to find the good frequencies the good numbers the good ratios of frequencies which correspond to the music intervals and that the first who really took care about this is good old friend mathematician Pythagoras and for instance here is the here are the numbers behind the pitagoras scale to go from the hogwash due to source so do we see and soul must be geesh it's a Quint it corresponds to a ratio of three halves or if you want a ratio of four three halves in the frequency which is the same as the ratio of two cells we respect to the length if you have a string vibrating and giving you a certain sound when you divide the length by three halves we will obtain the quint and so on if you divide by 2 we obtain the octave and the problem for them was to find the good ratio so that it would be harmonious and good this was the first attempt since then there has been several other constructions involving some tricky rules in some cases the tempered scale is entirely based on irrational numbers something which would have sounded completely heretic to the pythagorean's and so there are these numbers appearing here let me however insist that it's certainly not because of these appearance of numbers that music is artistically the favorite art of mathematicians rather it certainly has to do with the fact that music like mathematics in abstract representation of the world and the feelings also also with the fact that you know mathematical music is a bit like a reasoning with some logical steps some progression some surprises and whatever and in the fact that it's all in variations with simple elements like the like the various nodes and the various rhythms just like mathematics is all about combining number of simple ingredients together nice quote by like nibs which here I put in French let's say music is the pleasure of the human brain when it is counting without being aware that it is counting let me also note that parallels between mathematical reasonings and exercises on the one hand and musical schemes and artistic themes on the other hand have been used by a number of other than maybe one who was most successful in this one of the heroes of my youth I was reading his works when I was a teenager while two class hochstätter in works like my Timothy this was the French title of these short stories but also good le share and back which was the heat in the in the field drawing parallel between structures in thoughts in mathematics in art and so on now let me talk about another form of art which was very dear to me as a child rather simple but really taking us into what you would expect from an art this is a magic square what is it you see here it's a square grid in which you put numbers 1 2 3 4 etc and the rule of the Magic Square is that you should put them all in such a way that the sum in any column or any line or any diagonal will be the same this example you can try it pick up whichever line you want and you find that the sum is 65 I guess and why is it interesting why this useful the answer is there is no use whatsoever it's just it's just for the pleasure of arranging the various elements in a way that these Arminius and surprising and beautiful so to speak and you know what it's rather easy when I lecture in schools I teach the kids how to do it 10 year old kid can learn to fill a square like this as fast as writing the numbers is possible in fact any square whose size is an odd number even squares are more difficult but the odd squares are very easy to fill and even when you know the trick there is a certain joy in accomplishing this recipe a bit like the craftsmen would apply the recipe to produce the after work even though this recipe maybe centuries or there is certain pleasure in the pranky to organize them some people have taken this art to extremes okay you may think this is a big square but that's not what is impressive you may if I if I explain you the tricks you will be able to feel a square of 55 by 55 if you are patient enough that's not a problem this square is even that is more impressive even squares are much more difficult than odd squares but this one has an amazing property really amazing if we raise each of the numbers to the square to the power to so that the five on the top left will become 25 and so on the resulting square will still be magical that is the sum in any line and any diagonal any current will be the same now that is crazy I mean it's you would think look at this and it's like these tricks you know in the circles in which you put many things in equilibrium on top of each other and so that the sense of impossibility will be part of the artistic performance are there some deeper connections even between mathematics and art you see here it's about making something which is Arminius and very surprising and so on it looks like it looks like a beautiful game other some deeper connections the answer is yes and one of these connections can be found in the motivations of the people and the way that they work both the mathematical researchers and the artists let's here Claude Shannon about this Shannon is the father of information theory one of the most creative mind of the 20th century maybe here playing with videos so the mice she made which could get out of a logarithm of amazing one of the very first official intelligence devices and in a text about creativity he asked this question what are the basic requirements to produce some good science and there is a long discussion see the first requirement is obvious training and experience and you know skilled at cetera then there is the idea of dissatisfaction I mean a constructive is a dissection now that is interesting we know how much the satisfaction is important for the artists and we hear about Beethoven or Picasso or the others at one point of the other they're very dissatisfied what they've done so far they think I can do better I have to reinvent my style and so on and that is the same with us mathematicians if you are too much satisfied of what you've done it's not good another thing I'd put down here is the pleasure in seeing net results or methods of arriving at results needed if I've been trying to prove mathematical theorem for a week or so and I finally find a solution I get a big bang out of it now things like emotional passion big bang despair motivation and so on these are words which are so important in the artistic quest and also so important in the mathematics world and the quest for the inspiration Shannon could have added the styler typical of art we sing the style but mathematicians also know well that there is a style of disco or even that mathematician is not the same as the others the style of Shannon was extreme elegance always very concise to the point no more than is needed and the beautiful beautiful proofs and let me quote a famous mathematical text by Alexander Houghton geek one of the most famous mathematicians of all times who wrote long writings and in one of them he talks about the metaphor the Renoir you know the parabola the metaphor of the nut to explain the difference between his style and the style of his fellow mathematicians on pleaaase both of them working in the same area of mathematics and but very different ties and cotton dicks I'd imagine that we have not to open the style of ser would be take a hammer and Bank smash the nut and my style would be to take the nut and put it in a sea of acid so that it would be dissolved very slowly the cost of the of the nut without noticing anything and yes experts tell us that the style of Goten geek is like everything it's very incremental from one step to another to another by very tiny steps so that you have the impression that nothing occurs and we are really making no progress and at the end it's proven there it is the big theorem is is done these are very different ties and the metaphor gives you an idea of the wealth of various styles that there are in mathematics for a mathematician it's not just the result which matters but also the way at which you arise you arrive at this result now let's talk about beauty and let's invoke her well-known philosopher Aristotle she forms of beauty are order or comments or ability and precision I don't know about you but I have impression that he's talking about mathematics when he speaks this way and indeed in the secret of the text he explains that this is the reason why mathematics is regarded as the highest form of human in ink and the most beautiful let me take some time with each of these three words order commensurability and precision and develop them and why they are so meaningful in mathematics let's start with precision accuracy and let's invoke one of the superstars of mathematical history why BC seven to eight nine this is a clay tablet from ancient Babylonia maybe it's four thousand years ago or something and what is it you see there is a square with diagonals and there is some inscriptions and this is written in cuneiform writing and this actually is a computation of square root of 202 great accuracy like accuracy of one millionth it would be with six digits in our decimal notation first let us you know respect and and say hooray to the mathematicians from that time they already had algorithms so good as to be able to compute croute of two with such a precision I'm not sure in this audience how many people could do the same as these ancient mathematicians and next why were they doing this there was no use whatsoever in computing square root of two with such a procedure in those days but maybe they had fall in love with precision you know let's go on and refine the computation and the mathematics word get the value that is totally precise much more precise and what we can do in the reality by the way in the other of these ancient mathematicians it has been called the Babylonian method the fast algorithm which is used nowadays for the computation of square roots for instance Computers now these were the babylonians let's move forward in time and arrive at last year the great scientific sensation of 2016 the observation of gravitational waves at last after decades of wondering whether it was possible a triumph of experimental science and this cage it was the American project which got it first there was a European project which was also on way but which was not as fast now why is it about precision first because the observations were great and extremely close to the prediction actually it is the accuracy between the prediction and the observation that made it that nobody contested the results okay it's such a good agreement with the theory that we all believe you did observe these gravitational waves but then what was amazing also was the how tiny twas these gravitational waves you know when we are the gravitational wave goes to us it means that lengths are distorted but really it's tiny something like at our scale something like one thousandth of the diameter of a proton can you imagine this and still they were able to detect it a client and it is the trace of an event that is on the other hand amazing in its scope and amplitude like the collision of two black holes each of them more than twenty times as massive as the Sun occurring billions of years ago everything is crazy in the storage the amplitude how the time scale which is involved the length scale which is involved everything is totally out of our world and still mathematics you are able to paint it with great a cure great precision so this was triumph experimental physics of theoretical physics and of mathematics also for the description for the e by the way where the theory was useful in the description and the spotting of the gravitational waves so this was for precision now order in mathematics you like to order things notions and object and so on there are so many examples of this let me describe one of these many many examples bringing order to the world of the polyhedra here are some point he draw you have variety of shapes and whatever polyhedra they have vertices they have they have faces and they have gosh I forgot how you say it in English red eddies thank you and by the way I put the French initials but I should have put for this talk the English initials so S is for some a these are the vertices a is for a head these are the edges f is for faces and here is the recipe which sometimes is called the Euler formula we take any polyhedron and you compute the number of vertices minus the number of edges present number of faces and you obtain a result that only depends on the global shape of that polyhedron for instance without doing any computation I know that for the three polyhedra on top the result will be two because these are something like you know start from a shear and then with a hammer transform it a little bit and we know it will always be two not so far the two on the bottom these two have a hole you could put a string in between you can wear it as a necklace there is one hole for this reason if you do the same computation we will obtain the so we see here how we can bring order in this polyhedron and quantify the things such as the global shape and then you can classify the polyhedra according to their shapes there is also an analogue in the world of smooth surfaces not with edges not with vertices but very soft you know and so on this is called the Gauss Barnett formula the previous one can be still stored as a particular case of this one mathematicians will read this as follows you consider the total integral of the curvature along your closed surface and it will always be a multiple of 2 pi 2 pi multiplied by some integer number which number for instance with the shaykhs on the top because there are two holes this number will always be minus 1 for the shapes on the button because they have all one hole this number will always be 0 so the total the total integral will be equal to 0 and again that's one basic way to put order among all these shapes the one of the bases of topology now let's talk about commensurability the third one commensurability you can think about it in several ways you can think of it in terms of various numbers which you compare to each other maybe 2 and 3 and then we are back to these problems for instance in the construction of the scalar but you can also think of it as concepts which can be matched together one idea that is comparable to another idea or the some object mathematical objects which come together and here comes another Euler formula which many people consider as the most beautiful that there ever was actually there has been series of experiments conducted by in cognitive sciences and they have looked at the brain of mathematicians when they are presented formulas and they measured the level of pleasure which was expressed in the in the brain and they found that this formula was the one that triggered the highest level of pleasure in the brain of mathematicians so that it is proven to be the most beautiful in some sense so what does this formula say make sure is exponential I PI plus 1 equals 0 and what is beautiful about it is that it puts together the five most emblematic numbers in mathematics first one which is the basis of everything but then zero which was a great invention which we learned from our Indian friends and which was instrumental in making operations systematic but then also PI the symbol of geometry but also if the basis of the exponential symbol of everything that is growing be it in population dynamics or in the economy and so on and finally I the imaginary number such that the square is equal to minus 1 which was introduced to solve algebraic equations and the symbol of solving equations and all these five numbers which were invented or discovered at various epochs for various purposes finally are all linked together through the basic operations equality plus multiplication between the I and the PI exponentiation between e and I PI so the sign basic operations the five most important numbers and you get them all together that is what mathematicians will call beautiful because it's surprising because it's there is harmony and it is as if it had been planned this way forever only Planck array told in the same idea some order of ideas up to the he told of the profound beauty coming from the ominous order between elements and that pure intelligence can grasp not a beauty which you appreciate through your senses but which you appreciate through the brain and thinking now at this point many in the audience will tell me now Professor villainy that is good but beauty and so on it doesn't look very much like my causes of mathematics when I was at school and that is indeed a problem and an enormous misunderstanding there is a well-known pamphlet which was returned about this by mathematician and the writer Paul Lockhart the title is a mathematicians lament lamenting about these deep misunderstanding about the status of mathematics which has it being hated by the majority of population and what look after that is the first thing to understand that mathematics is an art said the first thing to understand there is such breathtaking death and heartbreaking beauty in this ancient art form how ironic that people dismiss mathematics as the intensities of creativity they are missing out on an art form older than any book more profound than any poem and more abstract than any abstract and look at tries to understand where the misunderstanding comes from and he is very very clear it is school that has done this now don't mistake him he doesn't blame schoolteachers he blames the school system in which it is all about putting the feeding kids with the technique and you duration how to solve this problem and that problem and that problem and the recipes and he says let's make a comparison imagine that you would teach music to our kids in a way that they would learn how to the logic of the scale and they will learn how to write the score and they would learn how to draw beautiful notes on the score but they would never hear any music or let's imagine that they would teach art in such a way that you will first learn about all the various shades of color and the various number that you attribute to these various shades blue is this code and the green is code and all the kinds of paintbrushes and how you will put the paint on the paintbrush and the paintbrush on the paper but you would never draw anything and that gives you an idea of the teaching of mathematics viewed from the mathematicians point of view insisting on the technique and forgetting about the goal which is about creating new forms of intelligence about finding new truth and so on and is there possibility to touch this beauty even at elementary level the answer again is yes and it's one of the goals when we teach mathematics to always put together the technique and the appreciation for the art for instance one of these stories stories which takes us back with the calculus Gauss is the story of the young Gauss at school it's a story I remember I was all ready to add already in one of the books of popularization of mathematics that I was reading as a kid let's tell it again so according to the story young Gauss and school elementary school one day was given the problem the teacher was giving the whole class the stupid problem of adding all numbers from one to hundred you know let's strain ourselves for good edition one plus two is three to press the 3 plus 3 6 etc but gauss did not do it dumb bre he thought about it after a second he wrote the results and took it to the schoolmaster how had he done it thought let's do it in an intelligent way ok we can do this um in any order it could be the same result if we start from the end 100 plus 99 % e 8 etc all the way up to 1 ok and if I write these two sequences of additions like this and then I do the summation of this all vertically 1 plus 1 droid will be 101 - plus 99 will be 1 1 etc and I will be counting 100 times 101 which now is not an addition but a multiplication which result is obvious just adding two zeros gives us ten thousand hundred now this is why at I obtained by adding all these numbers but each was counted twice so I should divide by 2 and that is the final result that the master wants 5050 now this presents all the characteristics of a beautiful reasoning first you can see that it is short arrogant you know I don't have to go through all the additions I have the result after a short time its effective it can be generalized with this method I do much less there is much less risk of mistake than if I do all the additions but also I can in one second do the same thing for adding numbers from 1 2004 instance but also in the way the reasoning goes there is this notion of commensurability 1 argument after the other first we reverse the other than we do this partial sums it's not since it's a repeat it's um it's actually a multiplication and then we divide by two and the important top being you know we say series shall we get to I don't know if there is the same inning with the cherry on the sorry cherry on the cake good and it's surprising like why on earth are we counting them backwards first at first you don't understand why there is this that's where the imagination comes from and that's where there is an element of beauty let me say that this beauty you can find it at all levels from the such a simple problem that it is a school type level to the most difficult and emblematic problems of mathematics let me actually skip the discussion for this one to concentrate on the rest but the most famous problem in mathematics is the Riemann hypothesis and why are people so concerned about it well it's so famous the best answer is that it is so damn beautiful and related to many other topics in a way that also would be extraordinarily beautiful and that one is not a simple school child problem it's one that has been a challenge for the imagination of mathematicians for half one century and a half ok yes let's skip the Riemann hypothesis here and let's now show with you a memory of my mathematical career to insist on how the notion of beauty is also a guide so this is an extract of a paper which is dear to my two men to me actually I think is the of the paper that I published and the theorem that I proved is the first one that I am proud of you know when you write your first research article it's such a big fuss and you are so proud of it but years later when you but you think oh that was not so good actually but this one when I look back I think oh that was not bad actually so this was 1997 I was a PhD student and I was visiting to the PTO's cannae a species of birds man equation in pavia I had met Tuscany a couple of months before in a conference in France I had shown him that there was a big mistake in one of his papers which is a very good way to become friends and Tuscany had invited me to come over and visit him in Perea and he told me you know I have this crazy idea for solving the chat in any conjecture about the bottom about the portsmen entropy production it's a crazy idea and so on so he explained me you do this you perturb in this way go to the limit they try see what two remains he was director of his lab so swamped with administrative duties and so he had no time to check even his own idea but I was a PhD student with all the time in the world so I sat down and did all the competitions and reasoning to try the idea and after I tried I discovered that the idea was not only crazy but in some sense stupid there was no way no way that it could work no way but but in the course of trying there was something that popped out in the competitions and putting together various terms it was recombining in kind of miracles way into a perfect square beautiful square and I thought that is cool that is too beautiful to be useless and actually this was the start of the solution spotting the small miracle the harmonious identity was the key to the seeker you know in mathematic there are so many paths you could try to go you need something to guide you and often that something is the aesthetic where it is beautiful we bet often that that is the direction that we have to dig in because where there is beauty there is more chance that it will be truth after all as Sophia kovalevskaya the great Russian mathematician said it nobody can be a mathematician without the soul of a poet now let's take on this and talk about poetry and again mathematics and poetry you think that is the opposite but quite not true mathematics is a poetry of science is the title of lecture which I was giving a few years ago in Belgium it's actually a quote from the former president of Senegal oh poor Sango the mathematics or a posey Decius see on this this was the poster prepared by eighteen lekawa a very gifted drawer of crazy comics with all kinds of logical rules on it you can see the mathematician getting on top of the elementary operations to reach for the infinity to which for something that is hidden a lot of poetry is about displaying something which is invisible and reaching for it what can we say about the relation between mathematics and poetry first we can say that mathematicians like poets believed very much in the power of words of concepts and of everything that there is behind when a poet uses a word it's not just the personification of the world it's the whole set of images and contexts that they will be within this and when a mathematician uses a concept is not just a definition is the whole theories that lie behind that has been transformed and repeated and so on and finding the right notions for mathematicians it's so damn important and playing with them and these notions was something that is not isn't initially in the problem but that will be crucial for the solution playing with infinity what is infinity infinity does not exist in your world but introducing the infinity and playing with it and handling it in the clever way is the key to many problems of mathematics integral integral raised notation that was invented by lightnings but then it was redefined rediscovered and when you write integral there's a whole bunch of theories and reflexes and context which goes into the mind of a mathematician there are other relations between mathematics and poetry first the role of constraint poetry and most cultures around the world is the most constrained art form with rules of the number of syllables or the sounds whatever which word you ought to use and similarly the mathematical writing is extremely constrained by the rules of logic and presentation and in both as a counterpoint to these constraints is the imagination and how important it is and we can also say maybe the most important of all poetry is about creation that is even the etymology of it about creating a new world invoking it and that is what Mathematica does create a world in the which is the reflection of our world with rules that are inspired from our world but which we can tweak and change and we can use mathematical shades and concepts and functions to reproduce the world around us to recognize some patterns some abstractions in the rarity around us and we can go much further we can represent and design things even with before they exist nothing that will never exist look at this crazy building the Silesia veto in Paris before yes by a American Canadian architect Frank Gehry before you construct think you'd better first created in the mathematical world otherwise there is a good chance that it will collapse soon after it is there and it's very important step to use sophisticated software to simulate all the you know the stresses and the strains in the building and make sure that it will be functional and when you do this you create something which does not exist yet but it's a full creation in the virtual world and it will help the creation of the artist look at this this is image from a famous movie in the recent years gravity oscar's whatever Fame a lot of success everything is fake in this movie or almost everything well the face of the actress is true but then all the rest is created with computations and algorithms and mathematics and it looks so true except that the rules have been changed by suppressing the gravity we could equally reinforce it do whatever we wish and this is possible in this mathematical world which we recreate which is a reflection of our world but in which we can change things this leads us to the fact that nowadays the movie industry very much relies this is a strong component mathematical recipes and modern image processing has been developed by visionaries people who are at the intersection of science and art like Edwin Catmull it has been implemented in emblematic movies like Toy Story by emblematic studios when you see in brave the motion of the hair of the heroine it's based on models of physics powered with mathematical equations it's not realistic it's better than reality it's a world in which hair obeys some physics rules which make it even more elegant so than in the real life see it's really it's it's poetry and there is research going on in this in this respect here is a evocation of some work by Mary port any one of the leading expert in these about how to create universes in the digital world graphic universes here what it would look like to have some you know digital play on which you could use to play with it and make the shades and distort them and so on and a few years ago Hollywood attributed tech Oscar to researcher Marcos gross from ETH Zurich for a new creation new algorithms so called wavelet turbulence which could be used in special effects to create fumes of flames which obey certain movements as you can see in these two examples created by the studio one more in Paris I remember a few years ago big conference in San Diego in which there was a session about movie industry and one expert had a research head of a big Hollywood major was telling us we should pay you guys royalties for every blockbuster in Hollywood of course we did not object let me tell you that behind this creation in the world and the enduring the movies and so on is play a crucial role some models from mathematics which are used to describe phenomena around us partial differential equations actually the feel in which I was trained these equations which have been developed in mathematics in physics to model all kinds of phenomena around us like waves fluids gases galaxies plasmas the cosmos atoms finance biology whatever all these phenomena all these things first had to be put in equations that would describe the reality before being used to modify the reality and create it as we wish and so all this is about poetry in some sense ok now I've told you about beauties poetry art and so on within the mathematics and some of you will say located very good but still we are missing something can we use mathematics to create art and if I am an artist can I find some inspiration mathematics the answer is yes to conclude this lecture I will show you some examples of real art that is inspired by mathematics either directly or indirectly and I will argue that all these examples fall into three categories three different connections between the art and math the first category is when you have some mathematical recipe that will produce or help producing a work of art a famous example is fractal theory fractals are these shapes based on simple geometric recipes which appear to be interesting at all scales and it says that the part looks like the hole in some sense so that when we zoom it looks like the whole picture they are not based on complicated formulas usually the recipe is rather simple to state but they are complicated objects let me show you a recipe to construct a fractal image there are various recipes I will not show you the simplest one but one that gives rise to spectacular fractals and the so-called Newton method fractal so it would be a bit more advanced than the rest of the talk but relax even if you don't understand all details it will be all right so it deals with complex numbers complex numbers have a real part and an imaginary part and you should think of them as pointing the plane rather than on just your line now let's consider a polynomial X is a variable and this point M LP will be X square plus 1 multiplied by X minus a is a point number of degree 3 a will be any complex number let's take one and write this polynomial now we may ask when we can solve this equation of this point will being equal to 0 the defining the root number one root is a obviously because an X equals a the whole vanishes but also there are two other roots which are I and - I where I is such that I square is equal to minus 1 now starting from another point another complex number I apply a recipe which is known as the Newton method to find the roots of an equation it's actually a generalization of the Babylonian algorithm that I was talking about here is the formula and don't worry about details if you are not comfortable with them but starting from a first approximation you construct another one which will be more precise through this formula from the approximation that n comes the next one which is that n plus 1 and then the next one and the next one and the recipe if everything goes right will converge to one of these roots either a or I or - I depending where you started from start from a over three that is your first approximation and go on apply the method maybe it will converge to a maybe - I maybe two - I you have to run it to know and then if it converges to a you will color a green color if it cover is - I will call color a into ZN + - - i will color it a deeper blue okay that is rule and with this we will create a work of art just by coloring the points a according to this rule in one of these three colors that is what michael hardly did for the project which i will show you in a moment for every point a you look where the methods you and you will color the point accordingly and this will produce a fractal you will see in the fractal you see these three colors that I mentioned the green and the two shades of group and also you will see some elements in black in that it is when the method does not converge and also various shades of these colors depending on the speed at which the method converges and we will zoom to see the fine details and as we assumed will slowly change the scale of colors just by shifting a bit on the numbers of the colors so these are very mathematical rules and let's see what we obtain how when we got closer it looks more complicated than it was it looks like imagination but it shows the result of that single mathematical rule which I gave see these kind of things which recur here and there they look like Mundell both sets for those who know but they are not exactly they will come here and there I look at these shades now it looks it's a completely different figure maybe inspiration from a tricity or from gardening who knows I look at this it's again changing but it's still the same mathematical rulers from the beginning and again these strange shapes keep on coming again again it's really a fractal type structure Wow we could continue forever but we have to you know go on quickly let us briefly talk of other mathematical rules which have been used by artists quasi periodicity which is not parody clearly but some kind of were used by artists in the Persia already hundreds of years ago long before it was found that these structures also exists in nature Antoni gaudí in barcelona for some of his acts like to use the shape which comes from physics the che network written in French I guess cutting a catenary or something this is the shape of this when you have a chain which lies under the action of gravity and Gaudi found them beautiful he watched them in mirrors to reverse them and use them to make these arcs used to say that he was taking the inspiration in the shapes of nature which as we know since Galileo are themselves written in the language of mathematics janaki's use the dynamical system then cows to produce some music hey mocha no member of a French group called woolly poem who is fascinated in mathematics also use combinatorics in this strange creation you know you see all the each banda has one line you can combine them however you wish to create a poem and in this way you create and he says 100,000 billions of poems it's a way to improve to put the combinatorics in your art your giggity who was also fascinated by mathematics made some pieces of music with crazy constraints very logical in this one one of the musical jacket are the constraint is simple only written with eighth you would think that the must be the most boring piece in the world but no not at all not boring at all okay first of all actually there is one v at the very end of the piece but more importantly there are all kinds of variations in the rhythm in the strength etc and it has work now these are examples in which the mathematics was used to produce or to participate in the production of artwork now for another possibility another possible link is when mathematics provides an inspiration not you don't apply the formulas but you think of the mathematical theory and this inspires you for work of art for instance by mathematician and artist and telephony anko this kind of dreamy picture of probability or for instance this artwork by a shame relativity no formula about relativity has been used to create this but it's like dreaming about a notion of changing point of view changing the referential which is at the basis of the relativity or for instance again by Ligety a very difficult study called disorder like cows which has some inspiration from the theory of deterministic cows it at the same time very regular you see the rhythm is always the same and very irregular in particular through these actions which occur at kind of unpredictable times and which create a whole impression of cows sometimes the inspiration can can build on sophisticated theories here is a business on one of the great mathematicians of the great geometers of the second half of 20th century and he's one of his best claims to fame was his work on three-dimensional geometry and topology beautiful book which was proposing a classification and ordering on all kinds of geometries in the local kind of possible geometry then actually paved the way to the solution of the Poincare conjecture and one day the Japanese designer II Samia K heard about this works found about it and decided that he would make a collection of high-fashion based on the work of Thurston with inspired by the nuts which Justin used for representing the possible geometries again no mathematical equation was used to produce this body twelve inspired from it and from the shapes and this was presented of course in place in the Louvre and this was called the Poincare a collection of fashion and now there is a third way which is not about inspiration or about using mathematics but which is about representing mathematics putting it in scene this is the approach which was used by the surrealist artists in the 1930s when they came to visit my dear Institute only point away they found these kind of figures big shapes with surfaces which are used to represent the nearest rate theorems they had no idea what this meant but they found it beautiful these works done by the hand of humans to exchange ideas from human to human they found it fascinating and they wanted to pay tribute they photographed it we know that they didn't understand the list of it because in one case they photographed the support instead of photographing of photographing the the shape itself and look they put it like you see this doesn't look like a mathematical picture it looks like a cat maybe or a mask man hey who was the photographer here called the Shakespearean equations here is another example in which somehow the mathematical here the mathematical lines for the rules of perspective are the artwork and what attract the the the look and again in the idea of representing without understanding there are these poetry's the songs of mother hawk by yellow Tiamo in which mathematical world are inserted within the the poetry as a tribute to the mystery that the container okay on a lighter note the singer Everest one of the very rare pop singers to have made a postdoc in Princeton University did these very describes songs with mathematical vocabulary inside ah this is one of my favorite examples this equation for so there are some around you who have passed very nearby without noticing this is a Schrodinger equation one of the periods of mathematical physics in the quantum world and it is represented in a structure which is on display in the centre of the Paris subway shut Lily Allen station I find it very ironic by the way that every day hundreds of thousands of people probably go near by this culture and I would bet none of them notices that there is the fitting or equation in there as a metaphor of the fact that we are surrounded by equations and we don't know this and the final final example again for representation will be that I will present to you is by jean-michel Paola contemporary artist he wanted to represent the magic of transmission of the mathematical ideas what happens when we talk to each other in the mathematical world and explain a mathematical result and so he portrayed the mathematician and it was me on this occasion talking about the mathematical result in this case it will be the one that I explained you that I started with recipie Toscani and catching any conjecture and just filling it putting it in film without understanding anything but to invite the viewer to focus on the magic of the mathematical writing and how the ideas are transmitted and even the details the chalk the blackboard and so on so let's go for it oh by the way it's 21st century and we never found anything better than blackboard and choked to transmit mathematical ideas it really is the best it adapts to the motions of the brain you can improvise modify and there's this beauty of the integrals or whatever signs my other little dust of chalk which is out from time to time I asked some time to time there are mistakes that you have to repair yes and the truck gets broken more than once and the continue one bit of wiggling and the other began let's put together and waited here near the assumption in the conclusion etc and all this translates the brain of the viewer into ideas and some impression sometimes confused sometimes very clear and so on oh this is the dramatic movement and some part of the blackboard are kind of in the dark sometimes are some pasta kind of lit maybe a metaphors like that some parts are obscure and so partner bright in the reasoning and in the end you'll have this result now for the mathematician this is working device you know it's part of our job but for the artists it's a piece of art it's something that the artist will choose to communicate to broader audience as a testimony and as to invite other people known specialists like him to Marvel about these miracles transmission of ideas through language through the writing through the mathematical formalism a piece of art thank you for your attention [Applause] mostly mathematical formulas excluding thank you on behalf of everyone here particularly those of us who are not professional mathematicians I want to thank you first of all for being the ambassador for us and also for and clearly in this in this presentation not under estimating the public's interest and capacity for understanding complex issues so I want to thank you for that we're going to have about a half hour just under a half hour for questions if you can there'll be some some positions for microphones you could start lining up as soon as they get lit up and if you'd like to send some questions in through Peter Wall Institute social media the addresses are up there and we'll try to get to through as many questions as possible while we're waiting for some people to to line up maybe I'll start with with first question omni Poincare a the namesake of the Institute that you run and who you reference number of times is it's often said to be the the last mathematician to have mastered the whole of mathematics math has become so complex so specialized and is that is that a good thing in your mind is that a bad thing is that perhaps one reason that you know in the time of Aristotle and and many of the great thinkers DaVinci oh you know math was part of a general intelligence of an artist of a philosopher of a poet today it's not it's not because of the specialization or at least partly because of us I think there are several trends first specialization has made it impossible for a mathematician nowadays to comprehend the whole of mathematics and there was never been another point carry and they will never be in the sense that we will never see another mathematician mastering the whole except maybe when they artificial intelligence manages to make superhuman mathematicians that we are not nearly there now this in itself is neither good nor bad thing it's a thing emitted unavoidable in all fields of human knowledge there is more and more material more and more diversification and specialization we have to be aware that it has to change the habits of working it implies more collaborations because it's more important than before to put together expertise of various people it requires also some mechanisms for more travel more discussions more meeting because the specialized knowledge which is not in your will will not come spontaneously to you if you just you cannot just get it from your reading and your studies it requires also more curiosity you have to be on the watch out about what other fields are doing and even if you don't understand precisely keep an ear open about what what is going on in there that is for the specialist now for the more broader audience and yes why are the physicists in there but philosophers or in the majority not aware of sophisticated mathematical arguments and the answer is also yes nowadays to study the few Sofi in itself is a huge amount of time to invest to study the mathematics also a huge time and so on and you cannot do everything at the same time I would say that it is then the same it requires more collaboration and dialogue if a philosopher wants to incorporate mathematics in his or her thought and works cannot be by just personal work it has to be through dialogue with some specialists Oshin I want encourage the audience members to please come to the mic this is an incredible opportunity to to get to to ask one of the leading mathematicians in the world some questions whether you're try not to keep trying to make your questions too technical and try to keep them short because we are short on time I'll ask one more question that may be relevant too I suspect there may be a few amounts of teachers in the audience I'm a former math teacher and I was particularly struck by the the the notion that the math teacher you you showed up there from from Santa in school in Brooklyn has written about how math is taught so poorly that it kills the curiosity and the beauty and the artistry for so many young people some are drawn to it the most talented perhaps amongst them or and pursue it but for so many people I mean how often do you hear math is hard I never liked math it was always my hardest subject what can we do what can teachers do what can we do is decided to make teaching math better and more accessible to a broader range of young people now that is a tricky question it's not one that has a simple answer and the very important is to find a balance between let's say the technique and the rest and the rest will be the engaging activities of the games the stories the riddles the marveling the beauty whatever the art in all kinds of components and I was plans to find the balance it would be a mistake to believe that you can do it and high early in the dreams and games and stories it would be it would be a mistake to believe that you can do it entirely in that way in the same way as in a music school you don't just listen to music and marveled about beauty and art you also have to learn the technique but you have to find the right balance between the two all right let's turn to a question here first off I'd like to thank you for such a wonderful presentation it's get a little closer I think I'd like to thank you first off for such a wonderful presentation this evening it was experience that I'm very happy to be part of I would how much of a barrier would you find language when it comes to trying to communicate your ideas to people that maybe speak different languages you need interpreters would you need to just use mathematics and numbers of myself there is no serious language barrier in in mathematics because the communication is mainly at the level of putting the concepts together and even if sometimes it's by being up using approximation about the world or repeating or doing it in a very in elegant way or by borrowing words from one language or another the concepts you can always go may go through it may not be elegant it may not be so efficient but you will or it will always go through you know even though mathematics can be described as a language it's not a language of the same nature as language in which we we speak and cognitive sciences have shown that it's not the same part of the brain which we use when we read a text so understand the text in spoken language or when we understand the mathematical statement mathematical thinking is mainly nonverbal so we use the language as a way to convey the idea but then we forget about that conveyor it's the arrangement of the ideas that counts thank you very much and have a question of the role of computers have now in research in mathematics we've seen a lot of the applications of computers in animation but not but as a statistician I couldn't see a day without me using my computer and every now and then when I'm looking at things the computer sings like me it's like there might be some interesting theory here that I need to work out the proof or something but I have seen that especially among mathematicians like I said of the dirty situation relying on computers to discover mathematics obviously wandering and your comment is like a valid form of knowledge or like anything can be derived from the abstract there is a whole thing of course computers and the influence of computers and mathematics and vice versa would require a whole discussion with many interesting examples first computers have made it possible to do mathematics check mathematics guess mathematics without having regular proof and by the way computer to some extent is a device that is able of performing any mathematical calculation and then status is uncertain and depends very much from subject to subject sometimes you have a statement that you observe in the computer world but can be mathematically disproved sometimes in the contrary you have mathematical proof but you would not observe it in computer in practice because computation time would be too large or because the it's an effect that you would only observer after a very long time or things like this but in many cases computers have had a good strong positive influence in suggesting new ways in suggesting statements in guiding intuition also in helping proofs so far the there has been no serious mathematical theorem which has been proven automatically by your computer but there have been examples in which part of the proof was based on computer action they have been example in which checking of complex proofs have been made through computer it's clear that checking proof is much easier than making a proof and there are some there are some impressive experiments in this right also computer science for for has influenced the style of mathematics and the fact that we now value more how to see constructive proof than before more a year algorithmic improves in their writing and structure is for full so influenced by the culture of computer scientists so there are reason influences at all levels at the level of what we regard as a proof statement or a true statement as an interesting statement or as a conjecture but also in the structure and the state of the positive influence in the all kinds of ways thank you let's go to a question over there first thank you very much for the beautiful and inspiring lecture and my question is to what extent do you think humans discover mathematics versus invent mathematics now that is a tricky question and it's amazing to see also how much this question is important to two people and fascinating to many people even hundreds of years after the debate somehow was formulated it has it is constantly being refueled this kind of debate and the mathematics human construction or mathematics engraved in the reality and in the universe and discovered by humans is an ongoing debate on which there are fashion effects I mean depending on the general context and the period we'll find different answers I belong in those who believe in the mathematics being discovered and I think we are the majority nowadays but capture decades ago we were minority and there was a different feeling about it why you know sometimes visions of the world change I tend to believe that few decades ago mankind you had the kind of illusion that it was possible to control the world and to master the world and that now it's bigger the delusion when we see subject that has climate change and control the economy around the world and control politics around the world whatever the impression on the country that we don't master anything and even though there is no logical relation between these human affairs and the status of mathematics I think this also influences us that maybe we are more humble after all it's a illusion to think that we can control things and we mainly witness or discover or see things as they are I'm going to go to a question from from the Kamath with social media you talked briefly about how mathematicians parts of their brains are stimulated by certain certain things you gave the euler identity as one that's objectively seen as most beautiful because it's most stimulating so we have a question about what is a Eureka moment feel like when you're solving a problem and you have a particular one that was particularly memorable I have some of them which were memorable and I talked about in my book but this is not shameful at the Tison for the book of course as a very good book and we all have in research these Eureka moments some of them big some of them small it feels like wow it is like sudden often Andre they famously compared it to sexual pleasure I think that it was in a way than that than the sexual pleasure because it last longer you know that think about it and wow it's a while that continues the amazement in front of the beauty of the arrangement of the of the reasoning and the mathematical argument let me share with you one of the one of the one of these stories again related with the still the same problem I was talking about and the entropy production and that work I did with the scanning at one point she later after that I was giving a series of lectures in the caleche de France in Paris as part of a world and in those days I was living in Lyon and so once a week I would go to Paris to give my lecture and in one of these occasions I explained the work that we did with Tuscany and so we do this and this and that and that and one of the people in the audience colleague said but don't you think you can improve for this done no no no we try cannot improve but still nada nada okay but on the train back from Paris to us that is thinking yes after all am I sure that we cannot improve and then oh the chance we can improve and all we can do this and this and all the way during the Train I found that's good and beautiful and you know what next week I'm going to do I'm going to tell them as a compliment to the lecture of this week that we can indeed improve it it significantly okay then a few days bye-bye and I'm very proud of this and I have written how I have this much better result now and you know just a day or day and a half before the next lecture I discovered that there is a big mistake in my reason that doesn't work and there's no no but it's so beautiful I have to show them I have to take the proof and truth and try and try a new trial evening and the night and so on and you know under the last dress before it is the time to go again it doesn't work wake up in the morning like how do i do i have to take this prove this and prove but these no no no doesn't work you know take your breakfast like a robot thinking how am i doing it and i don't know on go on the train station how am i going to do it arrived at the train oh my god i'm going to share them and go on the train and so on and then sit down and then tie off and the instant that I sat down I knew how to do it and I spent the train two hours of train between the yo and Paris to write down that argument now it was neat perfect and I presented it when I arrived here is the proof to improve it etc nice awesome experience that you remember you [Laughter] unfortunately I only have about five minutes left so I know we have a number of people who have questions I think we're just going to take maybe two more questions so we'll take one here and one there and I'm sorry the rest of you we're not gonna be able to get to your questions press avail I mean we'll be at the Pacific Institute for mathematical sciences on Thursday so if you'd like to continue discussing math with and you can but we'll turn here thanks for an awesome talk I really enjoyed just imagining all the different relationships in the mathematics and I was wondering what you kind of think of between mathematics and arts you kind of came from math towards art and compared it that way but did you like how would you see mathematics from a from the lens of art and are they equivalent are they converging are they parent-child relationship like what is that relationship now this is a this is an interesting question about yet we went one way from one to the other right from the math find us in the math but can we do the reverse can we find math in the art can we use artistic lenses to to inspire mathematics for instance there are something like this but so far it has remained a few curiosities some anecdotes and nothing to the comparable scale I mean the fact that there is an artistic side in mathematics is in everyday the conversations in the in mathematics lab but seeing math in the art is much more much more rare now some people would say it is still that there is a something I have regular collaboration with with the artist graphic artists we published one comics together and we're working on second one and he likes to say that there is a very there is a good dose of mathematics in a way in the way that you put we're drawing the composition you have to take care about the balance of the various ingredients there is some logic something goes there then something else has to go there and so on and even when you're not good at mathematics you can be very become very expert in this kind of mathematics of the composition so to speak also at the more elementary level we may say that some notions emerged in art and in mathematics quite quite parallel strong ways for instance symmetry has been the favorite of art ever since the start and we may argue that it's a mathematical notion which was inspired by your earth in some sense professor vidi Annie that was a very entertaining and inspiring talk so thank you my question is how do you nurture your creativity creativity requires lots of ingredients and there is never a sure recipe for them and of course this is the biggest problem of fear for creative thinkers be it in the field of research or art or whatever how am I sure that I will continue to have good ideas there's no recipe but some things are favorable constant or frequent discussions being exposed to number of ideas having a good access to what other people have done because new ideas are often inspired by previous ideas it is good also there is something very much about the atmosphere the environment creativity is of the group at a collective thing and you can think of when we talk about creative things creative laboratories creative cities and it's as important as to talk about creative individuals so it's all a very see ecosystemic problematic creativity also creativity needs constraints that's something that the artists know very well and one reason why they sometimes impose constraints on themselves without the constraints you don't have the motivation to break them to circumvent them and sometimes some of the most creative creative discoveries are also based on the constraints and by the way one of the reasons that maths has been such a creative activity is that it is so damn constrained by it constrained by the rules of logic well thank you thank you for your viewing [Applause] so this brings to a close our spring 2017 Wahl exchange lecture I would like to thank very much professor Villani for wonderful and inspirational talk and professor Klein for moderating and engaging question and answer period I would like to thank again our sponsors for this event the staff at the VOC theater and our wonderful house band and of course I would like to thank all of you for coming out tonight and being part of this conversation I hope that you take the ideas of passion and beauty and seek to find those in your own lives by whatever ways you seek appropriate and that the ideas that we've discussed tonight will stay with you for a long time thank you and we look forward to seeing you again in a future event [Applause] [Music]

Channel: Peter Wall Institute for Advanced Studies

Views: 42,481

Rating: 4.9216785 out of 5

Keywords: Mathematics, geometry

Id: v-d0ruh0CHU

Length: 108min 57sec (6537 seconds)

Published: Fri Jun 30 2017