Artur Avila and Alessio Figalli: The Fields Medalists (2019 WORLD.MINDS Annual Symposium)

[Music] so ladies and gentlemen on Tuesday two days ago just like every December 10 there's a big celebration in Stockholm the Nobel Prizes get distributed to scientist having done wonderful discoveries in physics in chemistry in physiology in medicine this year no mass Nobel Prize was given in fact no mass Nobel Prize ever gets to given and that's because the founder the donator Alfred Nobel decided in his Testament that math was not one of the areas where he thought prizes should be given to people contribute to mankind there's very speculation us why that is some people say a mathematician had an affair with his wife the most likely explanation is that no bail being an inventor very down-to-earth person simply did not see masses being terribly directly relevant to human kind and we'll come to back a little bit later but with time Adam additions got other prizes to compensate there's quite a few of them perhaps the best-known one of the most difficult to get is the Fields Medal fields medals are in fact even harder to get than Nobel Prizes and this on two accounts every year in chemistry prize will be given to one two or three people fields medals you get at most one per year and often this less than one per year second thing you need to be forty at the time you get the prize or you're not gonna get it so if you make it less than forty mathematician precision you have to you have to be less you have to be forty on the year at the January one of the year you get it at most you have to be at most forty on the January or out of the year you gotta very good so only 60 of these fields medals have ever been given since the prize was introduced between the two world wars some of these people have died of the surviving ones we have three of these field medalists working insert so 5% of all the medals that have ever been given on this globe or actually working here at the University of Zurich at ETH Zurich I think that shows how attractive this place is we've been able to convince two of these gentlemen to havilah and Alessio Vicari to come and to discuss a little bit with us about mathematics creativity and fame so after SEO mass is famous for being very hard to understand so my first intuition would have been to tell you tell me what you do and then we'd have 45 minutes from first gentleman and at 45 minutes from the second gentleman we would not understand a word so why don't you pretend I'm your grandmother hmm and explain to me in 90 seconds tops what excites you about math and it may be a little bit you know that I understand as your grandmother what you're doing with your life well to be excited is I'm excited by the abstract research which you can get an idea of only after a lot of study but you create in your mind whole universe that corresponds to what what other mathematicians have in mind so in a comparison is a there's lots of comparison with her art and when people think of math is it has been described as there is a whole universe that could be compared to the the music universe or something that that can only be appreciated after a lot of study so in a sense of what kind of takes me is that I can appreciate this universe and I can contribute to give my own new mathematical ideas and discoveries and what do you do I study dynamical systems that the study of you have something that's evolving with respect to something that we call time so but mathematical time which and we want to understand the very long term development that comes so some dynamicists study models of the solar system for instance and then try to see where the planets will kind of escape from the solar system going further away from the for instance things like this yeah very good Alessio okay so first of all what they do I've been working mostly in the last 10 years on optical transport which is easy to describe so it's a known problem where you wanna transport resources from one place to another you want to do it in the cheapest possible way so the the wolf the Sheep and right and that's that always been tricky right now this case this was actually a problem that was studied by monster during the Nepal Nikita was doing this for me a reason to build fortifications then country which studied from for economics he got the Nobel Prize in Economics and then mathematician got attracted to it because of its beauty you know there is always this concept of mathematics going after material we have two mathematical beauty whatever it means and it's very subjective right but so in my case what I got fascinated many mathematicians decided we could apply outcome transfer to Fields where it was difficult to imagine this could happen so for instance you can discover opium transporting the movement of clouds so it's equation describing clouds moving or you can try to use optional transfer to understand how crystal deform when you add energy to system so you can model the systems with the questions and then you have a tool you put things together because you see through formulas sometimes you know that's the help structure mathematics that allows you to look through different fields because you just look at the formulas does it make sense sorry say you know more okay so um the reason I'm sitting here actually is not because I'm university president or anything like that Rauf asked me because my father was professor of mathematics so I'm already damaged so there's no much more damage to be done my dad always was extremely proud he always said all the stuff I do it will never be useful at all Alfred Nobel didn't generate them as Nobel because he thought Matt was not very useful so what you take on that what's your defense against that is insignificant yeah you guys are cool but but not really Robin okay okay this is what I think mathematician like to say and I think it's a matter of sometimes we are proud of saying that and I think it's nice that we can think freely about our search and we can develop mathematics freely because mathematics you know it's very abstract in many aspects this being said all the major revolution that we see in our world exists only because mathematics exists so and many times this happened completely unexpectedly as actually most of the time so there are two nice example I was like one is just we use cryptography every day because when we send emails these are cryptid otherwise you know and my transaction credit cards and everything is based on cryptography this was this is based on number theory from the seventeenth century and there was no quit off it but then but without that mathematics we wouldn't have this and wouldn't be able now to record our voice and use you know record as microphones if Fourier didn't develop the mathematics in the nineteenth century to have transformed sounds in digital signals so doesn't is Ned it's complete false right I mean just that of course you need to build a machinery and it requires many many years and requires even more years to see the application but when it happens is big so that's my and that's what the federal government should invest billions into the equipment now we got it oh yeah anything to add yes so the thing that is kind of difference is that it's much harder to see the application of things that you're studying right now so there is this difference of time we can only base ourselves in the historical facts that we know that historical it has been extremely exciting are the applications of math and it's important to know that those applications are not the map that was led to these applications not created having these applications in mind so if you had kind of thought about that we should only do research that would lead to some specific application then you never get there so we should kind of go and be optimistic and just go ahead excellent so mass is often compared with to music actually that was mentioned already a few times today you guys play an instrument know what a played a piece piano for us no it's played okay so we heard from Claire Quan Chi people who want to become professional musicians you start very early and work hard when did you guys know you wanted to become a mathematician well I didn't know that mathematics but I liked the map since I was five or something but I didn't know that this was be a profession possible profession in Brazil there's not kind of repair crews may be many other place that you see mathematician and something compared to physicist or whatever but around I got in touch of a research institution and when I was around 14 or 15 and then around 16 I'll show that maybe even 15 I was sure that I wanted to do this let's go so I was actually so in Italy the same you didn't know Matt you could be a mathematician I thought that will maybe become an engineer but I mean it just to say I was studying classics in high school so I was lucky in studying Latin and Greek and had almost no mathematics I finished high school with basic trigonometry and then I thought I started to see Adam at Olympia it's right at the very end of my high school I thought it was fun I like the intellectual challenge of them and that's and then I decided to do math so I would say I started rather late interested so unlike music you can start relatively late and still make get a Fields Medal obviously related to that age question when often hears that mad missions do their best work when they're really young that's perhaps one of the reasons why they decide that you should be less than 40 on the January 4 stuff here you get the medal because after that no matter magician ever has done anything of value how do you feel about that is that true oh you guys are already on the other side of the hill or or your best day is still ahead of you let's think that this idea that you have of math should I think comes from the fact that it is possible to do a great mathematical work when you are very young and that other science would not have gotten to the point of learning enough to make a contribution and in math there was several cases of people doing great work early and so this becomes very visible because very nice to hear it those stories and so on but there is been also a lot of great work done after by people that were much up after 40 and so maybe especially nowadays we we can see the contributions and so I think that's more a matter of public perception and combine it with an existance of mathematicians that don't work early a setting is the same right and is much more fun to say Oh Galois did everything and then he died at age 21 you know and it was enough no it's not true anymore and I think it's a bad message to pass to the public all right so we'll bury the adage never trust mathematicians over 30 huh let's talk about creativity so obviously you need to be pretty amazingly creative to get a Fields Medal where do you get your creativity from what's your your fountain of creativity there where you get inspiration from I like talking to two people that's a good source that of mixing your ideas that are developing your head with the other idea so at the moment that you that you talk you hear their ideas and some also the moment that you communicate you think differently because you're trying to translate in some way that people understand so this is kind of a focal moment there is also moments that you are just kind of walking around and doing whatever activity that doesn't kind of bother you too much or not administration certainly and it's believed that a lot there are many stories about mathematicians where they believe that actually the lots of insight happen as to be consciously so there are people that are doing things and then they're not thinking about the problem and then the solution appears to their mind already ready solve it so that there are lots of theories about how it goes Alessio inspirational 3d you know I mean you need a lot of creativity but the values you need a lot of artwork so soon I don't know I think this idea of you know you just get a like ram anujan I don't know at night you have some God tells you something doesn't work so really you have to study a lot I mean as a student and then PhD then a lot comes so there is the creativity and ridged experience and also there is mixing knowledge and interact with people which is extremely important so one thing I saw in my career I studied in Italy I moved to France then I moved to us and in every country in every universities is very different to the kind of mathematics we do so it changes a lot and so as a student I was very much inspired the first by the mat in Pisa which has a certain consideration then the French Matt and I and then what I could do in Texas for seven years I wouldn't achieve what I did they fail and pass through all these institutions so it's there is more risk at the media but there is more than that let me pick up on this this idea of hard work so one of the interesting things about math is that you don't need much to be able to do math right so I give you a pen I give you my cars here we probably could start having some some discussion you don't need an augmented reality goggles from Microsoft so as what's the best place to do math and were you the most productive I'm I'm an office person so I'm mostly productive in the morning maybe I took this from my advisor but I wake up early and mostly in the office still at some moment and it breaks but this usually these breaks were maybe I don't know I I think I've got a problem and I get the idea while I don't know working or being an outdoor it comes after maybe several months were really the problem and everything is very clear in my head so it's not just you know I see it and comes usually there are so I doesn't matter if you're more office person I am like that so I mix I mix the two things having a sometimes you need fresh air sometimes you know you are just on the wrong part the worst part of research is that you never know if you're on the right direction to achieve what you want and maybe you have been thinking for months and months just you get the wrong idea and then you need someone to be able to say ok let me throw away everything I did and let me start fresh and there are so many times actually I mean notice that I sometimes I do computation and then I they don't work I throw them away and then I do the same composition again I can do this like 50 times but it's to convince myself that I'm really on the wrong direction and that's why it's called research because you have to search again you yeah I think I'm totally opposite mostly about this type no I I wake up very late so and I don't like to work at the office normally at oh it's a it's very nice office but still work yes it's actually very nicely I like to meet people when possible just go for a walk or so on or having a going to a restaurant do we also even like I like to work a little bit late like like maybe it for real time so that's like at 10:00 or something you can have a meal you can go to a bar you can keep discussing it so you don't need any kind of computer you just kind of talk one to two to each other and it's fine so it can be at any kind of environment can even abstract the music that's playing because you're kind of you're just thinking very concentrated in your head so any kind of things like this just you just have to be focused and not kind of having something else in your mind so what's the weird place you guys ever did math in like I was when I was not worried about my dermatologist was not annoying me I was going to the beach with my friends in Brazil we didn't fight then and we go to there and just sit there and get some in disgust without paper without anything well I can say that one of the results mentioned for the Fields Medal actually remember very well when we got it it was we had been trying for months with two good collaborators and then we were a conference we tried for really long and one evening we just didn't work so we went out dinner we get to beer it was like 1:00 a.m. we were going back to the hotel and on the way like came like this so you didn't it didn't happen it often so that's yeah this one I remember very I'll give you a glass of wine afterwards thank you so maybe one last question so Fame often changes people in in interesting ways so I remember an interview with their Carlos Santana the guitarist and people asked him you know how does Fame change you and he thought about it and then he said yeah you know pistachios huh you know sometimes you find it be statue that's completely closed where you can't open it I throw those away now now Nobel Prizes or feel Nobel Prizes fields medals don't necessarily make you famous in the sense of that you get recognized on Bahnhofstrasse I would okay you probably don't do adverts for a Nespresso you don't welcome people at the airport in Zurich but I'm sure somehow there must be some French benefit associated with being fields medalists so what's the coolest thing that happened to you thanks to the field medal what what did the metal allow you to do that you probably wouldn't have been able to do probably one of the funniest thing was when I got invited to New York it was a an event that happened in Simon's house in sounds with a very famous mathematician then went to finance and there there was a guy who's also in finance who happened to be the president of my soccer team and he knew that I was coming and they liked mathematics because he's in the one of the board of MIT and so then I went there a demon and if you give me the t-shirt of Francesco Totti with my eyes from a sort of fail with the signature of friendship so he made in shipped from Rome to New York there with a signature and so the now is in my office DTH very nice I think I should not answer [Laughter] [Applause] all right time is almost up last topic one of the nice things about mathematicians there's a lot of mathematician jokes now question to you do we have a favorite mathematician joke not really my favorite mathematician Joseph please so a biologist a physicist and a mathematicians or in a train going through the Highlands in Scotland they see lots of sheep suddenly to see a black sheep biologist go oh look at that they got black sheeps in Scotland they're physicists looks at in Thrones and scolds them says you biologists you're so imprecise what we can say is that there's at least one black sheep in Scotland the mathematician looks at the physicist frowns and scolds images you've resistors so imprecise what we can say is that there's at least one sheep in Scotland that is at least half black all right time's up ladies and gentlemen let's say I'll throw it up [Music]

Channel: WORLD.MINDS

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Keywords: WORLD.MINDS, Zurich, technology, science, psychology, talks

Id: rHthHdx7kgQ

Length: 20min 30sec (1230 seconds)

Published: Thu Dec 19 2019