 So I'm Lars Simon, I'm a French mathematician working in the field of partial differential equations and maybe most importantly at the interface with physics. And actually in preparation of the ICM I have been asked to present my research and also how I conduct this research. So one thing which is really important for me is that actually mathematics is a very collective and long time story. And so for me it was important that this presentation can be more like a discussion. And I'm very grateful that Natalie Aie has accepted to play this game with me. So actually it's not a random choice because Natalie is one of my former PhD students and she's actually now she is a professor in Paris. But I think she is very aware of both my research field and also what I'm dreaming of the mathematical community and this way of working actually. And so I'm very happy that we can try to figure out together what is important in this field. Thank you, thank you very much. So thanks for involving me. It's an honor to be part of such an initiative. And I think it's important for young generations. So let's start this conversation with something that I find interesting about you and you were mentioning. It's your particular vision about what does it mean to be part of a scientific community. Could you elaborate on this aspect and more precisely to start? What is your approach to research? So what I like in this job is actually that it's a very collective work. And so personally I like very much working with other people and just confronting different point of view. But I think that even though there are also people who are working alone, I think that they built upon things that have been already proved or disproved in the past. And so it's not there, they don't start from scratch. I think it's really important to remember that somehow this is a very big construction which is elaborated in this very long story. And for me it's really something which is important to remember and maybe right now we have a system which is a bit like a star system. And I find it's not really fair. Okay, I see what you mean. And what for you is behind the title researcher? I think it's a very good question and probably there is not just one definition of a researcher. It depends of course on the field. I think mathematics is very specific field. But especially because there is no experiment for instance so compared to other sciences it's of course different. But for me what is really important and probably it's not what people in the public can have as an idea of a researcher. It's that you have people who are creative and curious. I think it's really what I would consider as the first quality of a researcher is to be creative. So in this respect I think it's even though of course you need a lot of rigor especially in mathematics because say the earth of mathematics is to provide consistency or where everything is rigorous. But even though rigor is really important I think that mathematics somehow can be compared to art. Because I think there is really this importance of creativity. All right, so creativity I think it's one of the quality which is required to do research. For me I think the things that I've learned during this job is that you have to be patient and tenacious when tackling some problems. So another aspect is how you see yourself in the mathematical community. You said something about it. Could you precise a little bit what you meant before? Yes, so what is important for me is not say only my own contribution. Of course I'm happy if I can contribute and say understand deep things and this kind of things but it's really for me it's really a work that personally I envision with other people. And this is one of the things I like very much in this job is that first of all you have the freedom to choose your subject, you have the freedom to choose your collaborators and this is something that say working with other people is really something for me which is very fruitful actually. As you know somehow mathematics is kind of game but playing with abstract concepts so it's a bit strange because somehow different people will have different representation of the same object but I think it's both a bit crazy and very rich because just confronting these different views on the same object is actually very helpful to go deeper in a subject because you have all these views on the same object because somehow you are obliged to understand how your collaborator is just as the representation of this object and how you can conduct your reasoning and all these things so somehow you are obliged to be say to be a bit shifted in your own reasoning and I think it's really something which is amazing so for me it's really part of the job actually it's not you know fighting with this abstract concept but also trying together to figure out how deep these concepts are and how you can somehow build some bridges between different fields for me this is really all the points in mathematical research. Talking about the qualities to be a researcher another one I think is you have to have some communication skills I think it's also important it's an aspect which is a lot present in our job and actually since I've known you I've noticed that you are a lot involved in out which actions towards the general public the young generations why is it important to you? The first reason is that as I mentioned one say beyond creativity another very important quality is curiosity and I think curiosity is something that should really arose it's not it's of course young kids they are curious of a lot of things but being curious about science about understanding how the words around the gas is working I think it's something that that that you should learn somehow so I think it's really important that say even for very young kids we can have this they can have this this idea that research is not first of all it's not only for a very few number of people if they are interested in this in the field of science of course they they can participate this collective effort but also they they have to learn that some of science is not something that you which is past story it's really something which is still moving and there are still a lot of questions that have no answer and so that's really something where you should be active science is not just a listen that you have to learn it's really something that you have to discover also by yourself and so I think that this this is really important and I think if we want to have scientists in the future then we have to of course convince kids and and also maybe young people our students that can be not only interesting but that's really something which which is great yeah for me it's it's really important and it's also important to communicate towards the public which probably will not be a scientist because of course most of the people will not be scientists but still science is present everywhere in in our society and I think it's important to understand a bit just to be able to to vote and to participate the different debates and around I don't know technologies and biology and all these kind of things which are important just to be I don't know to live in our society yeah and I think also when we when we are in front of general public or young people we we we benefit from their refreshing perspective on some of the things we we talk we talk about in front of them because sometimes they don't approach the things the same way we do you were talking about that for colleagues but it's a little bit different again a little bit different for an audience which is not into science at all so I think it's interesting so still about communication could you also tell us how do you see communication within the mathematical community because I think this is one of the things which is important for you yes so there are different level of communication inside the community one is teaching of course I think so the community is is matter of researcher but also of PhD students post docks and even grad students so so of course there is this this this somehow communication just to help them learning things and and not just learning you know a specific course but also learning to be open-minded and to try to do all this connection between the different fields so just to have a very global overview of a subject and there is also this of course now even the field of mathematics is very broad and so we cannot really run everything but I think it's still important that that we still have a bit of ideas of what people are doing in other branches of mathematics and so I think this communication is really important I'm I'm not sure that everybody is really convinced that it's important and some fields of people are not really keen to try to communicate what they are doing but I think it's a bit like a pity because because I think that somehow the the strengths of mathematics is that that with this abstract setting you are able to to to catch a lot of say things which are really universal and so I think that it's really important at some point we can also understand what people in the different field are doing because maybe the same kind of reasoning and this are maybe there are simple ideas which can be translated into your field or into you know this kind of connection maybe surprising but but they can be very fruitful so I think it's really important that we keep as fear of as far as possible really open minded and and really aware of of course not of all the technical details and not of even even you know the terminology so maybe we should say because I I don't know we will look at this video but but mathematics so I'm not able to understand most of the mathematics that are done today but still I think that discussion with colleagues in other field are really enriching for for everybody so I think all these colloquia style lectures are really important yeah because you were I remember when we were discussing before you were saying that sometimes you can take an idea which she was designed for a completely different which has nothing to do with your problem and actually you see the idea and say oh my god I can I can actually use that for my for my things this is basically what you what you say but this is very this is very striking actually when you when you think about it so yeah I agree with you it's you definitely have to still be aware about everything happening in the different field even if you can you can't know everything but you have to try and we have to try to communicate far let's say not just to the people exactly in our field but we have and I think it's also a very good exercise for you doing this this trying to communicate for broad audience because then you have to do this effort to to try to to find what is really essential in the work what are the the arguments which are simple enough so that you can explain and so that people can understand how things are just that's just like a big puzzle and so you need to understand how the different pieces with with it will gather together so I think it's really both interesting for people who listen to the lecture and also for people who try to explain say to a non-specialist audience I think it's really this is really a way to go further together yeah yeah it's a win-win okay so let's keep digging this point and talk about science so could you tell us what is your field of research I can try at least and it's a good exercise as I told you so actually as I mentioned in introduction my my field of interest is partial differential equations which maybe is not very meaningful for for everybody but so what is important and what is very important motivation actually for me is that it's at the interface with physics and maybe I will not give you an exhaustive list of what are the problems I have thought about but actually I'm I'm I will probably talk about two of them just to to see that there is kind of variety of different problems so the first one is is kind of philosophical question and which is related actually to the sixth problem by Hilbert which has been asked so by Hilbert at the beginning of the 20th century and the occasion of the ICM in Paris and so this sixth problem is about the axiomatization of physics so you can say about but then it's just physics and mathematics but so the problem is rather easy to explain so for instance you you see that in this room there there is air so air is a gas it's constituted of we know now that it's considered a very small particles which are atoms or maybe now we also know that we should probably go to the quantum description but say let's say that it's a system of atoms so this this is a very first description of this this air and then you can try to understand all the forces which are exerted between this these atoms and and then you can write equations for this very big system of particles just following Newton's mechanics okay so that's the first way to describe the air of course this this is say essentially you cannot do anything with this model because it's very complex the number of particles it's so high that even with a very super computer and you cannot just say anything about the qualitative behavior of this this gas and so there are also models which are somehow more practical for instance fluid mechanics on this this kind of things and so there is a question which is okay but do you really describe the same thing just using this atomic description or using the fluid model so you said it's a very kind of philosophical question because you can say that you don't care okay just use this fluid model and apparently it's good description so you can be happy with this but you see that there is this this this problem of consistency somehow of the theory and I find it very exciting because because actually when you think about this problem at the mathematical level you see a lot of connection with a lot of branches of mathematics probability combinatorics even a bit of so number theory say dynamical system so it's really kind of of course it's the question comes from physics but you see that actually it will it will really be a very transverse problem and also the other thing is that say just looking at this problem so finally the question is is it possible to just discard a lot of information on the microscopic scale of course you don't care about the position and the velocity of one particular atom you don't care it's not really important so you are just interested in statistical quantity such as the average velocity of so just to say whether the air will just go out or go in and that's that's what you are interested in in the end and so the problem you see here at the mathematical level is to understand whether this all these details of the system are really important at this average level okay and so this is what is said this is one typical problem of say multi-scale expansion because you have small scales and you don't really care about the small scales but still they are important they have a global effect on macro scales and you are just interested in the end to filter this this macroscopic motion so I think that that's really a very large a very large category of question and problems and so this one may seem a bit a bit philosophical or maybe a bit theoretical and maybe it's not so important but but so that's the second problem that I would like to mention you see that with the same kind of techniques you can be interested in separating the different scales in for instance in austenitic flows so that's one topic that I like very much because I can really interact with with physicists both physicists doing experiments and also physicists say theoretical physicists and so for this this this motion of oceans you see that of course the main motion of the ocean is just to to move to move rigidly with the earth so the rotation is is the somehow the dominant effect but because of this this rotation you you expect the motion the fluid motion say the relative motion with respect to the earth to be very constrained and so then you can also try to use the same ideas of multi-scale expansion and then see that you can derive simplified models which are really important because of course even these fluid models if you think about the ocean so for example Navier-Stokes equation are not really relevant you have far too many details far too many things to simulate and so it's really important even in for practical purposes to to get this simplified model that you see that the from the mathematical point of view you see that it's essentially the same the same process you are interested in just removing small scales or small details and just in the end being able to to to describe in a qualitative way what you can observe and so I think you see that there are somehow two very different problems because one is is about you know statistical physics very fundamental statistical physics kinetic theory and so on the other one is about fluid mechanics and geophysics so apparently they share very few similarities but say at the mathematical level actually you can see that there are some properties some features that are are somehow a bit similar the way you can approach the this kind of questions at the mathematical level okay well speaking about the the six problem of Gilbert that you were mentioning in your first problem well actually you introduced to me this problem while I was doing my PhD with you and Florent Bertelin and it really influenced the way I do mathematics and it's actually what makes me fall for kinetic theory and and it keeps shaping the questions I'm asking and I'm interested in because as you as you just say it's relevant this kind of questions are relevant even for completely different context for instance recently I've been asking this kind of question in the context of opinion dynamics models dynamic opinion models sorry which is far from the gazes dynamics that I've started with so I think this is something very powerful and anyway what I meant is that this is this was the result that it really was at the beginning of my journey as a mathematician so do you have an equivalent a result that strikes you and that made you the researcher you are so from this point of view my my mathematical journey seems to be much more static than yours because actually I started from the sixth problem of Hilbert and now I'm back to the sixth problem of Hilbert and okay we have say some some of course some progresses but but still there this is very still a very open problem what I would like to say is that even though this seems like a static journey I think that there have been a lot of kind of small excursion and maybe that's the that's the occasion to come back on this this point that with one mathematical tool somehow you can you can study or you can adapt to very different situations so at some point during my PhD thesis I was interested in in Plasmas and Tokamaks so this seems to be very different from oceans but you see that in Plasmas the if you have a magnetic field and you have a very fast rotation in this fast rotation finally the effect of the fast rotation is not so different from the fast rotation of the fluid in the ocean due to the rotation of the earth so well I like very much with this with this say during a long time actually I I was hesitating between mathematics and physics because somehow I like very much physics because also because it provides a lot of intuition so you can somehow compare the representation that you have in your mind and and just the realm of the observation and so on so and I think it's it's kind of say somehow the observation guides your intuition and and somehow then when you prove something you can you can compare with so I like very much physics for this but in on the other end I'm somehow I'm I'm more comfortable with mathematics because I think that the missile of mathematics are really first of all rigorous so there is this set this framework which which is really helpful actually which helps you but but the other thing with mathematics is that you have this this abstract this abstract concepts abstract translation of of of this this mechanism and that's really powerful as you said because because then you can use the same tools the same kind of mathematics to to to study very different systems so just give you one example say micro-local analysis or semi-classical analysis where every technical things that I will not explain right now but but they were developed in the context of quantum mechanics so just to understand you know the behavior of one or two atoms and and this this so very very microscopic level but then you see that actually it's a very powerful tool just to separate the different scales as I mentioned and then we were able to use the same exactly the same mathematical setting just to look at this this big vortices in the ocean which are due to temperature so vortex like this is something like say the typical extent is about say 100 kilometers so you see that there is nothing to do with the atom okay so it's not the same scale at all this is not the same context at all but still you see that you are able to to to use the it's about to adapt there's this abstract representation of this this physical system and then and then you have this you have this surprising connection between two different fields and this I like very much actually this actually being surprised is part of research as well yeah yeah so so we are saying that okay so mathematics so you can do math for math and you can also use them for concrete problems attached to physics or other things but actually there is also beauty in mathematics and I often hear you talk about it and could you tell us what is for you an elegant demonstration so I totally agree that that this this aesthetics is part of mathematics as I told you in the projection I think that mathematics is kind of art so of course but then you see that aesthetics is a very subjective notion it's difficult to it's difficult to to characterize so well I find elegance is maybe not what you will find elegant so what I can tell you is what I find elegant somehow and for sure I like things which are simple so that may seem a bit a bit strange for definition but so this means that that I'm not full of all this you know and I think it's something which now happens very often that that you have very technical papers you know and read off pages of computation construction definitions and then okay you can read them check that you can go from one line to the other line but somehow what what is missing and for me it's something which is really important is to say catch the the whole thing with a single picture or maybe two or three but but say to have this this representation in your mind of what you are doing and so for me that that's what I call simplicity so somehow what I call simple is something that okay maybe I will not I will not of course check all the details with this this this big picture but it's something where I can find a big picture kind of representation in in in my mind where I see how all the things are connected together and I understood the mechanism somehow and as so for me being able to identify a single or three or two or find a number of mechanism and and I think it's part of the elegance of the proof so somehow it's kind of being able to to to extract a kind of structure and this for me is really what makes mathematics elegant say all these technical things are just okay of course they are necessary because in the end you need to check that everything is rigorous and so on but that for me it's really important that somehow you you can have this big picture in your mind and this this is part of what I call elegance and so when I I listen to a lecture say I will be happy in the end of the lecture if if I can have this this big picture and of course I can understand that that you have to check a lot of lemmas and technical things to to see that that this this big picture is really working in your your case but somehow if at the end of the lectures I just understood a couple of technical arguments then I'm not really happy because it's not not really mathematics it's just like competition yeah and maybe resonate with what we were saying before if you draw the big picture for the audience it's easier to extract what you could use for your problem which happened to be different which is more difficult if it's lost in a lot of technicalities I understand I think I understand what you mean okay thanks so one of the things that I enjoy about this job that I was not necessarily aware of when I started is that it's really not lonely if you choose it's not a lonely job it's it's a lot of collaboration and work in group and actually since you can choose who you work with you you can work with the people you appreciate and this is really one of the aspect that makes this job enjoyable for me and for you what makes it enjoyable I think that I join you on this this this characterization that that's think just doing things with others first of all because I very much you know talking with people and and and just I think it's also very a friendly way of working which which is very nice because actually this is part of the life but it's not my own life so I'm happy that that's I can somehow also have this friendly relation with with people I'm working with but but also as I maybe mentioned a bit earlier there is this this kind of very it's a very fascinating adventure for me to and for this I like really working with the same people during very long periods because somehow you you you learn of course you are not in the mind of other people but somehow you you learn really from from their approach from their representation from you know once again mathematics is as this this very particular feature that it say it's about abstract concept and so abstract concept you can have a lot of representation there is not just one which is relevant there are really many and and actually the more representation you have the the more you understand somehow the abstract objects and its main features it's it's and and so I like it very much to to to be able to confront my point of view with with the point of view of other people so I think it's really and in working you know on on very long times with the same people saying it's it's really a something which for me is really a great experience both from the human point of view and from from this this intellectual point of view in the end you obtain things that you you will never have imagined before and that's really surprise actually I think it's also a very a very nice particularity of our job probably in some jobs surprise is not very good things but for us I think it's probably the main discoveries are just surprises yeah I there is this quotation that you you gave on your speech for the French Academy that I really like and I think sum up a bit what you say is that alone you go faster and together you go further so you really benefit from the vision of others and and you can you can reach points you will never have alone so one of the things also you were saying I think that you enjoy is the fact that you can choose the people you work with but also the subject the the time when you you work the freedom I think is one of the points you yes I think that there is not so many jobs where you can show the resume okay so maybe I don't know whether there would be a young people looking at this video but we should say also that this job is sometimes difficult especially from the psychological point of view because say sometimes and it's a good surprise we find incredible things but most of the time you don't find anything and or you your right things which are completely wrong so I think it's also part of of the say it's somehow the price to pay for this freedom that's bad this creativity requires a lot of time and of freedom so if you have very strong constraint to to publish papers in within a short time or or to you know to to have a lot of connection with different people then you are say your mind is not really free for for trying strange things I think research is also about looking at things which maybe seem a bit crazy at the beginning so yeah I think I think freedom is really important and it should be respected which is very difficult because it's not really compatible with a lot of you know political constraints and this kind of thing we should be careful that especially young people can be can be free for for doing high quality research all right well well thank you very much for sharing your interesting vision and and your passion that we can feel I was very happy to spend this nice moment with you and is there anything you would add to to conclude thank you too