An Extended Interview with Manjul Bhargava

[Music] and my name is manju bhargavi I'm a mathematician at Princeton University okay we guess we should start with the sort of the elephant in the room you have a an honor that most mathematicians don't have can you tell us a little bit about the Fields Medal surprise that's given every four years at the International Congress of mathematicians up to four people every four years because the Congress has held every four years it has a strange age limit which was not officially in the original charter yeah unclear how it how developed it whether that's a good thing good thing about that yeah now our what were the other what what is your area and what were the area of the other fields medalists you mean the year the year that you I received it yeah there was a geometric hoop theory and geometry there was analysis obviously any given year you don't you can't represent all feelings right just cuz I you tend to I'm trying those fields I'm trying to get a sense of the scope in the range of this then your area is at number theory number theory yeah now number theory is a subtle area that people who don't do number theory especially the public fails to appreciate because it sounds like the easiest branch of mathematics because we all deal with integers and why do you think it is so subtle in which seems paradoxical just so many people why why is it so seems to be more subtle than most areas of mathematics yeah it's because the questions are very deceiving deceivingly simple which was part of the attraction towards the subject for me so many of the questions are so simple to state and yet when you try to solve them that same level of simple thinking does not lead to their answers and number theory has been amazing and that it's absorbed techniques from from geometry from topology from group Theory from from so many different areas in order to to tackle some of these very simple problems so we're at some very very as you said subtle and and deep techniques from a variety of fields in order to to solve some of these questions that are just so simple to state where you don't need to know anything and I think that's what makes it so so because in a lot of other subjects even the questions are difficult to state and then when you answer them they're about on the same level of difficulty even usually obviously the difficulty goes higher when you go to answer them but for a number theory that's that differences especially mic'd yeah it's hard to you talk about number theory and Princeton without mentioning Andrew Wiles yeah and and because he also drew upon other areas to augment standard numbers they absolutely is there a first off do know him does he still there do you work with him you know he was my adviser he was yeah yeah I did not know and yeah and wonderful as a PhD advisor he has this fantastic global view of mathematics which you can tell from his famous proof of course that he has a real sense of of the relative importance of different fields and how they interrelate and how they influence each other and that's a great quality to have an adviser I didn't work on the areas that he works in directly but having him as adviser just to look at the stuff I was doing and sort of generally guide me and push me in certain directions that he felt were more promising very helpful and just to have that kind of global perspective from somebody like that was was amazing we miss him he left for Oxford a few years ago oh I dunno no to go back home wasn't there a lot yeah well can you at least shed some light on the rumor that he shut himself into an attic for five years and then suddenly appeared with the proof all at once I mean is that a caricature of the what really happened or not well actually I hadn't arrived in Princeton yet I heard the same rumors when I arrived okay I I can't attest to how truthful exactly accurate they were I imagine they were somewhat true I don't think it's like literally truth well this the reason I ask is because it might affect how he taught you to view the creation process so he was your mentor so does he view is think that you should keep result too close to your chest for a long time or or being more open like most scientists are he certainly never recommended that I go shat myself in an attic okay but yeah he did recommend that I sit on things for a little while and let them sort of rest in my mind for a while until they sort of naturally take the next step and not prematurely I think that I've gotten somewhere before I've really felt that I've gone somewhere and especially for his PhD students I think this is true of many advisors that they you know what their PhD students talking about their work to seeing because they're teams of people working elsewhere who may be able to do it much faster than starting a PhD student but no it was never like that yes he's always encouraging to be fairly open very good enough that what I was working on with at least two other colleagues and fellow grad students since we are at g4g and we are based on the since of finding the intersection between mathematics and recreation and arts and everything else where where was your first who was the first time you noticed mathematics impacting the outside world and well it's everywhere you can see of course but where were you first drawn to well in the beginning it was just my personal experiences I would i love making games by myself and then trying to play with them I I always tell the story of how I used to like to stack oranges and pyramids seven or eight years old that take all the family oranges that were meant for the juicer and and make pyramid structures and I wanted to know if you take a triangular pyramid of oranges and you have this many oranges on each side how many total oranges you need in order to to make the whole pyramid hmm and does the first math problem that I really was excited about early on and had when I finally solved it but took weeks I think I found the answer that if you have and oranges on each side the total number of oranges you need for the pyramid is n times n plus 1 times n plus 2 divided by 6 and that was an amazing revelation for me that of how of the predictive power of mathematics then you can you can just put in a number n into this formula and I'll tell you how many oranges you mean that was like it that seems like a direct connection to the real world where you have this abstract formula and it tells you boom does M&E orangey and then you can actually build that permanent with that many oranges and it just works out perfectly and it was number there there was number theory yeah yesterday he perhaps it was today I forgotten you've previously given a talk we can edit this out um you gave a talk about the ramifications of some number theory results some corollaries from that that lead to the principle behind a lot of magic tricks did you have what order did that come in did you know about the magic first and the applications thereof or were you just sort of going back in the literature no I learned about the magic I first I mean as far as my tech goes I was talking about numbers such as one four two eight five seven we have this amazing property that you take its first few multiples and just get the same digits back alright when you take the first six months opposed of one forty two eight five seven you just get cyclic permutations of the same number yeah I learned that as a child I don't remember where I first learned it but I do remember eventually hitting a Martin Gardner article about it mmm-hmm and I found this number absolutely magical and of course it has many magical applications in the sense that is musicians actually use this number but I didn't know the full mathematics behind it but I always always wondered what is it that made that number take you that the way it does and then as I learned more number theory of course those ingredients started to fall into place and then are they're implementing such numbers that have that property those are things that are coming when you start taking graduate courses and number theory you start making those connections but those deep results the number theory they're often not presented with that recreational application in mind and I think it should be because it certainly excited me a lot to be able to make those connections and it made those abstract results more concrete if connected to something that I could understand as a child and have deep implications for those simple questions that has a child even though they're very deep results in conjectures a number theory that they actually connect to and that you can only really understand when you're in graduate school so that I found it's just absolutely amazing that that's something that really excites me about mathematics that you can ask these simple questions that it just looked like fun and then they connect to really deep structures later on but do you incorporate this in your teaching to you because number theory is always made relevant by talking about cryptography and things like that but recreational mathematics would be I think just equally motivating to students do you find you ever do that yeah I'd cooperate am i teaching all the time absolutely when I teach arson conjecture Harden's conjecture I certainly bring up one four to eight five seven bring up card shuffling and it makes it more exciting for me and if it makes it more exciting for me it makes it more exciting for the students for just the fact that you can connect it to things that are so simple in my experience definitely makes it much more exciting for students and I think Martin Gardner always said that play play should be the way that you even understand serious things and I I really believe that and then try to do my best in class to do that and I think we should really make it part of the curriculum even starting in you know in school levels you know there's a lot of it's very taught in a very abstract mechanical way sometimes and I think the play aspect is it's too often ignored and I think it should be right in its the school level all the way after the graduate school level I think this is something that can really be done in it makes math well that's what excites mathematicians when they do their work so why don't we share that with with the students when we teach it I couldn't agree more now we also know because we've seen the title of your talk for the Sunday lecture that you find some connections with music and drumming and rhythms do you want to remark upon that it's it's it's it's clearly quote unquote a application but most people would view it more as an art than an application right well it's one of the things I was going to talk about tomorrow is the fact that many of the fundamental mathematical structures that we we talk about such as binomial coefficients or Fibonacci numbers or memory wheels they help they sort of they arose in history for the first time by artists and poets thinking about their subject as an art and these mathematical consequences just came and we don't really know even in India so I'm gonna talk about some of the Indian instances that this happening this because I grew up in that this Indian musical tradition my family had lots of Indian musicians and so and my grandfather is a Sanskrit scholar so I was lucky to have grown up in this tradition and and got to learn some of these sort of these ancient works of literature that were mainly poet poetry and music related and yet they're writing about these mathematical objects and even in India the mathematicians are unaware of this it's only the poets and the musicians you know about this but in fact in history Fibonacci numbers were first discovered by poets a thousand years before Fibonacci binomial coefficients were discovered thousand years before Pascal and it really illustrates the fine line between art and mathematics that in ancient times people didn't really separate them the way we do now let me ask you about one intersection that I'm guessing you've heard of I don't know is the yama tell Roger but know Salah gum yeah right and yeah I was gonna take him to that a little bit tomorrow as well gonna talk about that tomorrow yeah I'll make a few remarks about that that if you could so that's a that's an example of a memory wheel where if you memorize this sequence of say long and short syllables it allows you to sweep out all possible in this case triplets of of long and short syllables so all eight possible long and short syllables are incorporated in this worth in this word you might fight eyes or - Allah gum and what it allowed poets to do in ancient times is to memorize very very long meters and not just memorize them but also preserve them for posterity so what they would do is they would write poetry so say they composed a new meter and they wanted that to be held intact for all of posterity for for all of history well it's very easy if you have a meter it's just consisting of long and short syllables it's very easy for the next generation or two generations from now to flip a bit and then when long comes a short and the composition is destroyed so how do you make sure that your composition stays of your meat of this meter stays intact for all history what they did is they they used this word to encode the rhythms because this has triples in it they break it up into triples they didn't code the rhythm and they'd write a poem they'd write a poem about the meter in the meter and inside the meter would be the encoding using this word I say and once you did that if anything flips in that it's like an error correction yes so any bit was flipped in that poem that they wrote about their meter you'd notice that the poem was not in the meter you noticed that the encoding of the meter is not correct it's not matching and you know how to fix the air so those like an ancient error correcting code that came came about well the air correction aspect is new to me I've heard it described as an exercise and I heard it described as a sutra yeah but it's an error correcting sit there error correcting sutra news to me now speaking of with the rhythms before I ask you about Indian rhythms are you equated with the mathematician or godfrid to sense he wrote a book called the geometry and musical rhythms it's a beautiful book I recommend it to you okay musical instruments musical with the musical rhythms and he has a very because he is a computer scientist and mathematician but he mostly he was studying African rhythms and so um but Indian rhythms are notoriously difficult for Westerners because they're always in 1513 or 19 or something like that so I guess I should start with the cultural aspect of it why are they so why are these rhythms that we consider unusual so natural to the Indian ear yeah the main difference Indian rhythms with Western rhythms I guess is their length I mean I just tend to be longer they're not quick moving necessarily but they're alive I mean they may be quickly moving within the cycle but the cycles themselves are long and these long cycles allow lots of play within the cycle and a build-up to the downbeat because the downbeat only comes every once in a while yes are you really so that's that's a huge basis for for the rhythmic theory of Indian music is that you want this build up to where is the downbeat and so if you want that build up you need time for that build up to happen and so the cycles tend to be long and there are points of emphasis within the within the cycle you feel certain sub down beats you know within the cycle but then the main downbeat is what here I worked towards and tell a story that that's a ends at the downbeat that's how the historical reason for this is that's how the poetry was written the poetry was in these long meters that I was telling you that they used a mod that adds abundance of it gotten to to remember and to preserve for posterity and these long meters were there and then the music was built around that kind of poetry which was also in these long in these long meters and then it eventually led to this way of practicing music where you had these long meters that would when that came to an end that was like the crescendo the climax and boost and the music would build up to that point and that led to really intricate ways of developing a rhythmic story that led to the downbeat and that's what makes Indian music so intricate and so complex or it's short cycles don't allow room for you to do necessarily well maybe because the Westerners are too impatient and they don't have the desire to let these things develop fully know which probably says a lot about Indian culture in general very patient cuts even Education Culture the rhythms such as you we talked about for that sutra are those translated directly into drumming rhythms toploader rhythms or they just somehow relate it or they let me say it more directly are these table exercises yeah yeah absolutely I mean they're so in poetry there's mostly a notion of long and short and so there's a lot of public compositions and in new music compositions where they're this dichotomy there is this dichotomy between long and short that's just one kind of a blur rhythm of course there's a lot there's a lot there's a huge variety of rhythms that have developed over the years but there is one kind of kind of you know rhythm that just does that plays with this dichotomy in between long and short I'll play a little bit of it tomorrow and that has its origins in the poetic traditions well the two most famous names of course are zakir hussain ali raka and father and son mmm father and son father and son and I was told that Ali Rocco was his for his entire life only played southern rhythms whereas actor Hussain is more cosmopolitan plays rhythms from all over India and the rest of the world right do the rhythms that you have been brought him brought up on are they the southern rhythms of Ollie Rocca or not you know it's been a long time learning from mr. Dekkers Indian so as a result of that yeah I get he loves to introduce rhythms from all over India and the way he's been able to master so many of the different kinds and bring them together has been wonderful for the for the tradition it used to be much more localized you know there via Delhi erina and there via different cameras from from Oliver karana just means a tradition and those traditions would net he kept separate because those were localities and there wasn't that much internationalization so to speak in now now combining those traditions after they developed separately it was actually very beautiful because they've got their chance to really develop in their own way separately for a while and now we see how that can they interact and that's been happening now in large part because of us and others and it's a really exciting time and for the subject as a result but again the rhythms that you were brought up on you where where would they be on the map deply New Delhi all right and your response surprised me enormous ly you actually studied with Zakir Hussain yeah yeah that's surprises me and I couldn't be more impressed that impresses me more than the Fields Medal because I am he's so much respect for him yeah has been a wonderful supporter and friend and teacher there in Sydney so yeah I can't I can't say enough about him and how amazing is in terms of the mathematics of the rhythms are some parts of India more interesting to you those rhythms I mean they're not the same everywhere right so are there some that are they all pretty much the same mathematically or there's some that have much more intricate deeper mathematical structure and I've noticed that in the south of India the real south I mean the rhythms of say a letter cut concept where we're still you know if the bomb you know Bombay area it's still northern India the southern part of northern India but if you really go into the South where they're called Karnataka Carnatic rhythms yes those rhythms I find it incredibly mathematically intricate and complex so I would say like that reason Gemini do in Kerala and Karnataka though those the rhythms there have really developed to a mathematical sophistication that it just still blows my mind will you be demonstrating those tomorrow a little bit yeah yeah I mean some of these long short kinds of things actually have the oranges in the Southern tradition of drumming but the blows mostly used for northern rhythms but again missed ads accuracy and as an example of someone who's really crossed over these rhythms that used to play be played on South Indian rhythmic instruments are now being played on the table and lots of it has been adapted by him and other public players today so that that interaction has been happening more and more it's there's a lot common between North Indian and South Indian drumming Hindustani in Germany and kinetic drumming but there was a lot that was different on the sort of mathematical side and that that kind of interaction maybe people in in the south would say similar things about what's happening in North since I grew up mostly in the northern tradition it just surprises me some of the kind of mathematical constructions they do in the south and I'm sure that people in the south would say things about the north northern traditions in the same way but that interaction is now happening and that exchange is making the music even richer than they were when they were separate now there's a sort of a folk theorem or folklore that the best computer scientists are musicians or a lot of them are concert pianists like Scott Kim in India is there a correlation between mathematical aptitude and this drumming yeah I think there is I think that's a worldwide thing I think that good scientists good mathematicians good computer scientists so common that they they play an instrument or they paint or they do some kind of art I think that's that's pretty common to see and I know Steve Jobs used to talk a lot about that he loved to hire computer scientists that were also artists on the side hers who loves his son side because he found that that made them a lot more creative more innovative had it they had a feeling of aesthetics that he really needed in his products to marry aesthetics and and and the latest science but I noticed that the best mathematicians in scientist you take a look at ya and you see that art is a huge part of their lives music and drumming a huge part of their lives there's something about developing both sides of the brain that are just excited a brain in order to be creative even in science and I definitely feel that in my in my own worlds that I spend enough time on art and I'm more creative also and I think about mathematics the Department of math at Princeton are they gonna start a band well actually so every year in Princeton there is a professional level concert that's just just math you know just the math department people they're incredibly talented musicians and then in the mathematics department and they do have many sub van little little vans that change every year and that's the look that was meant to be a joke but I'm not surprised by your answer do you know Ron Graham and I yeah of course he has he's expressed his his skills through juggling that's right yeah but I considered acrobatics but the juggling I think is an expression of artistic expression for him the way it is for drumming is for other people and trampoline and he's a multi-talented man I first met him walking on his hands down the hall of Bell Labs actually worked one summer at the labs when he was the chief scientist and I went to his office and there he is in his funny acrobatic positions and like this is Professor Graham yes he's 80 now so I don't know if he does that anymore okay so are there any other relationships that perhaps that you've learned here from g4g that you will want to explore when you get back I mean because there's so much being proposed and floated around here have you discovered some new oh my gosh this relationship just the conference has been incredible it's information overload especially my brain is full but there's certainly lots of things that have stimulated the mind for me in the past few days and yeah definitely I think lots of the ideas of tessellations and painting and I love that so many people are interested in mathematics and art here at g4g in addition to mathematics and magic of course which it's another one of my interests I meant to get back to the magic then I did not know you had a real interesting magic that's the reason I asked you earlier if you had gone which direction your talk came from where they came from magic to math or math to magic you do have an interest in magic he quoted from pallbearers review now no one knows about pallbearers of you he's not a magician all right because it's not sold to the public are you is this something that you part of your own magic library yeah no I I went and spent a lot of time with Paul bearer's review in in conjuring arts this is a magic library in New York City oh yes this is the best library magician magic in or testing yeah and it's just fun to just sit there and read and see the amazing ideas that come through the kind of creativity that you see in some of these magic journals it's very reminiscent of the kind of creativity to look for in mathematics journals you know the kinds of ideas that people come up with to solve certain magical problems you know here are the constraints we want to be able to do this and we want this kind of effect and here the you know here are constraints can we solve it and then they some of them said go and solve it sometimes they loosen the hypotheses in the same way that mathematicians I find quite a parallel between solving magical problems and solving mathematical problems well you don't need to be told that Gartner had a lifelong interest in magic yeah great first published in 1930 and he last published in 2010 and pretty much every year in between right and and he of course subscribe as you know wrote for Paul bearer's review as well it was a good friend of Carl foulest and a lot of what I how I got interested in that I mean I never practiced magic so much growing up but I loved reading Martin Gardner and things that he recommended to read sort of as it's just the theoretical problem solving of magic there's something that I really really enjoy Gardner I see yeah and then later on precede echinus when i I'm Tory later on when I went to college my thesis advisor one of my thesis advisor so that's persi diaconis oh my goodness yeah per say you've led a charmed life I'm very lucky yeah to have had the chance to see his perspective on there's a lot of good gardener stories that I don't want to repeat for you but they have deep deep relationships here today yeah but I was gonna ask you about shuffling as you mentioned shuffling briefly in your lecture mmm but I don't need to ask because now I know you learned about the relationship to shuffling from persi diaconis oh yeah one of the we certainly talked a lot about shuffling edge of course read about those things before I came to college but I was ready yeah yeah I was ready to go talk to him when I arrived yeah yeah well he learned magic from dying diverting so so can we say that you learned magic from Percy well yeah yeah I mean certainly a lot of a lot of stuff on the theoretical side it differently because he apparently practices many hours a day even now right it's very hard to get him to to show us but occasionally if he's in the mood to see some of it but only when I started meeting more magician said to realize his his repute in the magic world I mean in the math world you know these in the mathematics department people don't really know yes yes he's an amazing mathematician number theorist not a number theorist he's no worse there's kind of an everything instance I doesn't see he looks for magic everywhere wherever it's found and then he jumps into it he said he said connections to number theory every once in a while well let me ask you about your prehistory because anybody who goes from persi diaconis to Andrew Wiles must have had a good resume before that what what did you do to come to these people's attention and no actually I never I didn't have my survey I didn't have my Sarah we ended to win some famous competition or did you have a no actually yeah before I got to college I mostly was learning on my own or with my family or spending time in Jaipur India and learning uh blah I mean with my grandfather so I wasn't really on the radar of any anything national or international I was just sort of doing things on my own with family not going to school very much really well you must have either performed well or been a personally interesting person to somebody like like persi diaconis so I some however you did it it's it was a harbinger of their your future success that's all good so what else should you can you tell me about your I mean we really can't talk about your mathematics your theorems and your and your and your recent research but is there anything else we should know that now that we know your magician and interested in puzzles and interested in the mathematics of rhythms and so forth perhaps something else I haven't for asked you about that would be relevant at the g4g community cover look quite a lot okay that's quite enough I just feel like I I would hate to learn after we left the room that there was something else that you did that I should have asked about no but it was quite enough and your accomplishments and all these areas are extraordinary so we we're happy that you're here and I'll continue success and thank you for coming no thank you thanks for having me great pleasure thank you

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Length: 32min 55sec (1975 seconds)

Published: Sat Jun 23 2018