Fermat’s Last Theorem (with Ken Ribet) - Numberphile Podcast

so can do i have to call you mr president well you can if you want do people call you mr president uh sometimes jokingly what honorific is used when you're like at meetings and that i kind of live in berkeley which is known for its informality so i'm very happy if people call me ken and i've been called you know dr rivett and mr of it and professor rivet and professor ken and everything else but like at ams board meetings when you're wearing your president hat is there something that they have to call you when they're like addressing the chair and is there a proper honorific or oh no i have a gavel and basically we're all friends do you ever bang the gavel then have you ever had to like bang it or call something to order or um basically not i'm brady harren and this is the number five podcast today our guest is ken ribbet he's a math professor at the university of california berkeley in the world of mathematics ken's probably best known for his work on famar's last theorem but hang on i hear you asked didn't andrew wiles prove for mars last theorem well yes but this proof was a huge jigsaw puzzle with earlier contributions and one of the penultimate puzzle pieces was put in place by ken today he's going to tell us about it and what it was like to be in the actual room when wiles proof was finally revealed but first in case you can't tell i am a little bit fascinated by ken's current role leading the american mathematical society the ams how did you become president is it just like an informal thing among mathematicians is it a competition is it like a campaign well 30 years ago or 40 years ago i think each president would choose his successor they're all males and at a certain point somebody decided that it might be good to have an election and i know the candidate who lost the first election he was confident that he would just be elected without any question and his opponent actually campaigned by calling up some people and saying hey you know i actually want to do this so please vote for me and he won and there's a nominating committee that meets at joint meetings and also informally by email all the time and they're considering candidates for offices like the president and the vice presidents and so on when they choose someone as a potential candidate they approach that person and ask him or her whether or not person will run and in my case i was very flattered and i said absolutely and i ran in an election i had one opponent who is very much like me in a lot of respects he's from california we have similar mathematical backgrounds and i think both of us were viewed as very popular and very well known and there's no campaigning in the sense of debates or you know calling calling your opponent you know lying ted or something it's still very collegial but i did make it known to my colleagues at berkeley that i actually was going to be happy to serve very often if you see someone you know who's a candidate for something you say well we're going to do that person a favor by voting for the opponent but i actually wanted to do it and i was very happy that i won was it a landslide or was it a narrow one well this is confidential but it wasn't the sort of situation where we were having to look at hanging chads okay but it was reasonably close what is the role of the president you've already referred to presiding over meetings of the council and the behind the scenes thing what else do you have to do do you have to like go and cut ribbons and i do cut ribbons there's that every annual meeting the president of the american math society cuts a very large ribbon with an even larger pair of scissors to open the exhibits the president presides over the joint prize session at the annual meeting president comes to the congressional briefings in washington dc there are now two of them per year sponsored jointly by msri and the american math society well let's talk a bit about your background then let's go back in time a bit because there's so many things i want to ask you one of the first things i want to ask you is about your surname river where is that from it's from eastern poland it's from a town called graevo which i've never visited my grandfather was ribetsky and when he came to the united states in the early part of the 20th century it was the fashion at ellis island to make everyone american as american as possible and so i became ribbit which has become very useful to me in france and many of my colleagues they would phone up restaurants to make reservations and try to explain their last names and if the last name didn't sound french there'd be a lot of hesitation trying to get the name right and so on so people do think it's french sometimes ribeye or something yeah well there are many many french bay and in fact on facebook you can see they're big clusters of them and there are people who've contacted me saying my ancestors came from france through cuba were your ancestors in cuba no poland there was the ellis island corleone moment for your family where the name changes in just a few seconds right where were you born in america so i was born in brooklyn new york my parents were both born in new york city and when i was three years old we moved to a place called rockaway which is a part of queens but it's a pretty remote part of queens like they don't even have a starbucks nearby they show you how remote it is and recently it's become very brooklynized because it has surfing and so all the hipsters come from brooklyn now on the weekends and many of them have actually moved to rockaway so for example the rock singer patty smith bought a house were your parents mathematical academic type people my father was a cpa an accountant and when i was a little boy he would always be adding numbers either by hand or with a small adding machine and i was fascinated by numbers and i would ask my dad to give me you know long addition problem and i think that's what hooked me in this was the start was it yeah at school were you gifted at mathematics was it easy for you it was my best subject yeah so i was a pretty good student terrible athlete complete nerd but i was good at school in kind of all subjects and math was the easiest and was that the path you wanted like if i was to talk to the teenage ken robert would he have said oh i want to be a mathematician one day i don't think i knew that there was such a thing called a mathematician i've told the story many times but it started when i was a freshman at brown i went to my first mathematics course it was a course in abstract linear algebra and i loved the material and i was really taken with a professor and i you know looked at this guy his name was frank stewart and i said i want to be like that this is what i want to do i had still no idea what it actually meant you know i didn't know what professors did how they spent their time you know there's thing called research and committee work and reviewing and traveling i had no idea what the game was but i was very taken both with the content with the mathematics and also with this kind of freedom from the constraints of business what were you at brown doing well so i showed up as a freshman with some vague intent to look try math and applied math and chemistry i took one applied math course it was a year-long course i didn't like it very much i never took a chemistry course so i went straight for math i did math and broadcast radio i was on the campus radio station oh well i'll be watching your microphone technique with care then you have to excuse my ignorance about the us college system then you had been accepted and turned up at brown to start your university career and it still wasn't known what you were going to be studying that's correct in the u.s when people come to college they are not really expected to declare their major until their third year and so there's this idea that they can experiment and try different things in fact it's very common i mean if you look at what people are majoring in on say the berkeley campus while they're majoring in things like social relations and anthropology you know theater it's very rare to take a high school student and say what do you want to major in and people say anthropology you know people talk about their core subjects maybe they'll talk about computer science but they won't think well i want to be in geography so ken if i was america's most gifted mathematics student at high school and berkeley wanted me for this reason and offered me a place i could then say oh thanks for my place at berkeley but i'm not really interested in mathematics i happen to be good at it but i want to be an actor and i could just do theater and never even study a jot of mathematics absolutely all right okay i mean the admissions boards they choose people to try to sculpt the profile of their entering class and they have an idea of who's coming in and they could be completely mistaken this is new information to me you did follow this mathematical path and then you decided pretty early on oh i want to be like this this role model professor and you did that eventually did you i did so i'm the rare example of somebody who set out on a path and just kept walking straight i mean most people you know yogi berra said if you come to a fork in the road take it i mean most people end up doing things that that are completely unpredictable and my thing you know i just kept going forward and there was no obstacle and i liked it more and more and i here i am and then you started having a specialization in mathematics what was the field of math that inspired you it's a blend of number theory which is the study of whole numbers and geometry which also pretty well understood what that is so there's a kind of number theory slash algebraic geometry subject which has been coined arithmetical algebraic geometry so that was my subject and i came to it because i had some professors at brown who were kind of very very forceful and they said you're very good and math read this paper and there are these two people ken ireland and michael rosen and they were fantastic you know they were doing interesting stuff they were interested in things and they kind of kept pushing me in different directions they told me where to go to graduate school who to work with what subjects were interesting and it just meshed well with me so was it an aptitude or was it peer pressure well so i think i was lucky in that i was pushed into a subject that i'm actually good at i believe that people have very uneven aptitudes even within a subject like mathematics you know i may not have been very good at geometry or probability or some other subject i probably would have been okay because you know i was kind of good all around but by luck i was pushed into a subject that really spoke to me and i was able to speak back after a while at this point is your ambition to be a teacher like you know a professor in front of a class and inspiring mathematicians or are you wanting to be like a gauss and an oiler and you know the person who's making the discoveries and having the mathematical fame i think the mix is the best thing because if you do several things and on a given day you're not so good at one of them when you turn to the other whereas if you're just focused on one thing like for example suppose you have a sabbatical year and you're at a math institute and you know that the entire year you're going to be doing research well at the end of a day if your pad of paper is still blank you feel terrible you haven't done anything whereas if you start thinking about something and you kind of keep going in a circle and you've just come back to what you've done before you say well you know maybe it's time to make up this week's homework we're going to come to famar's last theorem shortly in which you played obviously a huge role but at this point when you're just starting out in this field and you're like you know you're one of the new kids on the block what was the holy grail problem of your topic what was the thing that you would be lying in bed thinking gosh if i could be the person to solve that that would be amazing well there are a lot of long-term goals for the subject one of them curiously is the theorem that was proved by andrew wiles with the help of richard taylor and brian conrad and so on the modularity of elliptic curves that was a very well known conjecture that i first heard about as a first year graduate student at the time it was called vase conjecture after andre vay who wrote a paper related to it in 1968 this was kind of a holy grail but not in the sense that you know everyone's trying to do it it just basically colored the landscape but at that point was that not connected to for mars last theory absolutely not it had nothing to do with fairmont's last theorem the thing that i studied that was my thesis and a lot of my subsequent work one topic is galwa representations and modular forms which came into the proof of fairmont's last theorem so when i was a graduate student there were countless courses and seminars on subjects like iwasawa theory gawa representations modular forms these are all things that came together you know 20 years later 25 years later in the proof of fairmon's last year were these kind of like riemann hypothesis type things where there was already mathematics built on assumptions and you needed to prove it for that to hold or was it more just like something in the distance like a finish line oh it's a mix i mean so certainly over time people became more and more confident that elliptic curves would end up being modular they thought you know it was true but something we couldn't prove so they began kind of driving consequences of it so if you derive a consequence of an unproved conjecture you have a theorem you can state it in different ways you could say assume all elliptic curves are modular then such and such is true another way to spin it you can say that all elliptic curves that happen to be modular have the following properties perhaps at this point we should deal with what for mars last theorem actually is now there are a few number five videos about it you can go and check them out i'll put links down in the show notes but let's give it a go in audio form now imagine in your head a pretty simple equation and quite a famous one a squared plus b squared equals c squared i'm sure you're familiar with this one you probably remember it from pythagoras at school in the right angle triangles and the question is what three positive integers so whole numbers can you put in the place of a b and c so the equation works a squared plus b squared equals c squared and well in this case there are lots of possible answers in fact there are an infinite number of answers for example 3 4 and 5 3 squared plus 4 squared equals 5 squared you could use 5 12 and 13. you could use 9 40 and 41 you could use 33 56 and 65. there are all sorts of ways to crack this nut these are called pythagorean triples but let's up the ante a little bit let's not square those numbers let's cube them raise them to a power of three so now we have a cubed plus b cubed equals c cubed hmm are there three positive integers we can put in there that will make this equation work and give it a go if you want but don't spend too long on it what about if we raise it to the 4th power a to the 4 plus b to the 4 equals c to the 4 or any number any n a to the nth power plus b to the nth power equals c to the nth power are there numbers we can put in that place positive integers that will make this equation work now back in 1637 a famous guy called pierre de famar said no there's not and i've got a proof he wrote in the margin of a book he just hand scribbled i've got a proof that you can't do it with anything except of course the squares but he said i haven't got room here in the margin to write the proof i think he you know i'll come back to it at a later date he never did he never wrote the proof no one ever saw it and this became known as for mars last theorem was there a proof that there are no positive integers that you could put in the places of a b and c with all these higher powers that would work was this impossible for hundreds of years no one knew they never found any but there was no like rigorous proof now that finally changed when an englishman named andrew wiles gave a famous lecture and revealed a proof and suffice to say you wouldn't be writing this proof in the margin of a book it was really really complicated really advanced cutting-edge new mathematics so there's for mars last theorem i hope you have some idea of what it is in your head we're going to get back to it in a minute but let's get back to our discussion with ken and find out where he's at in the years leading up to this big moment [Music] well i personally was doing pretty well although you know i had a deep sense of insecurity you know was this worth anything i wrote a thesis at harvard that i was kind of vaguely proud of and i wondered whether anyone will offer me a job what was the title of your thesis gower representations attached to a billion varieties with many real multiplications catchy okay so that was the title and in fact my thesis you know i wondered whether it would even be published it kind of sat on my desk for a year and a half and finally a mathematician named serge lang grabbed it and he said i'm sending it to the american journal and i'm going to tell the editor-in-chief to publish it i mean he did that and nothing happened for about two years and finally i kind of inquired you know whatever happened to this and they asked and finally it just got published you know i was wondering if anyone would ever read it but it turns out it has lots of citations and people think it's a good thing for background i was waiting you know to hear whether any place would ever offer me a job and before i expected job offers to come i got a phone call from princeton university asking me to come and be a basically a postdoc so i was there for it's hard to count the years because the third year that i was supposedly in princeton i got a fellowship to study in paris so that was my first year in paris and i actually taught at princeton for a total of three years with this year in paris kind of sandwiched between the second and third year you got to take that ribeye surname out for a test drive yeah in fact one of the first things i did was to take the metro to the ampascree bay which is a little alleyway and i certainly have photos of myself standing in front of the ampassry bay excellent and then what happened after that three years where were you next in the last year at princeton i got a phone call from berkeley saying you know how would you like to come out and join our faculty so this was completely unexpected i hadn't applied to berkeley but secretly you know when i thought about universities where i might go berkeley was probably at the top of the list because it was one of the top three universities in terms of mathematics the other two being harvard and princeton and i had visited berkeley once for a week on my way to a conference i just thought it was paradise so i tried my best to hide my enthusiasm when they phoned me up i ultimately accepted an offer of an associate professorship at berkeley and promptly went to paris again for a year and so i first came to berkeley kind of a year and a half after the initial phone call what was it about berkeley because the can i know you're berkeley through and through like you're you're such a berkeley guy to me but like i guess then you're a real east coast guy so what was it about berkeley that appealed to you well it was kind of the light and the kind of joy the informality and telegraph avenue was full of people wearing tie-dye shirts and it was kind of like the 60s was still going on but you're an east coast guy wouldn't you look at that like shun that weren't you this brooklyn guy who would think oh those hippies over there well you know i'm thinking of someone i know who works in san diego who applied for a job and in his interview he said i'm a californian trapped in the body of an englishman so maybe i was a californian trapped in the body of an east coast person okay that makes sense let's jump forward then to fermat's last theorem what did you do how did you suddenly find yourself in this spotlight this is before a while before that's right for a while so this is in the early to mid 1980s there was this guy gerhard frye who keeps coming up in all the discussions of it and he was the first person that i knew of to try to think about the links between elliptic curves and solutions to fairmont's last theorem so at the time there was a lot of study about elliptic curves with various properties and if you had an elliptic curve with various properties you could derive from that elliptic curve the solution to some equation and there was a movement one of the mathematicians was a russian mathematician demianko where you try to rule out certain kinds of elliptic curves by deriving from the existence of the elliptic curve a solution to an equation that didn't have solutions so that was the subject and it was going back and forth between elliptic curves and solutions and fry somehow stumbled on this idea that if you had a solution to fairmont's last theorem this would give you an elliptic curve with extremely problematic properties and he kind of went around telling people about this and he came to berkeley and spoke to me and gave a talk and i was very unconvinced i kind of really didn't believe it this is around 1982 or 1983 and over the next year or two he came to this idea that if elliptic curves were known to be modular it should be possible to prove fairmon's last theorem and he wrote a manuscript that was like two or three pages with an outline of the assertion that the modularity of elliptic curves implies fairmont's last theorem and he was well aware of the fact that his outline was not at all complete but he was hoping that people who were experts in the theory of modular curves like me i guess would fill in all the blanks and and kind of make the thing okay i was still completely unconvinced i didn't kind of know that he was right but he gave lectures in europe and a lot of european mathematicians in 1984-85 that academic year started thinking about his lectures in his little manuscript and thinking about ways to justify this idea that the modularity of elliptic curves could imply fairmont's last theorem and one of the signal things that happened was that jean-pierre wrote down a longer manuscript it was a letter to jean francois french mathematician explaining that if you could only prove what sarah thought was a tiny little assertion he called it epsilon meaning a small number then you could actually justify what fry had started to do so this was like a little screw or just a little piece of the puzzle but it was really really important to hold it all together yeah so in other words sarah's letter basically said fry looks like he's right you just have to prove this one extra thing and this was in the summer of 1985 and i got a copy of the letter we were all together at some conference in northern california and i started thinking about this epsilon and it was really right in the center of things that i understood were you thinking about it ken because it was like an itch in your brain and a curiosity or were you thinking greatness awaits if this can be solved well i thought that the connection with fairmont was kind of the icing on the cake but i'm not one of these people who say you know i've kind of went to the library when i was a 10 year old and read about fairmont's last theorem and it was my great goal it was a challenge it was a mathematical challenge it was right in my subject it was something that i thought i could do and i was responding to that challenge the connection with fairmont made it you know even more important to think about like any mathematician you knew of for mars last theorem it was just like a famous thing but i'm not going to ask you to explain and the proof in the mathematics because i wouldn't understand it and you can't do it in a podcast but how did you do it where did you do it did you do it lying in the bath were you walking along the bay did you just sit in your office with a notepad and a pencil where did you crack this nut oh so i thought about it off and on for a year this was the academic year 1985-86 and i you know was teaching calculus and whenever i had a spare moment i thought a little bit about this problem and asked myself whether i had any special insight into it that other people didn't have and at the end of the teaching so this would be in may 1986 i started thinking about the problem more seriously i was on my way to europe so the first thing that i did was i went to harvard for basically a week so i had an office that i was able to use and i was also staying with my sister in wellesley i remember sitting in her kind of breakfast table in wellesley thinking about this thing and realizing that i knew something that i hadn't realized before that i knew that i had the beginning of some complicated argument that seemed to do a special case of it so i got very excited and then i flew to europe i was in paris for a while and then i showed up at the max planck institute in bonn and in all these places i had my pad of paper and i would write the thing and by the time i got to bond soon after my arrival this is probably around june 1st 2 1986 i realized that i could do what i thought was only a special case of the epsilon conjecture so the epsilon conjecture you try to understand something mathematically you say well what's the first possible situation where you have to prove something the simplest possible situation so i kind of looked at the theorem in that case and this was really right up my alley it was this kind of thing that i'd studied many times before in fact i had studied conjecture epsilon in the special case kind of 10 or 15 years before and realized that i didn't know how to do it and wondered whether it was true but here i was thinking about the problem again and i realized that i could actually do something so this was kind of very exciting to me and i kind of wrote the thing over and over again on different sheets of paper and i convinced myself that it was actually true and i started talking to people about it in bonn and i might have given a lecture or two in bonn and i also wrote a letter a physical letter on paper to barry mazer at harvard and i mailed him the letter and i didn't hear back and then there's this famous story with the cappuccino in august of 1986 in berkeley there was the international congress of mathematicians that happened to be in berkeley barry mazur was there and i said hey you know i sent you this letter and i'm trying to work on the general case and you didn't respond to the letter and barry looked at me and he said well of course you know you have done the general case you just have to do something slightly different so he thought he was just you know sprinkling some powder on it and telling me something that i should have realized long ago so we went and had a coffee at some cafe at the edge of campus it's now called cafe strata and we sat there and as soon as he explained the thing in one or two sentences what i had to do extra i realized that there was going to be no problem that the thing was going to work why did barry not reply to your letter to tell you that or did he think you already knew oh i don't know i mean maybe he was thinking about other things or he thought i already knew and i guess his attitude was well kennel figured out by himself what do you say to barry about that now do you kick him and say why didn't you tell me a year earlier well i don't think we've discussed this subject recently so when you published this proof and it had all been set in stone this sort of bridge or pathway to proving for mars last theorem had been opened but not yet passed through was that a big deal like were you a celebrity for a week was this oh this is amazing or because the last piece because the step onto for hadn't been made yet was still just an obscure mathematical paper in the scheme of things or was this like making waves no it made a lot of waves not to the extent that fairmont's last theorem itself made waves but it made waves within mathematics so i was approached by journalists who wanted me to kind of talk about the proof for various popular and scientific magazines everyone knew about it in mathematics that this thing had happened and there was also a certain amount of skepticism is this proof going to work out you know because i didn't have a complete manuscript it hadn't been accepted for publication i gave lectures i explained all these things and a lot of the proof was so convoluted to people that they thought it couldn't possibly be correct at least some people felt that way [Music] you and others have helped open this door and shown this path does this create like a mad scramble is there now a race is there a frenzy now for mars available and are you in this race i thought that the assertion that needed to be proved the modularity of elliptic curves was completely beyond the techniques at that time so i thought what i had done was to convince people that fermat's last theorem was true morally because people believed in the modularity of elliptic curves but i had no expectation that anyone you know seven years later would claim to prove that elliptic curves are modular a bit like the riemann hypothesis everyone believes it's true but no one seems to be able to prove it right so i thought this was a completely inaccessible problem did people start trying i did it create this new buzz this new field of endeavor well not that i was aware of now it turns out of course wiles went to his attic and worked on this thing quietly but apparently other people were having kind of similar ideas you know maybe there's a way to do this did you know andrew wiles this guy in england oh yeah so i met him the first year that i was in paris let's think about this this was 1975-76 so i was in paris for the year and wiles's advisor john coates would invite me to cambridge basically he said you know whenever you're tired of paris and want to spend the week in cambridge just come over and we have a room for you you give a lecture we can pay some travel expenses we'll invite you to high table so i came to cambridge you know maybe four or five times maybe even more during that year and wiles was coats of student and in fact the thing that i had done by the end of the year was something that also created a lot of interest in mathematics i proved what's now viewed as the converse to a theorem of air brawl jacques braun and i was lecturing on this in cambridge and wiles got very excited and one of his first papers was to take what i did and go beyond that and then his most famous paper after that was a joint paper with barry mazer where they proved something called the main theorem of iwasawa theory and they did that by using techniques that were derived from mine so part of the mythology of andrew wiles now is that he was obsessed with fermar's last theorem from boyhood did you know this would he always every time you met him would he'll talk to you about oh how do you think we can solve for master's therama was this did he keep this secret or like did you know that this was one of the people in the world who i had no knowledge of it i mean i take him at his word and in fact what he says is that he was obsessed with fermat and the adults in the room told him you know don't think about that here are some fruitful problems that you can think about and he took their advice but he didn't at least by self-report have this special obsession so anyway he does go up in the attic well eventually he does crack this nut how did you find out about this you were kind of almost part of this too not part of the work but you were very much johnny on the spot when this all finally emerged into the light weren't you well okay so in june 1993 there was a conference in cambridge and i was invited i was one of the speakers and at a typical conference you have you know number of speakers maybe four or five six per day and no one speaks more than once and wiles had told the organizers that he had something very special that he wanted to present and it would require three separate lectures on three consecutive days and he was booked for this and after the first and second lecture there was widespread speculation that he was going to prove the modularity of a very wide class of elliptic curves and this would be enough to prove fairmont's last theorem but this wasn't like the title of his talk it was cloaked in some secrecy was it well the title of his talk i mean in fact i joke that both in my article and in wiles's article fairmont's equation appears in the introduction and never after that i mean the both articles are about the technicalities of modular forms modular curves gawa representations these are the tools that we'd all been working with and wiles's lectures had a title like that but it becomes clear that day three might be the big moment and you cottoned onto this didn't you yeah in fact someone kind of whispered to me that this was going to happen after the second day so it wasn't a surprise to me because i actually had some knowledge but even if i hadn't you know i would have expected something like that and there was a huge audience for his lecture a lot of people had cameras a lot of people brought their friends who were not in the subject and they said you know come to this lecture or something historic is going to happen what was it like being in that room it was joyful it was electrifying it was kind of a celebration you know when i was a graduate student my relatives would say to me what are you doing this for you know what kind of subject is this and i would say well you know basically what we're trying to do ultimately is solve equations because that's something people can understand and you know it's wonderfully validating after all these years that we're actually solving an equation you took a camera for which i am forever grateful because i think you got the photo i may have i certainly had a film camera there and i took a number of photos and then there were some group photos that i appear in that were taken by other mathematicians who were there there's one of him like at the blackboard i think i took a photo like that yeah he's smiling and it's like he doesn't seem like the world's smiliest man and he's got this like glove about him he did he couldn't suppress his pride and straight afterwards there was like all this buzz and attention and you kind of ended up having to be a bit of a spokesman didn't you yeah first of all the staff at the newton institute knew in advance that something was going to happen and they chilled cases of sparkling wine it was actually napa valley sparkling wine of course that was served after his lecture there was a lot of buzz and as soon as the lecture ended someone came up to andrew and said gina colada from the new york times is on the phone will you speak to her and andrew turned to me and he said can you talk to her so i went into an office it was actually my office and i sat underneath my desk in order to have some soundproofing because there was a lot of chatter in the hallways and i spoke to her you know for maybe a half hour and i outlined the whole thing and the next morning our names were on the front page of the new york times which is kind of remarkable so like my parents you know got the new york times delivered to their driveway and they open it up and there's their son on the very front page and there was this possibly unfortunate term that she used she kind of referred to me as andrew's spokesman so it was true that he asked me to speak for him in that context but then somehow it became known in the press that i was the official spokesman for andrew weil so i was kind of like his press secretary or something and i got hundreds of inquiries from all sorts of publications and radio shows and tv shows and my attitude was i would speak to everyone and they asked me the same questions over and over again you know did andrew wiles prove fairmont's last theorem and i basically said yes and occasionally i would mention that i had done some preliminary work but that rarely made the write-ups it was all about andrew wiles there's a whole number for our video about that again okay it was an interesting situation to kind of deal with the popular press i'd never had this happen in my life before and i found that i was fairly good at it i could explain things to people who didn't know anything about mathematics and i thought it was a good use of my time the other famous part of the story of course is that the wiles proof was then found to have a floor what was that like for you did that hang you out to dry it really did because first of all when andrew first heard about the flaw in july of 1993 i guess he didn't believe that it was all that serious he thought it would just need it patching up so he must have been aware that i was out there you know beating his drum but he never told me so it took months before i found out how serious the problem was and i had been kind of out there saying you know andrew wiles had proved fairmont's last theorem so i'm glad that it worked out right so just to patch up that story wiles worked with another mathematician taylor and they did fix the problem they brought it back from the brink and all held yeah so taylor and wiles huddled together and they thought about various things and finally they or andrew or richard found the missing piece and they published that as a joint paper you talked about when you were working on epsilon you were giving lectures and you were writing letters you wrote letters to barry mazzy it was this open book wasn't it you were sharing everyone how you were progressing and asking for help i was andrew wiles famously sort of didn't do that he kept it very secret and then he revealed everything at once in like a big grand reveal does that confuse you or does it delight you how do you feel about these two different ways of doing mathematics well i certainly like my model better but andrew had a very good excuse which is that fairmont was such a kind of sought-after thing that if he revealed that he was working on the problem people would have rushed in and he was very important to him to be the person who proved fairmon's last theory i'd keep it secret if i was close i think but then again i'm not a mathematician so you played a great role in this amazing thing probably one of the greatest things that's happened in mathematics in the last i don't know 100 years or so certainly where do you go from there what do you do next even you who like you know it was a side player and it's still like a big deal it must be one of your crowning achievements what do you do next well there is an encore problem there's no question about that and what i've done if i look off to the side and say you know what has ken rivet done well i've done a surprising amount of outreach and professional service and i think that's something that i'm pretty good at i've done more research i've had graduate students i've solved problems i've proved theorems but i haven't done anything as great as the contribution to fairmont's last theorem realistically i'm not looking for that so i'm looking for some balance where i continue to contribute to research and also now i'm pretty well known and well-regarded sort of senior mathematician so i do things at the national academy of sciences i'm also kind of the chair of the class of math and physical sciences at the moment i work with the american math society so i feel that i'm still contributing in different ways do you think you can't contribute in those other ways anymore there's this great cliche or this thing that said about particularly mathematics that you know your prime is leading up to about 40 and after that you haven't quite got it like you used to have it do you buy that do you believe that well there's just you kind of maybe lose some speed but you have lots of wisdom and you can recognize situations that some people may not let me talk to you about photography and photos because you seem to love photos i do love photos and you're always taking them we've taken pictures even today there was like a fan here in the room that captured your eye and you wanted to take a photo of it what is it about you and photography and photos it's just like a hobby it is a hobby there's no question about that so when i first came to berkeley i had no camera and i was as i said fascinated by the light and all the scenes in berkeley so i bought my first camera what was it it was an olympus om1 so this was a film camera and had no flash and i went around and i took photos and i would get them developed in photography stores so i'd come back you know with color photos and then someone said to me well you really like photography why don't you do black and white photography and go in a darker and there is a dark room on campus and the dark room is beautiful had lots of equipment there were courses you could take with accomplished bay area photographers so i did all that and i spent a lot of time in the dark room and it became the thing that i would do at the end of a day of mathematics you know at five o'clock i would go in the dark room and i'd kind of emerge three hours later with lots of prints and lots of negatives and start thinking about dinner and with digital photography it became a lot easier you can just snap pictures and post them in various places so that's kind of a sideline anyone who's been on your website in addition to all the mathematical content on there there's all sorts of other little bits of trivia and interesting things and one of the sections i can't stop looking at is the haircut section tell me about that oh well so many years ago i started taking haircuts with one particular stylist who is no longer coming to berkeley and we together hatch this idea of taking photos of the two of us at the end of every haircut i kind of believe in the power of a sequence of photos even if one photo doesn't reveal all that much having a long sequence of similar photos again and again shows you kind of the arc of time and there are various details that appear and disappear people walking past in the back so i really like that and i took a photo of every haircut and then when my stylist decided that it was no longer worth her time to drive to berkeley from san jose the photos ended and this was quite a few years ago the other thing i mean i follow you on facebook and the other thing i find interesting is you have these really regular lunch meetings explain what they are when i was a student both at brown and at harvard there was some tradition that faculty members could have lunch and other meals if they wanted to with students and i found it really valuable to me to meet all sorts of people who would come and sit around with students i remember for example meeting yo yo ma when he was a freshman he was at one of the tables and there were lots of public figures who would come in and sit with us and i thought that was really wonderful and when i came to princeton i asked whether or not there was such a program and there was so i became a faculty fellow at various dining halls and when i came to berkeley there was no such thing and i kind of wondered for a long time whether such a thing might crop up and when i started teaching very large courses that had formerly been small courses in the math department at one point we began teaching third year courses in large rooms whereas before they'd only been taught in groups of 25 or 30 students i thought you know this might be a way to get to know the students and i would organize lunches in the dining halls and i pitched this to the college of letters and sciences and they were all on board they gave me a card so i could get free lunches and i would sit with the students and i found that was really valuable and they liked it and then somehow this morphed about five years ago into organizing breakfasts and lunches at the faculty club the faculty club likes it they get lots of business the students like being in the faculty club and i tell them they can come back anytime they want they don't need a faculty member all they need is a credit card or a wallet and some of the students have taken me up on the suggestion and i think it's a nice way to get to meet students informally and find out a little bit about their lives so you normally put like a post on facebook don't you and you basically say this week i'm going to be here at this time come along if you want and then this handful of students will come and you'll just hang out over a meal that's right what do they normally want is there a pattern to what happens in the conversation or it depends on the size of the group so a small group they'll ask me about myself and they'll be a little bit uncomfortable you know it's kind of intimidating to be with a faculty member and they're addressing questions to me like you know how did i come to be a mathematician what do i do in my spare time what is it like how long have you been at berkeley so those sometimes if i don't know the students can be a little bit rough but then there are bigger events where there'll be you know 10 12 students and then what happens is they just talk to each other and i'm there kind of almost like a fly on the wall i mean some of them will talk to me but everybody's much more relaxed and i find those to be the most successful and then coming back to your passion for photography it seems like at the end of almost every one of these there's like a group photo there's a staff member at the faculty club jerry fowler who's a fantastic photographer and he takes photos of the group and he really gets the best expressions out of people i think people warm up to him immediately so if you go like on your facebook almost every week there'll be this it's almost like the exact same picture but with a different cast of characters each time right and you see the seasons changing or the colors of the leaves some of the photos everyone's wearing an overcoat some of the photos people are in summer clothes you do seem to enjoy teaching more than a lot of other academics i know sometimes academics seem to treat it like it's their chore it's the pound of flesh they have to pay to be allowed to be researchers but you seem to really delight in it well it's a kind of communication it's a different skill it's a different activity it's not explaining technical math to people who are committed to mathematics and i think everyone on the berkeley campus because it's such a large public university is committed to that kind of teaching because someone who comes here and realizes that there's that kind of teaching almost every semester and doesn't like it we'll go elsewhere and what's next for you then as we come to the end of our chat what's your next big thing i guess the next part of your presidency is a big part of your life at the moment as my presidency is coming toward an end it ends on february 1st 2019 and your term limited well there's never been a situation where someone has done it twice my successor jill pifer is a mathematician at brown after her there are two candidates who are now recruited for the next election one of them will be jill's successor on february 1st 2019 i will become the official immediate past president so this is an actual title of the ams and for example as immediate past president i will be the representative of the american math society to a joint meeting with the vietnamese math society next june you're taking on almost like a deputy or a vice presidency type role when you're the immediate past or yeah so at every moment there are two presidents in the ams there's the president and then there's either the president-elect who shadows the president or the immediate past president who helps out as needed and after my one year as immediate past president the next person who will have been elected will sign on as president-elect and then you've got any plans we should know about any you're not secretly working in an attic on another proof are you uh i'll uh i'll stay mom as to my my plans [Music] thanks for listening this episode was recorded in a small office overlooking the san francisco bay at the mathematical sciences research institute which is in berkeley california i'm sorry you couldn't enjoy the view with us the episode was also sponsored by a company in berkeley called maya sound they're an audio engineering and manufacturing company they're not here to advertise or sell anything they're just supporting the show but they're always doing interesting things and love sharing their research going on in the labs so if you want to check them out go to mysound.com there's a link down in the show notes and we'll be back again soon with another episode here on our number five podcast [Music] you

Channel: Numberphile2

Views: 64,335

Keywords: ken ribet, fermats last theorm

Id: NPOw4iIxN6o

Length: 48min 23sec (2903 seconds)

Published: Fri Dec 14 2018