The Heidelberg Laureate Forum Foundation presents the HLF Portraits: Terence Tao

[Music] professor to begin at the beginning um describe your parents okay so my father was a pediatrician he still is like he almost almost retired he was born in Shanghai my mother was a high school math teacher she was born in Hong Kong they moved to Australia in 1970 and I was born a few years afterwards why did they move to Australia um I think my Australia had a shortage of medical professionals and those soms special visa program I think for which my dad took advantage job what is your birth order where are you in the I'm the oldest of three okay I'm to your Co brothers so all all boys Oh boys yes okay all mathematicians uh well my younger two brothers they do have PhDs in mathematics but one of them works at Google right now and the other works as a researcher for the Australian Defence Force agency so two in America maybe in one or not ready no one is in Adelaide one this in Sydney they both live in Australia okay well let's look at the young prodigy I mean it's a boring word but you were called that comes from the first what would the early signs of what would become your intellectual life well of course awesome you worry this is a key second ham because yeah I don't remember at the time but yeah so my parents tell me that when when I was two I was at a party with some friends and they found me teaching some slightly older kids you know five and six you know how to count using these number blocks and they hadn't taught me this and I had apparently picked it up from watching Sesame Street yes so I don't remember that yeah of course the the earliest memory I have like that was a bit older maybe four or five and my grandmother was washing windows at my home and I was telling her to put the detergent on the windows in the shape of numbers so I always liked numbers and patterns and and you actually remember that this is not hold you by your grandmother you remember yes although I think I also remember remembering it yes all right the memory changes a little bit because of that yeah so there's an affection to say the least for numbers other intellectual curiosity that has been described in you or is a pretty much focused huh yeah I I did cuss of very nerdy things when I was a kid I I loved these fantasy novels where you know that there were the ones with like there's a big map although opposite imaginary world yes I like making my own maps I would go on the back yard of chalk and draw these huge maps which wouldn't get washed away by the rain okay but yes yeah you say you lived in a world of your own that mean that's a melodramatic way to put it but um did you have friends I I had a couple of close friends yeah I was often not in my class because as I said accelerated several years although that my parents had managed to negotiate is very complicated arrangement with with the headmaster some of my second principles of my school where where I would at least take some classes near my own my own yet like like physical education for instance right and try to get math and physics classes at several years above it led for a very complicated schedule my my mother in particular would always be picking me up from primary school to drop me off at high school or to pick up high school drop me off at the local university in a way you were a problem for a nice problem but you were just gonna be able to progress in the normal way you weren't gonna be able to just go to the local school so there must have been a sense it must have been when you were 4 to 6 or something like that that they needed to direct your education more or figure you the best path for you right yeah so so there wasn't as much infrastructure for these things as there is now so you know when I was 2 or 3 they tried putting me actually in a in a very fancy private school and it lasted like a week I did not I was not ready for it I think they talked us to some psychologists and various gifted education experts in and they eventually settled on what I just said to to to have it as much of Mike class time with people roughly my own age as possible but to have some classes at higher level in some ways maybe it was because there wasn't as much experience with these things you know so the the principal headmaster did have a set amount of flexibility to try various things I don't know if my particular educational path could be replicated now actually there may be more Wars but you know maybe they're all so there's all have more options and more systemic resources I'm gonna ask you another question but it's appropriate for this stage of your life looking back with their things left out of your education and we will get to the actual mathematical progression but what yeah losses as well as gains in the childhood yeah so something is sort of happening in weird order so you know I mean you so my probably in high school I graduate from high school about 12 or 13 I I so I didn't have my normal teenage sort of social life right during high school but when I went to IQ I went to Princeton 116 that's when I started you know going to clubs you know like you know like movie clubs and gaming clubs and so forth and and finding friends my own age there I was a graduate student by then been your army of undergraduate you know my own age those might have been social disadvantages but also intellectual disabilities were you given history courses we were given our history were you I liked history actually yeah English I was definitely not my my strongest subject as a kid I would interpret things way too literally yeah I did not really understand sort of so I mean what I like about mathematics and things like that was it was very precise like those ooh yes quite answered a wrong answer and I was not good with anything subjective I did sit in on a few classes when I came here as a professor you know I kid you know I sat in on a history of Bach class and you know I I enjoyed it so I did take one or two of these things for fun sure natural inclination was not to go into let's call it the bay but that's not a good description for Humanity yeah I was objective yeah yeah I guess I just said I didn't I didn't understand it like like what was you know so with mathematics I still understood the goal you know like this is what you should do and how you and yeah yeah I I didn't pick up a long time you know like what was the purpose of you know save say but literature yeah yes a little bit criticism or you know oh okay to writing you know you think you know that now well okay I mean I do realize now that that you know I mean my job you know it's mostly you know scientific but you know there is you know like you know when I give talks I have to I have to present the fact that but also have to present a narrative yes and that's essentially what literature is about yes yeah yeah and so yeah I can I can appreciate these things oh yeah once once you a narrow I think it says you can pick up these things look you said something and one of the articles I read not so long ago really that as you look back you don't think you've got what math really was as a kid can you explain that right yeah so as I said I I'd like numbers and symbols but to me it was like a game you push some was around and and and and you you kidnapped I was like computer games and logic puzzle was in you know they did a Sudoku back then but they had things like that yeah yeah so it was only a while I was in high school I I spent some weekends with a retired professor and he would tell me his experiences as a math addition and during the wall and you know he would solve ballistic problems or all the logistics problems or and it was the first time I realized that that mathematics was actually good for you know for many things when people were to ask me what I would do I suppose I grew up you know I had no idea I think I couple of times I thought maybe a shopkeeper because I thought I guess I can I can balance the books in and but I didn't really know Aniki house I don't wear that I can you know that you could have a job as a professional mathematician where would youwould work on problems which I not which I find a lot of research you know they're not tied to it with me I made an application this is interesting because of course for many reasons but also the whole notion again of parental guidance in this period I have a sense that they weren't necessarily force reading you or sending you occasionally in a direction they were just enabling your curiosity is that fair to say yeah so I mean early on they you know we try to come in they try all kinds of things I remember you know I took a lot of piano lessons when I was young but at some point I rebelling I didn't started crying a bit I was total practice and they eventually stopped and I regret that because I you know my son plays piano better than I do now also sort of my brothers you got actually like bugs me more but you know I mean looking back I would have continued what would but but they're they're not saying you're gonna be a scholar you're gonna go to university you're gonna do this that or the other yeah well I mean they state they try to encourage me to do various things yes I'm I remember they one point they were thinking maybe I should go into the the physical sciences rather than mathematics because I thought it's more practical yeah but I you know there wasn't really a Porsche you know I think I think once they saw what that I was you know what I was best at and what I was comfortable with I think you do they found a good path for me yeah another thing that comes across reading about the young professor was the fact that you were best described as studious oh no no that that that is certainly the case yeah yeah so I was very quick and I could retain a lot of facts in my head for short periods of time and so you know I might note taking skills were quite terrible if something was interesting and then I would not only take down what was written but but you know sort of make my own variations of it but if song was boring out out but almost nothing and then yeah maybe a week before the finals I would I would I would study my notes in crying out cram and out I would pass my tests although my great stevia declined appetite you know really at what level I mean where where were they in decline so let's see itself when I finished high school I was top five percent it's not clear they don't have the ABC letter grades in Australia and like I've forgotten that what they the system is but um yeah I remember an Inc as an undergraduate like if a year my grades would basically I guess in us total drop from A to B to C I fail the two o'clock classes in my last year no yeah it was one was a programming it because I was stubborn actually so uh one was a introduc in a Fortran class I believe and I just refused to learn four-track III learn did not like to be language were basic and I felt like I could ya could do that I remember I had assignments that would you know to programs when you do something unfortunate and out of turn in Sam isn't basic I just yeah yes my feel at that class a family yeah the the two the two professors that I failed me they they they they they bragged about it in the common room you know they they're the ones the only ones who who who the other one was introduction quantum mechanics where you know so half the course was doing always calculations and so forth but but we were warned well in advance that as part of the final that would be an essay component talk about the history of economic Alex and the effect on how changed physics and this I also refused to do and I it's like I just did not study for and then when the time came yeah of course he was a 50-point he's questionable and there's nothing to to say I'm upper crying and and they proctor had to escort me out of out of the room and have you learned your lesson um so to speak not then I mean I still passed yeah I think my real wake-up call actually was a bit later as a graduate student actually when so in Princeton the system is is that after or two or three years you take this call except which are these ro exams with proposals and they ask you questions in your chosen field and if you ask asking these if you aren't easily learning where it's harder if you struggle you think it's simpler and so again you know I use my usual studying method to to to practice verso so most of the most diverse students that you know they were very stressed out they for they practice for months they gave mock exams to each other yeah I think I just did two or three weeks of study and the subject which is my main subject of study well originally which is called harmonic analysis so that I studied the least because I thought that was that was what I was best at and whether the time came how I could not answer basic questions in subjective so I struggle and they asked me easier questions and I struggle with those and was it was quite embarrassing the only thing has saved me was that there was another topic which I had to select number theory which at the time I was not as strong it and so that one I actually was concerned about in that when I practiced quiet you have yeah and the professor who was brought in to examined me on that topic had actually was had a misunderstanding he thought I was actually to select a different area mathematics as my topic and so he had prepared a completely inappropriate set of questions and so he only loved not me very standard softball questions which I could very easily answer off so I had locked out of passing my qualifying sense but it was it was quite quite close to panel and it registered on you what it had well my adviser who is on the committee you know thinks you know let us talk to me afterwards and said that you know he's disappointed you know they know what my letters recommendation was strong and you know this wasn't what I was expended gentle about it but it was it was a real shock I think it was the first time I really saw that those were real consequences to sort of not studying yeah now we always have to register the fact that when you're speaking of yourself in graduate school whatever we're speaking I'm still a very young person yeah I guess that's what 18 or something in Italian yes so a lot of these issues are the natural issues of growing out I guess so yeah although tell me though I know some 18 you were so extremely mature I mean yeah there's a lot of variance let's again just register the sequence of your education so you left high school in what age about 12 or 13 another 13 you then let the flenders yes locally which was yeah in Melbourne in Adelaide actually heavily of course although it's very complicated because during my last years of high school I did take some classes in its thinnest reach classes right and they counted it for credit actually so when I fully did enroll actually finished my undergraduate degree in two years but I went to that that said that's a an illusion I mean I spent two previous years pounding what was your thesis did you have a thesis I did a master's thesis yes with yeah harmonic analysis yeah how are you determining from the the child who like numbers and do the development of an understanding that there is a field to the interest in particular aspects of the field well that's a guy mostly just I mean so there was a professor at Flinders who wanted you decide to advise me and at that point you know I was better at analysis him and then other areas of mathematics and so he to him was his area too so so it worked out well I mostly just did what my what what my professors and teachers just suggested me to teach to do so you know folks I thought when I finished my undergraduate I didn't really know what to do but my advisor strongly suggested I apply abroad which I wasn't I wasn't playing suit myself but here so we applied you know to to Europe in England and the u.s. there click on the Princeton um again I suppose through through your advisors are you getting a sense of the competency competencies and various departments because graduate the decision for graduate work is the first really serious professional my decision it's going to shape a lot of your intellectual life so what was it in in the end that drew you to Princeton as opposed to some other place well okay I have heard of it okay but mostly because my my my advises yeah recommended of this was a good place to go um I don't know where else I was accepted they want that many places actually there weren't that many places that you apply or not that many places that you were accepted which my parents did most of application process uh I don't remember now okay so actually stubborn though you are by nature at this point you're you're willing to be directed in terms of the shape of your career right yeah I guess these things didn't I mean the things I didn't care about I mean I think I didn't think that hard about about where I should be in suppose I was never really ambitious in that respect I think I don't like being told what to do if it's involves something that I want to do a different way at least I hope I'm not quite as tough these days but who was going to be your mentor turned out to be your mentor at Princeton yeah so I ended up working with a professor Eli Stein who was a walk world expert in how warning analysis which was the feel what that about that I started it yeah so so he he was an amazing so he's he's so legend he's had like 50 60 greater students which is much higher than most other people and he's very effective at it um yeah and cured me to all of us regularly often I remember when he um I've been meeting himself be a queue outside his door you know we'd meet immediacy of each was for half an hour or now and then you know you just say wait for next wasn't it yeah I'm gonna now ask a very general question for laypeople and catches as what looks within the field but at the field of mathematics and begins to become interested in this direction rather than that through guidance and personal interest is it really the nature of the problems to be solved that attracts you to a direction or the other or a sense of the history of the field and what some of the major issues have been how does one think with it it's a it's a mix of everything you often go as a graduate student thinking I'm gonna do X & Y because I learn about some topic as an undergraduate I thought was exciting but you may not be aware of the current area of research yeah so there were some areas of mathematics that I've thought I would be working on going to Princeton and I came to Princeton took some classes I thought either that they were too challenging for me that they've quite a more background than I was always ready for or this the questions which I thought were interesting were also 56 years ago they're still working on other questions but those didn't interest me as much so I mean you you and your advisors tend to guide you towards research that is that is fairly current you know that that that ties into two very active areas that other people are working on right now you know I mean you know full of purposes of your career you know it's much better to work in an active area so there's many places who would be interested in hiring someone who was just bad shorty then in an obscure area that no one cares about you know even if you like it a lot I mean so there's a few I mean one nice thing about mathematics is that this room oh it needs a lot of diversity you know so there so we have a lot of mainstream a petitions who who who focus on sort of yeah it's over so mainstream core areas of mathematics following you know profiling using techniques good and and this is very important but but we have a small minority of more idiosyncratic mathematicians who who try things that that very few people looking at and they don't often so they don't succeed as often as us but but when they do is thinking it can be big can be quite quite valuable and they can although I was hoping a field yes yeah yeah no we've we've had you know several exams of that you know there was recently a math edition of who have almost dropped out of a khadeem eeeh the hiko he couldn't get a regular teaching job you know at one point he was making sandwiches for Subway and he solved a major problem number theory yeah now he has a tenured job again yeah but yeah we get all sorts you said something that's slipped by that I want to return to you actually said them certain things you found too challenging now there are few people would expect that you find anything challenging at that level that you would drop it in in mathematics no yeah no and I know the job of well so you know research level mathematics is is um it's not so much about the raw intellect or or memory or speed I mean those are helpful but it's a lot of it is just knowledge and yeah knowing knowing the history knowing what what else is is this true and there's a lot of what's called folklore like little tips and tricks rules of thumb that are not in textbooks you only pick up despite by listening to the right people talking about people or working on these problems and yeah and you know because I didn't pay attention to a lot of the classes I didn't think I care about I had a feeling no no knowledge base initially in fact I think I've learned more mathematics after my PhD then perform a PhD so I've worked with a lot of collaborators in our fields and through them I've been exposed to too many hilarious mathematics you've hit on something that is often remarked about you which is that you're very collaborative usually seventh in a celebratory sense people admire that in you can you again for laymen describe the various choices literally about isolation and intellectual endeavor in mathematics and then the notion of collaboration and how it works yes I think the nature mathematics has changed over the years so if you go back to a 50 years ago almost all I talked to the majority of they research papers like what single author people yes yeah there was sort of this this this archetype of a load method ition working in an ivory tower you know scribbling away in his attic and not talking to anybody else and you know eventually solving solving a problem and you know if you go back hundred two hundred years you know people were very competitive writing people they would masters will challenge each other you know almost like duels you know they can you solve this problem you know and and they will not reveal their answer until they'd seen you know yeah but it's over time with this it's changed for the better I don't have to say um the nature of the problems has has has changed a lot it used to be that you could specialize in one very tiny area mathematics be the world expert on that and not know much about anything else and and you could you know you could do good work but but you know many problems now if they connect Tiffany was mathematics together or like in again that PI thanks to physics computer science biology finance whatever and you need so much expertise there this is there's no one person to get to do it all also I think people found the collaboration is just more fun and III certainly the most enjoyable projects I've had other twenty ones and also collaboration is easier now you know with the internet and what I mean it used to be happy physically in the same location as I so collaborated to make much progress well you have to write these very long letters by hand yeah well you know make these long phone calls open but now I know it's so easy to collaborate if you were a specialist a musical comedy I would understand collaboration there's the Lewis's there's the the composer there's the one who writes the book and so forth collaboration mathematics is it tossing problems at each other that you have collectively defined and then having a conversation about that what is calm well it's what's the talking usually um you know you you there's a problem which you can both see requires you know someone all the from from subfield X which you have and some notions of you why we collaborate has and so it's a natural opportunity here and you talking you suggest something with open what happens is that that problem naturally splits in two parts and everyone sort of grabs one part says okay I will do this step and you do this step and then often this this this negotiation because you know there are ways to make yours to be easier for yourself at the expense of making it at the other step harder I and then so you have to sort of bargain with you know that I can't do this but I can do this this this weaker thing can well that we enough enough for your step no I you really need this this harder thing but often the other thing is that some somehow when you are talking and explaining math.max to other people it engages more more of your brain then you're sitting quietly and I think it was at least powerful for me and somehow ideas come more more easily after when when there's an audience and and yes yeah sometimes that must come as a teacher with students as well yes yeah yeah so yeah my style of teaching is I I do improvise along I prepare my notes in their knife and head contentions which I wouldn't have thought about if I just going off you know if I was just preparing by myself but you know and and the students don't even I mean it helps a lot if they ask questions but somebody just just it's just the main factor having an audience somehow it can it can inspire you maybe it's truly a performing arts as well yeah who word that occurs to me as I speak to any number of people who have achieved in both mathematics and computer science is just the nature of their curiosity it seems that that is often what directs things not because a corporation has said make this happen not because even a university has said we want to do this but curiosity roams is that right yeah yeah so it's pure research you know so so you know there are big problems which which everyone loved a solvent and they make many applications but but they're difficult so then you start looking for similar problems which look like the big promise book but which are easier and then you can look for subproblems you know you can look for problems which if you could solve that you might develop a tool which and so some of the what you find one thing interesting you'll find other things interesting and that's what happens is that this there's a breakthrough you know that some somebody solves a problem by introducing a new method interest he or she in your interest is a new tool that no it done before everyone and I'm very excited because now their favorite problem which had been intractable maybe now they have the right taught to crack it open and so you get interested in what they do and yeah so it's a yeah it took a while it takes a while to get used to to the style of curiosity driven research you know like you know as a and your school education system you're it's really is usually very Authority based you know it's some some a teacher or something gives you an assignment you know you have homework yet an exam and you not much time is spent on why you want to to solve for X or whatever it is yeah so yeah but this that something you pick up later again its narrative actually somehow we only give you the narrative later the the analogy are key because sometimes is that mathematics doing mathematics is like jumping in and watching a TV show one thousand episodes in and initially you don't know who the main characters are who's the good guys who's the bad guys what the whole bottom plots are but over time you you pick it up make sense yeah part of the lore again about you is that people buy to intrigue you with their problems yeah yeah someone said that and that it could and then once that made the meet hit the media I got a lot more unsolicited problems phonetic know what to do with yeah yeah yeah I do get a lot of I mean in your responses to be interested or not to be interesting yeah so well I I now have two standard disclaimer unknown on my webpage that yeah you just send me some unsolicited paper I would like the ignore it uh-huh but you know I do enjoy talking to to colleagues you know I go to conferences in etiquette I talk to be able suppose people visit here yeah I told sometimes I can be helpful also one of the mysteries is too strong a word one of the things that intrigued so many people about you colleagues of course is the amount of your productivity and which is often perceived as that in human but beyond a normal range of energy how do you get so much done it doesn't feel like I could I feel like I always have much more to do than I actually do in any given day are you quite orderly and the way you organize your day I do you I have a calendar and I think about how to how to schedule things I think just one thing is I said you you you and I try to match my what I do with was sort of any level and my you know like if I'm really tired I shouldn't be be doing that you know I should be you know doing errands or yeah or it is yeah I think one thing is I found the internet this is tip is there's some Accord structured procrastination if there's a task that you don't want to do find another task for you you don't want to do even more and then you say in and then just justify not doing that by doing the first thing and so you can still play games where you might and I'm also follow of doing things which which have an upfront time investment but will save me time over the long run so you know like I would nowadays when I teach a class I might like your notes for it and I put them online on my blog so you know this does several things so it forces me to actually prepare in the tool properly yeah at the next preparation for the classes very easy and they never teach class again it is a lot less effort also you know in subsequent years if someone else is interested in that Arastoo I come to my noticing and so for bringing up that makes me ask a very broad question about communication vehicles and for intellectual endeavor mathematics of course in your case first of all I'm very struck by the fact that mathematicians seem to still use blackboards in the age of computers that's one form so can i let's talk about that a bit yeah um we would switch I think oh well not everyone uses a foot not first but not everyone is blackboard zone but yes um I mean you know I mean a blackboard is extra memory space you know yeah if you have a complicated calculation you know you can't keep it on your head so you put certain things down um the next question is also been in the rent range of communication and that is the phenomenon of course classically of the article and increasingly of the blog as a form of communication of of interest in meeting can you describe your choice of the blog I mean you you write articles to but your choice of the blog is a community right so it's sort of for me I just sort of happened by accident so I had a web page for many years seven if I think back in 96 97 and I put up so I started uploading my papers on there and so forth and I decided at some point to put up a what's new page and so like every time I would so a log of the most recent additions to my weapon you know so we have two semi SEP 17 1998 I got loaded this paper and so okay I just did that as a habit and and at some point I remember I had a math question and I did not ask for it and I was updating this watch new patient so I decided you know what the heck hardest part of the Cir here he's an open question that I were to solve and within like three days I got an email saying you know this question has me study by so-and-so look at this paper and he could know I solved it and so so what I had not realized was the people actually reading my wife's new page and also that they also had feedback and then I I realized that this is something that one could benefit from more systematically now I read about this time they were already about half dozen people who are already starting to do to to block Indian mathematics so I the example that I started to block and it just took off I got a lot more feedback than had expected you know no hundreds hundreds people you know a day what would come in an extent you really have collaboration in the mail now facilitated through this medium yeah yeah and it appealed to me I think one thing I I hate it I hate duplicated effort you know I you know I find that when I talk my graduate students who I teach them the tools of the trade in various tricks which are not written down at me the spoke logs talking about before and then they would graduate and their new creditor would come in and I find myself teaching them the same to his littermates I haven't told you this no okay it's and so yeah it's not a frustrating me to said you know if I could put all this on in one location like on my blog and then just train my students to go these from her further yeah and then you know then yeah something that you know in the long run that saves me time back to your professional I don't mean progress but development we're sitting at UCLA which has become quite an important place for you to be in your career um what gets you do UCLA well what are the opportunities of an while it's a bit it's a nice big Department very friendly the administration is very supportive mathematics in general we get good direct kind to students it's there's a lot of activity you know there's there's a mess Institute just down the road and in fact there's so much the conferences and seminars of going on that you can't go to you have to consciously pick and choose what what to go to you know and so that's about freedom is there a concentration of expertise here that works for you and your um to some extent yeah we have very good people in in premature every year about almost everything about mathematics so yeah this early been times when I've had a math question and the simplest thing to do is just go down the hall knock on somebody's door although more and more now actually the Internet's and even better resource I think it and you know normal cat as necessary as it used to be to be at a topic university to do talk with mathematics that's very important I'm saying yeah but yeah because of this medium of communication yeah you know so you know um actually I've had sort of virtual graduate students who actually learn a lot of a lot of mathematics reading my blog and you know I I myself you know I I learned a lot from Wikipedia and there's always other methods where you are is not as critical not not anymore yeah I mean you know you need good internet access in the librarian and you know a decent living conditions yeah but do you find yourself participating and maybe this is what communication makes unnecessary in the region of people that Caltech people oh yeah yeah now we have a joint seminar example in an analysis with Caltech only every other Friday week we go down there they they come up here we have dinner and simple the other and so yeah I mean it's a social part yeah yeah Padma medical I'm now gonna ask something that's more challenging for me than for you but maybe for you to explain it to somebody who's not imitation and that is I'd like to look at a few of your Eureka moments with you we're in the attacking of a problem or a framework something clicked that you're quite proud of it as a product okay yeah so then something I did 10-15 years ago there was a certain differential equation I was trying to solve it's for the wave Maps equation and okay so a model of competition or waste yeah it doesn't matter what take what what it does but it was it was it's what's called very it was very what's called nonlinear and so it get the keep oscillating too much and I couldn't I couldn't see it was the way it was going and I needed somebody to straighten it it's like if you were trying to navigate like you know drive down a road but somehow you're maybe you weren't seeing the the road directly but but but through a camera and the camera was tutoring and so it was you he was was very jittery and it was very hard to steer in the right direction so it was very hard to write down a solution to this problem and I needed to way somehow stabilize the solution and I remember trying to connect a mental model what I'm trying to do so I remember actually lying down the floor closing my eyes and trying to roll around imagining that basically I was his way of evolving and trying to to to find and the right sort of frame of reference to actually make make the system reasonably stable and yeah I had actually got that we very help working I keep did find to my transmission and so my problem I remember I was I was at my aunt's place at the time in Indian in Melbourne and and she walked in on me rolling about like this and that's what I was doing and I couldn't explain yeah so that's rather extreme situation so usually I use pending people yes yeah but yeah occasionally you you you keep try to and in fact this one came yeah yeah yeah usually said so that's maybe the my moment closest to some of the traditional a stereotypical Eureka Tecna right and most often it's it's at a climactic you know you you work for months on on the problem you you you eliminate certain strategies as being impractical you you isolate the key difficulties there if I can solve this I can post a problem I have no yet I solve this you work in a special case and say oh maybe I should be using this technique but I can't see how to use this technique you so you keep failing to solve the problem but every time you fail you kind of see what the solution has to look like and you narrow the right right and the pieces are getting closer and closer and then at the end Oh what am I just connect so you know you realize that that technique X is important to you why it's important and at some point you just make some trivial observation I want I just do the both the same time and then because you've already spent months thinking about problem and you understand everything else about the problem once you think about that last step this oh if I can click someplace oh that's that's it okay I think I've solved the problem and they say oh why didn't I think of i-10 you know two weeks ago right right you need to really sort of internalize everything yeah so it's a it's a funny process there's a famous meth addiction couldn't take whoo-hoo-hoo likened it to opening a walnut so you know so there's some people who'd just try still using a sledge hammer and sometimes that works but actually often what you do music when I kiss preferred way of solving problems is that he soaks in you be so water in water and eventually the the shell become so soft that that entity just really just falls apart right we spoke about communication but of course electronically and with colleagues and so forth but the framework in which I was initially thinking was within the world of mathematics but one of the things that seem to signal our own time is the cross feel oh yes when the discussions encounter exception do particularly find have you done interactions with let's I'm just gonna say biologists for example it doesn't have to be the right answer but across fields where you see Jocelyn's going I 5 talks G apologist astronomer listen so yeah I'm not collaborated directly with them I have worked with this decisions and like electron engineers so there's one thing I've done which actually you know some so most of my work is basically surface has no immediate practical impact right the one thing I did that a queue was has to practical significance was something called compressed sensing it's it's a new way to acquire data like images from very limited measurements and there's a mathematical technique and we found some mathematical explanation for why it works the way it does and it's now used for example to speed up from MRI image imaging so a scan which may have taken three minutes to acquire a good image you can now take you know ten seconds thirty and still get a medically useful image out of it there's a method mathematically determined solution yes yeah so yeah it is a I mean it was it was discovered by Mike my colleagues were working in statistics and and they had found a technique which when they tried it on test eight it worked a lot better than they had anticipated but they couldn't explain completely why you're so effective and so I worked with on YouTube to find so the right mathematical explanation for why this magic algorithm worked and once we understood why it worked he could see so you could see that it was actually very widely applicable so a key it had to this technique had had previously been being discovered in seismology actually to to to to to discover the the levels layers of rock and so forth again a very limited of the most seismic measurements but there was a trick which people discovered and I said well this seems to work we don't know why but they but because they didn't have the right man I thank honest had no idea that it was much more general than just seismology that this technique could be applied you know it's now using astronomy you know yeah very broadband wireless error correction it has many many applications which which you wouldn't have seen unless you see you be honest with the mathematics behind it so you might be doing more of this in the future um well that particular field has exploded and I'd and what things get very crowded in in the area I tend to do to move away oh yeah I don't like you know what I'll be working on several years from now I keep changing fields it depends on what what happens to mathematics who I talk to there's some long-standing mathematical problems that you have in the back burner to try to do your part to solve yeah there's a list of of billion possible questions and then you know you should spend like one or two days a year not doing something ridiculous you know there is a danger that you can consume you know so there are unfortunately stories of meth additions you've sort of gone off the rails a bit because there's a problem at obsessed them and it's just not solvable right any current techniques but but for some reasons they think that they have a chance and and you know so it's good to try that for a day or two but yeah when you spend like oil every working moon for a year doing it right right although nothing said sometimes big problems have been solved by exactly that approach there was a famous open poem called at the point where a conjecture and it was sold by a very reclusive Russian mathematician who was working by himself on those pamphlets was over seven years people had lost track of what he was doing like you know it was a great Parliament you know people had no idea what he was working on it and suddenly Bruce Lee a company could I prove this conjecture I there's a bit of a terminology that continues to intrigue me very often mathematicians use aesthetic terms to describe the world that they are trying to understand that this is a beautiful solution this is an elegant problem and so forth do you find yourself ever using that language and if so what do you mean yeah yeah I think elegance more often than beauty but well there is also beauty - but yeah well when when someone when you've had a trick which you know something that turns a very complicated problem in into and diverse simple problem so elegance is related to simplicity right I can give you give you one example um so okay so I can give you the following game so there's two players and there's number one tonight and I pick a number like three and then that's my number and then you pick another number like seven and then I pick six and so forth and and the objective is that you want to you win the game if you if you can find if you pick three numbers that add up to 15 so if I pick one and five and nine and maybe some other numbers the moment I pick one five and nine I win so I go first and then you go and so forth okay so this is a game and you can play it and and it's it's I mean when I discover like it's very hard to be good at this game but this game is the same game as tic-tac-toe that if you take the take echo port and your number that the numbers in the car you want one through nine you can know them in such a way that they're getting a line is the same as getting three numbers that helped out of two to 15 years you have to use what's called a magic square and once you see that if you can see so if you have in front of you a little square with those you can always win this game it gets against an opponent who doesn't have this this that this this little graphical Hey because because you can see the line seventeen use your geometric intuition and not just you know a thematic one and so that's a trick which transforms a difficult problem into imagine a much more tractable yeah so you know it that kind of trick is something which upon unexpectedly simplifies a problem that that I find particularly yeah or yeah you're in mid-career although your career started a lot earlier than yeah people so maybe you're late and I think you you said that you don't know what you'll be working out in two years just as a word to those who might be watching this are there broadly in mathematics areas that you see increasingly exciting that they might might look into I think mathematics is becoming more quantitative one quantitative and more random so in the past people were to be interested in in in just sort of very qualitative questions like you know does this thing exist does exist finite or infinite you know is it but you know but now it was particularly since we've now motive my application here you want to eat one you wanna know so how I'll find out how infinite you know so and then maybe I was out in mathematics it says that you know there is some solution to this equation but now you won't know how big is it how easy is it to find support and and play much every field mathematics is people as now has a quantitative component it used to be analysis was so they only want to administer that come on Horrocks and probability and how would you burn in geometry now it's all become acquainted it and also more random so maybe we used to work with very explicit so deterministic think of um like like ponies that you can write down by a single formula but but you know the data in the real world you know like it if if I want to know how the stock market is doing today or or where the next buyer is gonna come from itself of the you won't find a phone that predicts exactly but but you might statistics know that this is certain 30% chance oh this will happen and so just more and more we have to do random numbers random shapes random random everything so yeah I think those are two general trends I see and also matter is coming more more interconnected as we already talked about that is there an easy way to talk about the difference between a choice and apply mathematics as opposed to theoretical or pure mathematics how's that sort of decision made by a mathematician or ism applied mathematics now essentially computer science well there's a spectrum I mean yeah so this is the pure mathematics applied mathematics and computer science engineering and then industrial mathematics and you know and people move between the depart the boundaries and like you collaborate with we all have a common language we all speak mathematics different accents but ya know so I you don't have to declare I mean maybe formally have to declare a major or something but you know you can there are many good apply partitions who who started out uniform or pure back on it and vice versa it's a spectrum yeah yeah I think if I'm right there was a time when there was some condescension toward apply yes yeah he opposed to pure no there was there was certainly some almost the key system I would say you know it is so high mathematics and it's a little mathematics yes yeah no this this I think has largely dissipated I think it's a poly period that is which is only young younger generation wait web you know the aptitude has is that you use whatever mathematics you don't turn your nose up at something because it is it's got too many you know of the wrong type of mathematics it right the final question I want to ask again it comes from my experience responding to yours I'm so struck by the fact that it's almost as though time doesn't exist in your field now what I mean by that is it it still seems like you're having conversation with colleagues who died 300 years ago yes yes yes so this is a striking thing about mathematics oh um I think all Sciences so have a transition point at some point in history where they become cumulative where where they build upon the go to the past so so we come with physics this started around with the page or Galileo you know so so before Galileo you know you know historically has been theory but then it was wrong and ended and so have a different theory but Galileo is the scientific method okay it then Bennett started becoming cumulative don't know chemistry became accumulative fluency at the periodic table and so both you know Paulo do you want your Darwin it's yes but mathematics mathematics stop that this post is start with Euclid okay so yeah three thousand years ago as yes and so yes yeah so you know I still use you know Pythagoras's theorem you know on a regular basis often a very generalized version but yeah I still use you the films of Euclid again you know much in a very modern form be another scissor so this this is a feature I really do like I was very struck coming to your office the line of photographs of great mathematicians there are very few departments I've been to where those earlier in the field are presented as colleagues that's what it feels like huh okay so it's funny I think people mixed reactions to to yeah so it's a way we do have an array going back to like the 10th century it at least and yeah some people with find it intimidating yeah ok but ok I can see they could also be inspiring yeah thank you very much you

Channel: Heidelberg Laureate Forum

Views: 75,062

Rating: 4.9360929 out of 5

Keywords: Terence Tao, Heidelberg Laureate Forum Foundation, Fields Medal, Heidelberg Laurerate Forum, Laureate, mathematics

Id: VJLQj4hQs2Q

Length: 55min 24sec (3324 seconds)

Published: Thu Aug 02 2018

Reddit Comments

[u/Mastian91]

Actually sounds like he was a pretty normal student, but super quick to learn things he was interested in.

[u/crystal__math]

https://old.reddit.com/r/math/comments/9gbq53/hlf_portraits_terence_tao/

[u/halftrainedmule]

Transcript anyone?