The Institute for Enquiring Minds presents a lecture performance by Professor Arun Ram of The University of Melbourne.
Professor Ram is an internationally recognised mathematician and an inspirational teacher. In this unique presentation he tells a series of stories, interweaving mathematics and music. Humorous, educational, personal, often all at once, these collected stories illuminate the remarkable journey of an enquiring mind who became a mathematician.
A mathematical mixtape from a life long road trip.
That one, that was one of my father's very favourites. Mine too, it's a beautiful song. My father used to talk with fondness in his voice about the first time he saw that film, in India, in the cinema hall in 1954. It was an incredible experience for him.
Of course, I didn't grow up in India. I grew up in New Mexico. That's in the southwestern USA. My mother was from that area. From New Mexico, Colorado, that whole area is where she grew up. She was of Hispanic heritage, which meant that, you know, we would have these annual Christmas parties for Christmas every year, some of the time not everybody in the family would come so there were only like 94 cousins there. Juan, Freddy, Susan, Delfina, ... you had to remember all their names, it could be very embarrassing.
So I grew up in a town, it was, I think it was about the size of Shepparton, I guess. It was about an hour to the Mexican border. That meant that there were a lot of hispanics there in that town, you know. This kind of hispanics. Not just the bandana. They got the walk, you know, they got the talk, "Ese dude, hows it going?" you know, They got those cars, you know, 1957 Chevy rebuilt, with the big pipes, hydraulic suspension, dice in the windows, statues of La Virgen on the dashboard. That's what we used to do, I used to hang out with those guys. I don't know what we did. But we would hang out all the time. I mean we would drive; That's what we did, we went cruising. Cruising means that you drive up and down and up and down the same street, You know, we only had one big street in our town. And we used to drive up and down and up and down, I don't know, just, hanging out, whistling at the girls, "Hey baby, you wanna get lucky tonight??"
A song from the soundtrack of the movie La Bamba , the story of Ritchie Valens.
So, you probably get the picture. Mathematics wasn't really in my consciousness. I didn't really think about it. I suppose there was one incident, there's one memory that I do remember, somehow, I was kinda confused about this -(-5) = 5 thing. I mean, I had thought about it. I was a young kid, and I had thought about it. You know, a black black hole isn't white. It's just really really black. And if you turn left, and then turn left again, that's not turning right. And I had enough street smarts, I kinda knew that two wrongs don't make a right. So, somehow I brought this up at breakfast one morning, I thought that the whole world, and my teacher at school especially, they were a little bit off their rocker with this -(-5)=5 thing, they were so adamant about it, you know. But, this little proposition got my father very, very animated. "Let me explain to you. You need to understand." He was really into it. He started giving me this big lecture, about how I should understand. You know mathematicians, that's one thing we do as professional mathematicians we study logic, and we study proof, and we know what are the different kinds of proof and how it goes, and my dad, he was doing a proof, it's what we call proof by intimidation. Anyway I told my dad "yeah yeah I got to go to school, I'm gonna be late, the teacher's gonna bawl me out". So I'm taking off, going down, walking to school. I wasn't like halfway down the block, Here comes my dad running after me "Hey you come back here, I got to explain to you, what is going on, you know" So he brought me all the way back to the house, and he started giving me this lecture about how if you walk backwards backwards then that was the same as walking forwards. I mean I never saw anyone walk backwards backwards except for Michael Jackson, and we called that the moonwalk. So, I certainly didn't bring up -(-5) at breakfast ever again.
I did get bawled out at school for being late.
But it's interesting, because when I was doing my PhD,
I learned what's going on with this -(-5) thing.
You see, in the world of math,
-5 is the thing that you add to 5 to get 0.
That's what minus means.
And it works with anything.
In the world of math, minus is the thing that you add to get 0.
So, like antimatter is the thing that you add to matter to make it vanish.
That's minus matter, it makes total sense.
And it works with anything. minus mother plus mother is 0. -truth + truth is nothing. It's great. And so, -(-5) has to be the thing that you add to -5 to get 0. That's what minus means.
And now, if you think about it, there's something, ... you know what to add to -5 to get 0. You add 5 to -5 to get 0. And that's the reason. That's the reason that -(-5) = 5. Cuz it's the thing that you add to -5 to get 0.
Teenage years are tough. At least they were for me. They were really tough. My parents were headed on a big deep descent down to a very messy divorce. Home was not a healthy place to be. I didn't go home. If I could avoid it I didn't go home. I played the violin in the orchestra and so I would arrange it so that I had a rehearsal that ran late every night. And then I didn't have to go home. I got home late, I would go to bed, and I'd get up early because I had to go practice or something. I'd sit in the orchestra room and practice or do homework or something like that. The only problem is there were those nights where you didn't have a rehearsal. So what are you going to do with yourself. So, for me, I don't know, somehow, kinda, by accident, I would end up at my violin teacher's door, knockin on the door. My violin teacher would answer the door. "Arun ... did you eat??" Ahh! That's what a teenager always wants to hear. "Naah" "Ah well,... come on in, ... get the onions, we'll fry something up for you, get the pasta, we'll cook some pasta for you" She taught me how to cook. We would cook Italian food. I learned how to make sauces. I learned how to use a knife, fry onions, I learned how to use the olive oil. And then, she'd make me this dinner, pour me a glass of wine. I was, like, 14, or something. And we'd finish off with her wonderful cheescaker, She had this amazing cheesecake which was fantastic. And then, of course, at the end of dinner, inevitably, she would say "Ahh! I got this new video, Pavarotti is fantastic You got to come and watch this video" She would pour me a drop of cognac, pour one for herself and we would go to the den and we would watch opera.
And she would tell these stories about the world out there. She would talk about Paris, where she had done her degree at conservatory. She would talk about Milan, where she had played in I Musici. She would tell me about art museums, and about fashion, about cities, orchestras, conductors, ... and I decided I had to see the world too. I was gonna go to Paris, I was gonna go to London, somehow I was gonna get out there.
So I went to my Mom, and I said, "Mom, I want to go away for college". My mother wouldn't have any of it. She's like, "You can stay right here at home. You've got a scholarship to the local University. You can get a good education there. Won't cost us anything. You go away it's gonna cost us a fortune." Certainly there was no arguing. She wasn't gonna ... In her mind, it wasn't a possiblity.
So I went to my Dad. I said, "Dad I wanna go away to school, but, you know, Mom isn't very keen on that." "Beteji, There is nothing I can do for you. You know, your mother and I, we don't talk. But, if you go to the best school, then, ... I will fight the fight, and I will send you."
So I went to my violin teacher. I said, "My Dad will help. My Dad will help us out. But I have to go to the best school. So what's the best school for violin?" She says, "Well, Juilliard, Curtis. The Juilliard school in New York, or the Curtis Institute in Philadelphia. You got to go to Juilliard or Curtis, those are the best schools, ... or you could go overseas."
So I wrote to Juilliard and I wrote to Curtis, and I got the audition requirements for Juilliard and Curtis. I got the music, and I starting preparing. One Bach Sonata
One Paganini Caprice
One classical concerto
And of course, a romantic concerto.
And there was me. Practicing. Learning those pieces. And every week, of course, I would have my violin lesson. And Dr. Gabbi would help me. She would sit in her chair. She would say "play it again", ... "a little more phrasing". And then one day, she stopped me. She says, "Arun, I have to tell you something. It's better that I tell you now. You know I got to tell you sometime. Somebody's gotta tell you." She says "You can't play". "And the kids that audition for Juilliard and Curtis, ... they can play". I mean, it was devastating. But I knew she was right. I'd been to the Aspen Music Festival. I had seen Dorothy Delay line up her students, 6 years old, 8 years old, 10 years old, 12 years .. and they could play. I had ears. And I couldn't play. I could actually hear that too. So I knew she was right. It was still devastating.
So I went to my dad. And I said, "Dad, ... Dr. Gabbi says I can't play. So what do you think is the best school?" "I don't know" "MIT, Harvard, Princeton, ... maybe Stanford." So I applied: MIT, Harvard, Princeton, ... maybe Stanford.
I didn't get into any of them. But by some miracle I got into MIT. And by an even bigger miracle, MIT turned out to be in Boston, home of the Boston Symphony Orchestra!
Boston was fantastic. It was the greatest musical education you could possibly have. I remember, even the first week, I went to the opening concert of the Boston Symphony and it was the Boston Symphony with Itzhak Perlman, playing the Mendelssohn Violin Concerto, which was the best Mendelssohn of that time.
So I gave myself a fantastic musical education. I went to all the concerts. I bought records, I bought CDS, I went to master classes, every major artist, I saw singers: Te Kanawa, Pavarotti; I saw cellists: Lynn Harrell, Yo-Yo Ma, I saw them all in those days. I went to master classes: Henryk Szeryng, Isaac Stern, I saw them all, right there, It was great, I learned a lot of music. Just one thing. I was a student at MIT. MIT is Massachusetts Institute of Technology. It's the premier Science, Engineering, Mathematics intitution in the US, maybe the world. It's really focused on it. And I was not really focused on it.
Of course, I didn't fail out, because I wanted to stay in Boston. So I took the core courses, you know, I don't know, Calculus, first year physics, stuff like that. At some point I had to declare a major. I declared a math major, because that was the most flexible. You only had to take 5 courses and the rest could be electives, so I took Music History, Music Analysis, Harmony and Counterpoint, Composition, Chamber Music, ... it was great.
So, because I was a math major, I had courses in Real Analysis, I had a course in Algebra from Mike Artin. That had a little bit of an effect on me. You know, Mike Artin is an impressive man, and he really thought that subject was beautiful. I could see that he really thought it was beautiful. I don't think I did particularly well, I think I got a C in that class, but ...
Anyway, at the end of my third year, you see, Uni in the US is four years, So at the end of my third year I sort of freaked out. Because I was going to graduate the next year and I had no idea what I was going to do with myself.
I mean, I knew what I wanted to do. I wanted to travel the world. I wanted to go to Europe, I wanted to be in Rome and Paris, I wanted to see conductors and go to restaurants and experience good wine and art museums and maybe perform ... But I still couldn't play the violin.
So, ... at some point, I thought about it. I thought about it alot actually. And I thought, you know, if you do research mathematics, it's kinda like playing the violin. Because, if you're a violinist what do you do? You sit in your practice room and you practice, you practice, you practice all your recital stuff, and then, after you've got it all prepared, you go somewhere and give a concert. And if you are a research mathematician what do you do? Well you sit in your office and you work. And you work, and you prepare your mathematics and get it all right, and after you've got it all prepared you go to some conference and present it.
And, you know, after the conference you go out for dinner, and you're in Rome and you're in Paris, and you hang out in the coffee shop in the morning, you go to the bookstore, maybe check out the art museum, go back to the conference, so I thought, you know, Maybe I Could be a Mathematician. And the world never was quite the same again.
There was only one problem. If you want to do research mathematics, the easiest way is to get a PhD, and if you wanna get a PhD, the easiest way is to go to graduate school, and if you wanna go to graduate school, the easiest way is to get admission, ... and that didn't look so good. So I had to think about that one too. I said, you know, in the music world, if you can play, then you just get up and play and people can hear that you can play and they arrange concerts for you. So I said, maybe it works in math too, if you can just do math, then maybe you get in. So I thought I'd try. So I signed up for 4 postgraduate courses at MIT that semester. Algebraic topology, Commutative algebra, Advanced Algebraic Combinatorics and Advanced Cryptography.
And for the first time in my life I worked, on mathematics. I actually worked on mathematics. Just the same way that you would work on violin. When you work on violin you play the same passage over and over and over again until it just comes out of your fingers, easy as pie. And when you work on mathematics, you do the same problem over and over until it just comes out of your pen. And when you work on violin, you prepare for a competition, you do everything possible to recreate that feeling, those nerves and everything. And when you work on mathematics and you are preparing for an exam, that's exactly what I did, I would go pull off the textbooks out of the library, get the textbooks, get the problems, one by one, make lists of the problems, figure out what they could ask, make sample exams for myself, and then I'd go make myself really nervous and give myself only three hours to do this sample exam. See how good I did. And then afterwards, I'd analyze and figure out, ... "Tssk, I coulda done better on this" "I'll just do this problem 65 more times, just like when you are playing Kreutzer, you know you play Kreutzer etudes 65 times.
And it worked! I did pretty well. It was tough, I was always working. I was in the library. I always listen to music when I'm really doing math, and to this day, if you ask me about algebraic topology or commutative algebra, it is associated in my mind with Berg's Wozeck, because that is what I was listening to that semester.
It was exhausting. It was alot of work. It was tiring. I wasn't really used to doing mathematics but I was starting to get the hang of it. I remember in the evenings, on the weekend, I would just have to take a break. Even though there was still alot of math to learn, I would take a break, and I would go ... I was really into "Alternative" music, Alternative Rock and and so I would go to Central Square, to this bar, that was down in the basement, with a big bouncer at the door. You go into that bar, and everything is dark, and it's just kinda smoke in the air, and just the lights of the stage. And there was one show, that really sticks in my head from that time. It was Jane Siberry. It had an effect. It was like a trance. It had an effect on me, it was so ethereal.
It still blows my mind that picture. She's so right. Jane Siberry is so right. Symmetry, is the way ... You know, that's the picture of E8 symmetry, symmetries of an 8 dimensional universe. It's just one of those things, it makes you feel like the world is right. It fits together. And I think, for the first time, the world was starting to fit together for me: my music, my mathematics, ... it was starting to fit together.
Anyway, there was another problem. Even though I did pretty well in my courses that semester. You had to find a place to go to graduate school. It wasn't like it is now. We didn't have the internet. So you had to ask advice and you had to find the right place to go to graduate school. So I thought, you know, I liked this kind of stuff, I like this algebraic, structure, it's just, it's beautiful to me, But I was a little worried about algebra, just like I can't play the violin, I thought, maybe I can't do algebra. But I did pretty well in my combinatorics class, my algebraic combinatorics class, and that sort of has that same feel of algebra, so I thought, OK I'll do algebraic combinatorics. I went to the algebraic combinatorics professor. His name was GianCarlo Rota. He was a very elegant man. Wore nice suits. I made an appointment. I said, I wanna ask your advice.
At that time he was godfather of the journal Advances in Mathematics, one of the top premier journals, and so when I came to meet him, he was carrying this huge pile of mail, of all the submissions that he had received that day for Advances in Math. He had me come sit down and he put the big pile of mail down on the desk. He sits down in front of there and he picks up the first piece of mail and he says "So, ... What can I do for you?". "well, um, I think maybe I want to go to graduate school, and I'm thinking maybe I'll do algebraic combinatorics, and so I was kinda hoping that you'd give me some advice on where to apply." "You should stay at MIT, it's the best place", and then he took the piece of mail and he flung it across the room into the rubbish bin at the other end. My turn to talk. "Well I thought maybe I should have a few other backup places to apply" He's looking at his mail again. "You should stay at MIT, it's the best place", and he flung the second piece of mail over there into the rubbish bin. My turn to talk. "You know what, the honest truth is, I probably can't get in to MIT, I don't have the grades, so, um, I'd really appreciate it if you suggested a few other places that I might have a better chance of getting in." "All right. ... You should apply to Ohio State and San Diego. Anything else?" My turn to leave.
So I applied to Ohio State and San Diego.
Actually, I did apply to MIT too, but I didn't get in, so I did call that one right. Anyway, Ohio State gave me this fantastic offer. Full fellowship, no teaching for the first 10 years you are in graduate school, penthouse apartment across from the University and a stick shift Ferrari so you could drive around as coolest PhD student in town. They flew me out there, they had me meet all the algebraic combinatorics professors and learn what research they were doing. They took me to the colloquium and to the party after the colloquium. It was pretty attractive.
San Diego gave me this bottom of the heap kind of offer, you know, like, we don't really want you but we're going to let you in. I called them and asked them, "Will you fly me out there so I can meet your guys?" "No, we're not gonna do that for you." But I decided, it's too big a decision. It's a decision for my future, and Rota recommended it, you know, so, I should really go see. So, I charged a plane ticket. I made arrangements with a friend who had a friend who had a friend, I don't know who, whose couch I could sleep on while I visited. And I checked with Rota, who were the Algebraic combinatorics guys out in San Diego, some guy named Garsia and some guy named Remmel.
All right, so I flew out to San Diego. I got to San Diego and I headed to the Uni. I could not believe this place man. This was just paradise. The sun was shining and there were just miles of beaches. You go swimming, .... you play volleyball, ... you lie on the beach. I thought to myself, I'll never learn anything here. I can't go here.
So I went to the Uni. I went to the Math department. I looked on the directory, I found Garsia's office number, went up the lift down the hall to his door, Plucked up my courage, knocked on the door. Door opens, some woman answered. Now, I thought that Rota said that Garsia was a man, but maybe I got that wrong, so I started my little speech, "I'm a prospective graduate student and I think maybe I might want to do algebraic combin .." "He's not here" "is he coming back or something?" "I don't know, tomorrow, tomorrow." The door closed.
All right. That wasn't looking so good. So, I went to the beach. Next day I came back, went to the math department, up the lift, down the corridor, plucked up my courage, knocked on Garsia's door. Door opens, BIG man, looks like Santa Claus, electromagnetic energy coming out of this man, looks me up and down. "I'm a prospective graduate student and I think maybe I might want to do algebraic combin.." "Oh, No time now, No time, Come back later." "well what time can I come back?" "I don't know, this afternoon." "what time is good this afternoon?" "auuh, Two o'clock, come back two o'clock" and the door closed.
Okay. That was better at least. I went and sat on the steps of the gym, absorbed the sunshine, went back two o'clock. up the lift, down the hall, plucked up my courage, knocked on the door. BIG man answers, looks like Santa Claus, electormagnetic energy coming out of this man, looks me up and down. No recognition. So, I started my little speech, "i'm a prospective graduate student and I think maybe I'd like to do algebraic combin.. " "Oh, Oh yeah, ... right, ... sure, .. uh, yeah, come on in, come on in, sit down, sit down." He had me sit in the chair, and then he looks me right in the eye, and says "Do you know what a representation is?"
I thought to myself, 'No forget it man, this was all a really bad idea, I don't need to do this math thing ...' But of course I didn't say anything. I was just in shock and kinda shrugged no.
And then this man launched. He launched into this lecture about what is a representation. Writing on the board, you know, some equation, and then a big diagram with lots of arrows, and then FANTASTIC all in capital letters with exclamation points. And he kept on going, some other equation, and another big diagram, ... I didn't understand a word. I only remember the last sentence. The last sentence was: "So. That's more or less what we do around here".
I thanked him. I left. And I went down to the student union.
I found a phone and I called Ohio State and I said,
"I'm not coming".
Cuz I was going to work with that man.
That man had fire.
That man passion.
That man had Latin blood.
That man had culture.
That man yelled and screamed at his students.
And I could learn mathematics from that man.
And that, after all, was the point.
The end of college was fantastic. Lots of great parties, lots of great friends. And then I packed up all my stuff: my records, my sheet music, my CDs, my 4 math books, and I put it in the back of my truck, and I got in my truck and I drove, across the country to San Diego.
And so, 3 days later I was out in San Diego. I went to the Uni, and looked on the notice board and found a place, a room in a shared house to live. I went to the lumberyard. I got some plywood and some cinder blocks, made myself a makeshift desk, made myself some bookcases and unpacked my stuff. Unpacked my records, unpacked my sheet music, unpacked my violin, unpacked my 4 math books, got myself ready for graduate school.
Graduate school was horrible. You had to take these qualifying exam courses in algebra and analysis that had had the juice squeezed out of them until they were so dry it just was totally uninspiring. Garsia wasn't there. Garsia was away on sabbatical. I didn't have any friends. It was lonely. The music scene, ... I wasn't part of the music scene. I was actually pretty depressed, to be honest.
I decided, ... I had made a commitment. I was teaching tutorials, ... I had made a commitment for the frst year. I would make it through the first year, and then I was going to leave. I was going to go to New York and make a guzzillion dollars in finance or something.
Second semester, it was looking up a little bit. I made friends, ... I had a friend, her name is Tamsen. She is, to this day, a very dear friend of mine. She was a little bit more senior graduate student and she was already working in algebraic combinatorics. Her advisor was Remmel, the other main algebraic combinatorics guy, and she already had a research problem to work on, a project. Garsia was back, and he was teaching a course in symmetric functions. Of course, he didn't remember me -- I didn't exist for Garsia, but I sat in his course on symmetric functions and I said, yeah, this guy has fire, that was the reason I came.
I really wanted to do research. So I would ask Tamsen. "You know, you're already doing research. What are you doing? What's your project, explain to me, what are you doing?" She would try to explain to me and I just couldn't get it. I couldn't figure what she was supposed to be doing. So that semester because Remmel was away in semester 2 and Garsia had been away in Semester 1, So that semester Tamsen would go to Garsia for her supervisor meetings, because Remmel was away, they would take care of each other's students. So she would have a meeting with Garsia every week to get direction on her project. So finally I told Tamsen, because I couldn't understand what she was supposed to be working on, I told Tamsen, You know, next time you go to your meeting with Garsia, I would like to come along, just introduce as some friend of yours from high school, he doesn't know who I am.
She we did that. We went to Garsia for her meeting and she introduced me as some friend of hers, and I sat in the corner while they had their meeting. And it was perfectly clear what Garsia wanted her to do. There was some element p. Some expression, kinda messy, but not too bad, in the group algebra of the Weyl group of type B, well I had no clue what that was, but that's ok. It was very clear what Garsia wanted. He said, "Take p times p, multiply it out, simplify it, collect the terms, and you'll get p again". That's called an idempotent. I didn't know that at the time either. p times p would be p, that's what Garsia said. And, you know, I learned to multiply out in grade 8 or something, so I thought, well yeah, this is ok.
So I told Tamsen, well you go home and do it, and I'll go home and do it, and then we'll compare notes in the morning. We met for coffee every morning at 7 o'clock anyway. So, I went home. And I got my papers out. And I put some pasta on for dinner, and I started doing this calculation.
It didn't take very long actually. I'd say, by the time I finished dinner I had finished the calculation. It wasn't bad at all. The only problem was, ... it didn't work. p2 was not p. So I thought, 'aaaa, I must've made a mistake somewhere in my calculation.' So I checked it really really carefully, but it just wasn't. But, but, ... but Garsia had said it would be.
So I thought, 'Well, I must've copied something wrong. This 2, what if we change it to a 3?', and I redid the calculation. 'This plus sign, what if we change it to a minus sign?', and I redid the calculation. In the end I worked all night on this thing. In the end I found seven different ways to fix it. Fix it, ... I mean p2 would be p, but I didn't know which one was right.
So in the morning, at 5 o'clock or something, I wrote them up really nice and neat, the original one that didn't work, and my seven "fixes". And I wrote them all nice and neat and took a shower and went to go meet Tamsen at 7 o'clock.
I said Tamsen, "Did you do it? It doesn't work." "No. My cat got sick and had to take her to the vet." I said, "No, but Tamsen, it doesn't work, you gotta check my calculations". And so we went and sat in the coffee shop and I made her check my calculations line by line, step by step. Everything had to be exactly correct. Three hours later we finished checking my calculations. I said "Tamsen, we've got to go tell Garsia it doesn't work. What are we gonna do if it doesn't work?" She said, "No, we'll wait till next week in my meeting." "Tamsen, we can't wait till next week! What are we supposed to work on!"
So I dragged Tamsen, up to Garsia's office door, and I made her knock on the door. And Garsia answered. The tension was to omuch for me and I blurted out "YOU WERE WRONG!" And there was fire in Garsia's eyes.
But, amazingly, only for a second. He calmed himself down and started inviting us into his office. By this time, I'm ... putting my papers in his face "I found seven different ways to fix it, and I don't know which one is right ..." He would not look at anything that I had written. He just, he sat us down in the chairs, and he sat down at his desk, and he got a piece of paper, he got his pencil, and he started doing this calculation, himself, one step at a time, explaining each .. step ... as .... he ..... went. The next step, ... and the next step ... and the next step.
It was EXCRUCIATING! I had done this calculation so many times the night before it was tattooed onto my cortex; I knew that the next step was! But, I managed to keep myself quiet for 13 minutes, while he did that calculation.
And he got to the end. And it wasn't idempotent.
So then Garsia didn't really know what to do. He said, "Maybe you should read this paper on Free Lie Algebras or something and I'll think about and I'll tell you what to do". By this time I'm asking him a hundred questions. "What's an idempotent anyway? What's an algebra? Why do we care about Weyl groups?" But the conversation was over, he was shooing us out of his office, and the door closed.
So I told Tamsen, "well, I guess we have to read this paper, this paper on Free Lie algebras." So we looked at this paper. I couldn't understand a word of this paper. Of course, I probably couldn't understand a word of anything, I had been up all night and had 15 coffees. So, in the end, we went up to Tamsen's car, and we listened to Sisters of Mercy really loud on the radio.
So the next day, I was sitting in my office, preparing the paragraph that I had to prepare for the working seminar that we had, and Hélène Barcelo pokes her head in the door. You have to understand, Hélène Barcelo was like a goddess for us. She was Garsia's most senior PhD student. She had already finished her PhD thesis problem pretty much, she was just putting the final touches. She used to work with Garsia all the time, and then they would invite their Québecois friends over and cook big meals and talk mathematics. I was so envious, I wanted to be part of that circle. She already had this fancy job offer from University of Michigan for a postdoc, and so, for us, Hélène Barcelo was like way up there on some pedestal.
So I'm working in my office, and she pokes her head in. Hélène Barcelo is poking her head in. She looks around the office. You know we had these multi offices with several graduate students, so she sort of looked until she spotted me. Then she came over to my desk and she says, "Garsia wants to know who you are".
You see, before that, for Garsia, I didn't exist. But after that incident, I did.
So after I existed, I sort of got rolling. I did work with Garsia, and I did learn a lot from him. And I learned a lot from a lot of the other professors there at San Diego too. I learned a lot of mathematics, and I did get my PhD. And right after my PhD I did get an invitation to Basel Switzerland. So I guess it worked in the end.
There is one more story from that time, which is pretty definitive, so I probably should tell it. Right after my PhD, I was in New York visiting my brother. I used to go visit my brother, he lived in NY for quite a number of years. Just hanging out with him. Sleep on his couch. Just absorb New York. You know, New York is really a special place. It's just got vibe, and energy. Actually you don't have to have a lot of money to hang around New York. Cuz you just walk. That's what my brother and I would do. We would start 115th and Broadway where my brother lived and just walk downtown. And it was a whole day's entertainment. You know, you just watch the people, absorb the vibe. You just feel New York.
This particular day, we were walkin' down, and we got to Lincoln Center. For me, that's always a special event, because ... Lincoln Center, that's where the New York City Opera used to be, the ballet, ... same square as where the Metropolitan Opera is, the New York Philharmonic, the Juilliard School of Music. That's where all the music happens. And so I would have to go check it all out. You know, which operas are playing, which symphonies are playing, which artists are coming to town, what are they playing? Who's up and who's down. So we would go check out all the different halls.
And that day there was a big poster. It says, LEONARD BERNSTEIN. Leonard Bernstein was one of the great conductors. Musical genius in every respect. Doing MAHLER 2ND SYMPHONY. One of the great symphonies. With the NEW YORK PHILHARMONIC. Which was his favourite orchestra. I mean, they loved him. For good reason. And then a big sign, SOLD OUT.
I told my brother, "yeah... well... sometimes there are cancellations, let's just go to the box office and see if there are cancellations." So we went to the box office and they said "well you can stand in this queue here". There was already a queue forming there.
We didn't have anything else to do, so why not? You always meet cool people in the queue, interesting people. So we went a got one of those New York hot dogs, and we stood in the queue, talking to people. It didn't take very long and we were up at the front of the queue. We'd made our way up, maybe a couple of hours. And I knew that the next tickets coming out there, they would be offered to us. And sure enough, 20minutes later or so, 2 tickets came out, "you want to buy these tickets?"
I looked that the tickets. They were expensive. But, I said OK, and we took out the credit card and we charged those tickets.
It turned out hose tickets were right in the front row. Right underneath the first cellos. There's the conductor, there's the first cellos, there are the violins over there. Concert started, Bernstein comes out. I thought, 'The guy's gonna die before the concert is over'. I mean, he just looked so old and so tired, ... He took his bow. He got up on the podium. And then all of a sudden his body went into this convulsion.
And that sound came out of those cellos and basses and it blasted us to the back of the auditorium. It was the most amazing opening of any concert that I ever experienced. And from that moment on Bernstein was intense, focused, energy, it just was going through every pore of that auditorium. And the orchestra was right on, right in the same trance that he was in. It was just Mahler's second symphony coming out of every atom and every molecule of that concert hall.
It was the most amazing concert I've ever been to. After it we were just totally blown away. And I followed my brother out of the auditorium, he was the New Yorker. He runs into some friend of his, some Jamaican guy, he was a security guard at Symphony Hall, My brother was like that, he always knew people like that. "Whatcha doon Symfohnee Maan?" So, yeah, my brother's talking to this guy, "Yaa, yu be gon down maan?" We said goodbyes and we headed off down the hall.
Then my borther turned left into this room. I don't know about half the size of this room. And I couldn't believe my eyes, there was Leonard Bernstein sitting right in the corner! And there was a big queue of New Yorkers waiting to go talk to Leonard Bernstein. We had ended up in the VIP after-concert reception for that concert. It helps to know the Jamaican security guard.
Anyway, I was in shock. There was Bernstein, smoking his cigarettes, drinking his whiskies, he was always smoking and drinking. Talking to each person in turn, with the utmost grace. "Ah, Stella, such a pleasure to see you. It's been years. How's Samuel? Oh, I'm so sorry to hear he's not doing well.... Of course I'll sign your record." And he went through that queue, one by one, talking to everybody.
And then, there we were, and I was meeting Leonard Bernstein. There we were. I said, "Mr. Bernstein, it was just a fantastic concert and a fantastic evening, Thank you very much." And he looks at me, right in the eye, and he says "Who are you?" You see, everyone in that room was someone. You couldn't get into that room unless you were someone (or you knew the Jamaican security guard). So I said, "Mr Bernstein, I'm a mathematician. Thank you for a very inspiring evening." And I looked at my brother, and we headed off into the New York night.
So you see, ... I was a mathematician. I mean, I had told Leonard Bernstein I was a mathematician. People ask me, "Did you always want to become a mathematician?" Well you've heard the story now, certanly the answer to that one is "no". And then they ask me, "Well, what made you decide to become a mathematician?" I tried to think about that one. And you know, I think it's very similar to the answer to "Why do we choose to live in Melbourne?". Something about it keeps you, ... it's got the right atmosphere to keep you creative. It's the culture or something.
We've got culture in Melbourne. Well, for me, I go hang out in the Italian district next to the Uni, and have my coffee, and just let the Italian go through my veins in the morning. It keeps me going. Or you can go, take the train out to Sunshine. You know, you get off the train in Sunshine, you head down to Devonshire Road and pass Classic Curry and Sagar Spices, and then your hand starts to go like this, and you feel like Indian. We've got culture.
And it's good. Because culture helps you push your boundaries a little bit, and that's what you need to be creative. When you've got different cultures you are always pushing a little bit on who you are. And you create things. You know, for me, with mathematics, it's like woodwork, you work a little here, you make the shape right, you smooth it out on this side, you put some varnish on, polish it up, and at the end, after you are done, you say, "I made that". "I wrote that paper." And you're proud of what you did.
But, you know, even more than the culture, it's the people. I think it's the people. Here in Melbourne you meet interesting people. People that inspire you. That keep you going. I look at my firend here Gigi Valeri, he shows me pictures of art from the Italian churches on his iPhone, and when I see him I hear Sonny Rollins over in the distance somewhere. I look at my friend Emilia Cross and I can practically taste the Osso Bucco, and I hear Prokofiev's Romeo and Juliet. I look at my mate Darryl back there, who's trying to avoid it, and I smell Carlton Draught, ... It's the people. It's the people that keep you going.
It's the people that inspire you. And most of all, I think, it's the students. You know, I have to say, that's probably the best part of my job. Because, 4 or 5 times a week, I go, ... I go pick up my stuff, go over to the next building. There's a lecture hall, like this one, 150 seats or something. And there are students there. And I get to show people, my beautiful world of mathematics.
This is the script of a public lecture given on 31 July 2018. Many thanks to
Ok, Now, I don't know what Doug has planned. But, you know, If you've been a student in my class you know how it begins: "Ask me a question".
Doug: "And I was just going to ask you, if you'd like ask ... Arun, or myself, or Andrew, any questions about the talk, the story, being a mathematician, or The Institute for Enquiring Minds. Please, if you've got something you'd like to ask, ask now."
"Yeah, I was just wondering what your deal is with YouTubePremium?"
It's fantastic! You know, I used to have to pay,... I probably paid 12 bucks for this record, in 1986, and now you just pay 12 bucks a month and you've got everything! It's amazing. I mean I spend my whole nights just glued to YouTubePremium.
"How much would you spend on your average day doing mathematics
would you say, ... research."
Well I try to do, ... so I get up early in the morning, I mean there's a lot of things in a day, ... once you ... once you get to be a full time professional mathematician there's a lot of pressures on your time. But, every morning I get up early and I have a couple of hours of really good work.
"What time, ... in the morning?"
So, ... my .. my main research time is 4-6 in the morning. But of course, that's not the only time, because when I go to the office we have research seminar, and I have meetings, and we have discussions with coauthors and with colleagues, and so on. But that's my time to do the hard, ... the real work that I have to do for research.
"What do you listen to?"
It depends a lot. As you can see I have a few different tastes here and there, and so it really depends, ... alot on the mood, ... on what I'm trying to get done.
"So, Sisters of Mercy on bad days?"
Not always. There's something peaceful about that Sisters of Mercy trance.
"Do you still play your violin?"
Of course. I couldn't leave that.
"Whats your opnion of the Fields medal?"
My opinion of it? You mean, ... you're asking me to guess who will win? Is that what you're asking?
"Whatever... open question."
I mean, The Fields medal is a great thing, because it does bring to the community who are not necessarily research mathematicians, it brings some of these people into view, and I think that's very important. I mean, perhaps the sadness for those of us who work in the field, is that there are so many great mathematicians, that don't get recognized, that don't get a Fields medal, but ... are still fantastic and amazing and there's only a few Fields medalists every 4 years, so we ... Certainly inside, on the inside, we recognize those people as well.
"Something we've talked about alot, in our journey through mathematics
at University, was the evolution of thinking into, like you discussed
earlier, bringing proof into the doldrums of mathematics,
you know, of learning maths in the early stages. Do you have any opnion
of your own, when proof, or when logic of that sort should be introduced to
I don't know, ... maybe 6 months. ... Is that too late? No, I really do think that. I mean, certainly, in my family, with my daughter, we talk about it, we organise it, from the beginning. I don't think that there is, ... it's just part of ... It's like music, you don't say, oh well, my daughter was born, she can't listen to anything until she's seven. You don't not listen to music. ... So it's just part of the every day fabric, and it works from the very beginning as part of the everyday fabric.
"I suppose the reason I ask is, through my own education, it never really came up. ... until University, that was what fostered the interest."
Well you should come to the pub with me a little more often.
"At some point, did you feel you were talented as a mathematician?"
Absolutely not. No, ... in fact, to this day I don't really feel that I'm talented. I work. I work hard, and, you know, if there is talent then it's at that very top level that it makes a difference. You know, sort of like the difference between Michael Jordan and all the other basketball players. Maybe at that very top. But if you want to be in the NBA, just go be in the NBA. You just have to work.
"The people, the matheamticians who were really smart around your age,
what are they doing now, compared to you?"
I mean, it depends what you mean by really smart. Of course there were people who did really well in the courses I was in, and so on ... and um ... actually most of them I have no idea, they are not part of the community any more. I don't know, they might've gone into finance and made a guzzillion dollars. Most of them, I've just mostly lost track of them. There are a few of them, that we are still in contact, they are colleagues at another University, and they are still working on mathematics.
"In the morning, in your morning research 4am to 6am, do you know where you
are going, step by step, or is it ..."
If you'd like to help I have a list of like a thousand things that need to be done. No. That's the real truth. Is that, I have lists of things ..., you know, this calculation has to be done, this calculation, this has to be checked, we got to ... I got to read the paragraph 6 of Chapter 16 of this book, and ... It's just a list of ... really, a lot of it is sort of menial, mechanical work, but it has to be done in order to get to the product.
"Is it anxiety provoking, or enjoyable, or do you just sort of flow through?"
Well, of course, it depends a little bit on the day, but it's very peaceful on average, you know, so much of it for me is like the violin, when you sit in the practice room, and you practice. You know, you practice, an hour, ... or two hours, ... there is something sort of meditative about it, ... it just goes along.
"Did you ever figure out what p was?"
No. Yeah, it's a good story but he'll kill me if I take more time to tell it now.
"I really enjoyed that talk, and it was really nice to hear about a journey
of someone becoming a mathematician, and I, ... I wonder if you think that
it's detrimental to our field that we, ...
we tend to hold up this very romantic notion of the math genius,
where they seem to just emerge out of the womb as someone destined to do math.
I think that that is particularly intimidating to a lot of people."
Well, I think, I think that the only ... I mean, ... Of course I have this idea of the tennis great: Roger Federer, you know. And, of course, you have to have that. I find Roger Federer inspiring. You know, he can hit that, right into the corner every single time. It's pretty awesome. So, you need that. But the thing that that loses, it's too narrow, ... because mathematics is huge. Mathematics has so much flexibility, you can do mathematics in all kinds of different ways. I mean, I do mathematics one way, but you can do mathematics in a completely different way, where you don't travel and you don't go to countries and you can have a peaceful life with your kids at home. So there are so many ways to do mathematics, and that is what that stereotype loses, ... is we don't show those other ways of doing mathematics as well.
"I was just wondering. Have you always been the researcher, or
have you had like a side career at all, ... contracting work or
something like that?"
I do get distracted sometimes. :) Yeah, I think I get distracted quite a lot actually. But, there is something that keeps me in it. So I keep coming back. There's something ... and it is something similar to the music, it's something about that artistic thing that I, for my personality, need. I do like that idea that I'm doing something, you know, like making good wine, or something, that doesn't ... it tastes really good, but it doesn't really have an application to building iPhones. So that is attractive to me. On the other hand sometimes it happens that there is an application, to building encoder-decoders or something. So, I don't know. You follow your heart, I think that's what it's really about.