After a reluctant start, mathematician Ken Ono makes an unexpected discovery.
Ken Ono is the Asa Griggs Candler Professor of Mathematics at Emory University. He is the Vice President of the American Mathematical Society, and he considered to be an expert in the theory of integer partitions and modular forms. His contributions include several monographs and over 160 research and popular articles in number theory, combinatorics and algebra. He received his Ph.D. from UCLA and has received many awards for his research in number theory, including a Guggenheim Fellowship, a Packard Fellowship and a Sloan Fellowship. He was awarded a Presidential Early Career Award for Science and Engineering (PECASE) by Bill Clinton in 2000 and he was named the National Science Foundation’s Distinguished Teaching Scholar in 2005. He serves as Editor-in-Chief for two Springer-Nature journals and is an editor of Springer's The Ramanujan Journal. He was also an Associate Producer of the Hollywood film The Man Who Knew Infinity which starred Jeremy Irons and Dev Patel.
This story originally aired on Mar. 9th, 2018, in an episode titled “In Honor of Pi Day”.
Story Transcript
I’m up here by accident. My father, some of you may know, was a mathematician. He, for many years, was a professor at Johns Hopkins. I don't know about many of you but when I was a teenager the last thing I wanted to do was be anything like my dad. Definitely, the last thing I wanted to do was anything that my parents told me that I should do.
I’m not trying to be funny and I love my parents, but when you're sixteen that’s not unusual. So in 1984, that’s when I was sixteen, so you'll know I’m about to turn fifty. Hawaii five-0, right? When I was sixteen in 1984, a letter came to the house addressed to my dad written by a widow, a widow of an Indian mathematician by the name of Ramanujan. We made a film about him.
It was the most extraordinary letter. I'd never heard of Ramanujan before and his letter to my dad thanked him for being one of eighty mathematicians that helped give Ramanujan’s widow a bust. You see, Ramanujan turned out, as I learned, was a major mathematical figure. When he died in 1920 as a hero in India the government had promised to erect a statue in his honor. But by the 1980s, well over sixty years later, the government had not come through with it, and the mathematicians of the world gave Mrs. Ramanujan the statue.
I thought that was a lovely story but, I have to admit, when I was sixteen, what I heard was there was a two-time college dropout who ended up inspiring the mathematicians of the world. And when you're sixteen and your parents are like super Asian, telling you to get 800 on the SAT math test or getting straight A’s, the only thing you hear is, “they look up to a two-time college dropout,” and I thought that was so awesome.
I know that sounds funny, but it was really important for me because, and certainly for all of you who are professors, you see the kids in class that are mindlessly pursuing good grades, forgetting that they're in college, forgetting about the content part. And for whatever reason, there have been a lot of accidents in my life, and I've ended up following Ramanujan first as a source of inspiration but certainly for the last twenty or so years a source of mathematics.
He's actually really crazy. He was kind of like an incomplete prophet. He left behind three notebooks. I don't know why you all don’t read these notebooks because I can’t tell you how many papers I've written because I've gone through these notebooks and found really deep suggestions.
But that’s not my story. My story is actually very difficult to tell because I was a terrible student. I was a dick. I was one of those kids in college that didn’t want to go to class. I was one of those students that, rather perversely, got a lot of pleasure out of getting by in math class by not going to class. And I’m not proud of that.
I have to say that I had great mentors along the way. You know the names. Paul Sally and my advisor Basil Gordon and others, later Andrew Granville who rescued me at times when I almost quit. Jeff Lagarius, who is here, will remember me as a PhD student about to quit. I can’t believe that twenty years ago I was about to take a job at a bank. If you work for a bank that’s… I mean, my point is that there are a lot of accidents, there are a lot of mentors along the way and there can be a lot of luck in one’s career.
So my story is about how I accidentally ended up having a career in mathematics that somehow ends up with me standing, bumbling in front of all of you about whatever it is I’m going to say. The story I want to tell you about is my big breakthrough, how is it that I became discovered and ended up having a good career. And it’s totally by accident.
So it was 1997, about twenty years ago. I got an email from Bruce Berndt. Many of you probably know Bruce. He's a professor at the University of Illinois. He's devoted his career to studying Ramanujan and I’m so grateful that he said that he had an unpublished manuscript that Ramanujan had left behind and he wanted some help editing this manuscript. I thought that actually sucked. What experience do I have at editing a manuscript? But it was like the most incredible experience.
So in 1997 I was beginning tenure track assistant professor at Penn State. This is Happy Valley. I was so grateful to get that job. Quite frankly, I didn’t believe I deserved the job. I was certainly an impostor, a fraud.
Let me just tell you a little bit about my circumstances. I had an office on the fourth floor. The building is called McAllister Building. It was built in 1904. It was originally intended to be the women’s dormitory but by 1997 it was in decrepit state, but somehow it was good enough to be the Math Department.
How awful was it? It was this awful. The internet went out probably every month, and I can exactly tell you why. Because the cables, which were in the attic, the squirrels -- we had squirrels living in the attic, so certainly the squirrels enjoyed the taste of internet cables, or at least the mouth-feel of them and so the internet went out all the time.
My office was in the corner. The ceiling was so low that there are places where, well, for half of the office you really couldn’t even stand up, and I’m not that tall.
I had an air conditioner. It didn’t work. And my window, it had a lock. That’s not right. It once had a lock, presumably broken off decades ago, but it didn’t even really matter because this building was in such decrepit state that there must have been like five or six layers of paint that made it impossible to open the window.
Anyway, getting back to this manuscript that Bruce Berndt asked me to help him out with, it was a chore. So we started going through the notebooks and there were some things in the notes that were just wrong. But it turned out that they weren’t wrong. It was that I wasn’t smart enough to figure out how right they were. You see, Ramanujan in his notebooks sometimes used the equal sign in a way that’s so different from what we would agree as. If A equals B, that’s supposed to mean A and B are the same thing. But to Ramanujan, it didn’t mean anything like that.
So over the course of several months, we went through the notes. I had this freakish yellow couch in my office. When you're a poor graduate beginning tenure track assistant professor, you can’t actually furnish your office. So I was so excited that when I went to Penn State Salvage I bought this stained orange couch for twenty bucks and it was like my most prized possession. By the way, if you need like adding machines from the 1960s, go to Penn State Salvage. You can buy it for five dollars.
So anyway, it was on this couch that I did most of my work. And in the course of going through Ramanujan’s notes, I finally began to figure out one of these formulas. It was so wrong that, just like Hardy said, it had to be somehow right. It had to be borne out of genius. I can’t explain this but it was one of those flashes of insight where I finally saw what Ramanujan had meant in this formula. It turned out it was related to an 80-year-old problem.
I went to the computer and I started computing, and term by term it actually worked out in spite of the fact that it had no right to work out. So I went back to the orange couch and I tried to build a theory out of it. And then it was another thing. I finally figured out it was related to things I had actually been thinking about. I hate it when someone tells you when they're dead after sixty years that you don’t understand your own subject.
It was an epiphany. I never had another epiphany like that. I sprang up from my yellow couch, I banged my head on the gabled roof of this ceiling of this building. I still have a notch here. It’s more than a scar. My skull is indented here. And I couldn’t believe the gift that I was given by going through these notes.
I ran out into the hall. I went to the bathroom. I washed my face with cold water. I was shaking, kind of like I’m shaking now because I’m petrified. And I got water all over. It was awful.
Then in walked my colleague Dale Brownawell, he's like, “What the hell happened to you? You're all wet. You're bleeding from your head.” And I couldn’t admit to him that the most amazing thing in my career had happened to me so I lied. Something like, “I hit my head on the coat hook in the bathroom stall.”
But any event, what I wanted to say about this story is that I have no right to be here. I’m not really smart. I’m really lucky and it’s one of those things when you're young, when you don’t know where your career is going to go that there are those miracles if you kind of believe in yourself.
So any event, to make a long story short I wrote a paper. It was solicited for publication in the Annals of Mathematics. I ended up winning a prize from the President of the United States for this theorem. I gave a speech about this theorem in the Indian Treaty Room at the White House and, at the end of the day, what’s going on at the back of my mind is not even my theorem.
I got a gift from God. Ramanujan was someone whose ideas came as visions from a goddess. Who am I to argue with that? I was a 2.7 GPA student at the University of Chicago and somehow that was what was going on in my mind. What am I doing at the White House?
Any event, if that inspires you, I hope it does because I've been following this genius and I can’t explain, I cannot begin to explain how amazing that’s been. Thank you.