Finding Ramanujan

IRA FLATOW: This is “Science Friday.” I’m Ira Flatow. In 1913, the British number theorist G. H. Hardy received a strange letter with his morning tea. It came from far away Madras, India. The sender was a poor Hindu clerk, a two-time college dropout named Srinivasa Ramanujan.

The letter contained mathematical formulas so fantastical, so strange, Hardy would later say that they had to be true. No one would have the imagination to invent them. Among mathematicians, that long ago correspondent, Ramanujan holds mystic status. Among us lay people, not so much.

Well, a new movie is trying to change that. “The Man Who Knew Infinity” tells the story of this outsider mathematician who died at just 32 years of age. In his short life, Ramanujan filled three notebooks with strange, enigmatic formulas that continue to boggle the minds of mathematicians, mathematicians like my next guest. Ken Ono is the Asa Griggs Candler Professor of Math and Computer Science at Emory University, and consultant on the movie, “The Man Who Knew Infinity.” He’s also the author of a new memoir co-written with the late Amir Aczel, “My Search for Ramanujan.”

Welcome to “Science Friday,” Dr. Ono.

KEN ONO: Ah, good afternoon, Ira. Glad to be here.

IRA FLATOW: It’s a great story, a great book, a film, as I saw a little bit of it. But let’s start first with how you first heard about Ramanujan. The story also involves a letter, right?

KEN ONO: Oh, boy. Actually, Ramanujan, for me, seems to be nothing but letters. I first learned about Ramanujan when I was a reticent teenager. I was 16 1n 1984. I was about to drop out of high school myself.

And a letter came to the house. It was April 7, 1984. I’ll never forget it. And it was a letter written to my father from Janakiammal, a woman in her ’80s who lived in Madras, who turned out to be the widow of an Indian genius, Ramanujan, who had died 64 years earlier.

IRA FLATOW: Wow.

KEN ONO: Right.

IRA FLATOW: Well, you’ve called Ramanujan math’s greatest anticipator. What do you mean by that?

KEN ONO: Well, so as you mentioned a moment ago, Ramanujan died very young at the age of 32. And what he did in his notebooks is, he wrote down formulas which, for him, were flights of fancy, only for us to find that, as mathematicians of his future, that he wrote down formulas and functions that we’ve ended up needing. People have won Fields Medal for making use of his functions. Fermat’s Last Theorem probably would not have been proven had Ramanujan never lived. His legacy go so far beyond the questions that people were even asking when he was alive.

IRA FLATOW: And these ideas were not around when he was alive–

KEN ONO: Right, well–

IRA FLATOW: –is what you’re saying.

KEN ONO: Right. We’re using his formulas to study black holes today. People didn’t even know if black holes existed in 1913.

IRA FLATOW: Ramanujan got into math because of one book, right?

KEN ONO: That’s right.

IRA FLATOW: An old math tutoring book.

KEN ONO: Right. Ramanujan got– it’s not a very good book, honestly. It’s called “A Synopsis of Mathematics” by a British tutor, like G. S. Carr. And what it is, this is a list of 6,000 theorems and formulas, laid out systematically, but with almost no text in-between. It was something like an almanac of mathematical formulas. And somehow, this incomplete list of formulas ignited his passion.

IRA FLATOW: And then he dropped out of college.

KEN ONO: Twice.

IRA FLATOW: Because of the book.

KEN ONO: That’s right. Because of this book, he felt that the mathematics in the book, they were laid out like puzzles to him. And he needed to finish them, and then find formulas of his own. And kind of like a college kid might be addicted to video games, Ramanujan became addicted to finding his own formulas. And as a result, was a very poor student. He didn’t do his homework, didn’t attend class, and, well, it didn’t end up very well for him in school, at least.

IRA FLATOW: Yeah. And then, Ramanujan writes to the British mathematician, G. H. Hardy, with some of his formulas. And here’s Jeremy Irons as Hardy in the movie, opening Ramanujan’s letter, in the film, “The Man Who Knew Infinity. ”

[AUDIO PLAYBACK]

[LETTER RIPS OPEN]

HARDY: I beg to introduce myself as a clerk in the accounts department.

SPEAKER 4: What this time?

HARDY: Quite impressive, really. Someone’s gone to a lot of trouble. A Hindu clerk? And who claims he can give meaning to the negative values of the gamma function.

[END PLAYBACK]

IRA FLATOW: Well, were not getting into the gamma function. What was in the letter that convinced Hardy that Ramanujan was the real deal here?

KEN ONO: Well. It’s a fantastic letter for several reasons. First of all, Ramanujan writes in a very humble way. He begins with the words, I beg to introduce myself as a clerk in the accounts department. I’ve had no university education.

But what followed were seven pages of mathematical scrawl, almost with no words. One of the claims is that, if you add up the positive integers, 1 plus 2, plus 3, plus 4, and never stop, well, we all know that goes to infinity. You can’t add up all the positive numbers and get anything other than infinity.

But Ramanujan claims, well, not only don’t you get infinity, you get a negative number. You get negative 112. That seems crazy. But to Hardy, Hardy would have understood that was actually a brilliant observation.

The letter also had mistakes, but amazingly, the letter ended on the ninth page with three formulas, three formulas that were so startling that Hardy said, nobody could have the imagination to invent these formulas. And you know what’s true about those three formulas? We didn’t figure them out until about four years ago.

IRA FLATOW: Wow.

KEN ONO: So that’s how crazy some of the formulas happen to be in his writings.

IRA FLATOW: Let me play you another clip from “The Man Who Knew Infinity,” and this is Hardy, played again by Jeremy Irons, talking to Ramanujan, played by Dev Patel.

[AUDIO PLAYBACK]

HARDY: Listen, I’m hard on you for your own benefit, so that you can be published.

RAMANUJAN: But Sir, you can publish the notebooks and my prime number theorem. You’ve had them since I arrived.

HARDY: There’s nothing I’d like more. But if I was to publish them in their presence state, I’d be sent to the lunatic asylum.

RAMANUJAN: You don’t understand this. I don’t think about this the same way you do. These steps you want, or what you want, I do not know how to do.

HARDY: Well, you can just begin by trying your best. And see if you don’t surprise yourself.

[END PLAYBACK]

IRA FLATOW: So he was not a mathematician in the classical sense?

KEN ONO: Oh, no.

IRA FLATOW: A professional mathematician?

KEN ONO: Right. Well, try to remember the time period. This is around 1913, 1914, and India was subjugated by England. And it was quite extraordinary for Hardy to invite an Indian to be a distinguished scholar at Cambridge. And in particular, one with no university education whatsoever.

So Ramanujan, when he was recording his formulas in a notebook, he might as well have been living in a desert. Nobody understood him. He didn’t know how you did mathematics. But somehow, in the areas of math that he worked in, he was able to basically eclipse the accumulated wisdom of Western Europe, and that was astonishing.

Whereas, Hardy, your image of this distinguished Cambridge professor about, you have to go through these courses. You have to earn the right to prove theorems. And there’s an actual procedure that one has to follow when writing up papers. These two men couldn’t have been more different in how they did math, from different countries, and never mind that Ramanujan was a devout Hindu who said that his ideas came to him as visions from a goddess, where Hardy is an atheist.

Everything about these two men should have meant that they would’ve been unable to understand each other. And that’s one of the beautiful things about this film. It’s about how two very different people with the same passion can somehow forge an incredible relationship, no matter, and independent of the fact that it was very short. And it’s a beautiful film because of that.

IRA FLATOW: And why was Hardy different than everyone else? Why did he accept Patel?

KEN ONO: Ah. Ramanujan.

IRA FLATOW: Ramanujan.

KEN ONO: Right, well–

IRA FLATOW: Call him the actor, right? Yeah.

KEN ONO: So I write about this, actually, in my book, among other things. I think Hardy, perhaps, was the only man alive who would have been able, at that time, to recognize Ramanujan’s genius, the skill that Ramanujan exhibited in his letters. Even if you were to show those letters today to professional mathematicians, maybe only 1 in 100 would see the beauty and importance of the work.

What did Hardy know? Hardy was the, at the time, probably the world’s leading analytic number theorist. So he had spent some time thinking about these kinds of objects. And some of the claims, Hardy knew, and others were so foreign that, well, he felt that he needed to get to the bottom of all that.

IRA FLATOW: So he was visualizing all this stuff in his head. And that’s what upset to see the status quo mathematicians, he didn’t write the proofs down of how–

KEN ONO: Right.

IRA FLATOW: –he knew what he knew.

KEN ONO: Well, even to this day, it has to be said that paper was very expensive in India. So to have three notebooks was a luxury for Ramanujan. So he did most of his work on this little slate. And his calculations would end up with some sort of result. And all he did was record the result in the notebooks. So there is that component, too. It’s not just that he didn’t know how to write down proofs.

IRA FLATOW: Yeah.

KEN ONO: He just didn’t have space in this notebooks to record his steps.

IRA FLATOW: When you look at his notebooks, does the math look different from other math that was done?

KEN ONO: It does. It does. If you happen to see a poster for the film, you can see some of the reproductions of Ramanujan’s work, and it’s beautiful. There are no words. His handwriting and his script, it’s gorgeous, but it’s very difficult to figure out what he meant.

So for example, halfway through the first notebook, you’ll find that he writes out the first 30 digits of pi. Why would it take Ramanujan half a notebook to get to the first 30 digits of pi? And it turns out that nothing on that page around it seems to have anything to do with pi. It’s all a mystery.

IRA FLATOW: Now, you learned about Ramanujan from your dad when you were 16, right? Not long–

KEN ONO: That’s right

IRA FLATOW: –after, you drop out of high school, too.

KEN ONO: About that time. So the letter, when the letter came to my house, I had never heard of Ramanujan before. And the letter thanked my father for making a small gift to help pay for a bust of Ramanujan. And my father, who was a very stoic man, it was a very emotional moment for him.

You see, when Ramanujan died in 1920, in his widow was promised a statue. The government promised to erect a statue in Ramanujan’s honor, and they never came through. And by the early 1980s, the mathematicians of the world got wind of this, and they had a fund-raising campaign, and my father was one of many who made a contribution.

So the letter– presumably Janakiammal sent hundreds of them– was just a form letter, really. But it was an opportunity for my father to tell me about this legendary man I’d never heard of before. And to tell you the truth, that was the beginning of the healing between the two of us, because, at the time, the reason I was about to quit high school is that I felt like I was being suffocated under parental expectations. I was supposed to be the straight A student, supposed to get perfect test scores, and that’s not what I was about at that time.

And I needed a hero. I needed someone who could inspire me that said that, well, there’s a lot more to test scores and grades. There’s a lot to creativity and actually producing content. And it was important for me to hear that from my father and my parents, when, honestly, they were a large source of the parental expectations that I was struggling with.

IRA FLATOW: Talking with Ken Ono, who is Professor of Math and Computer Science at Emory University. His memoir is called “My Search for. Ramanujan” on “Science Friday” from PRI, Public Radio International. So that’s quite interesting, he was a bridge for you, too. I mean, in your youth.

KEN ONO: Several times. In fact, this is why Amir– regrettably, he passed away– it would have been wonderful if he could be here with us today.

IRA FLATOW: Yeah.

KEN ONO: Ramanujan helped me, as a teenager, recognize that my parents looked up to someone like Ramanujan, who was a two-time college dropout. And later, in college, I had a great professor, Paul Sally at the University of Chicago, who helped, I almost want to say, rescue me as a senior. And he helped me get into graduate school. And that was shortly after the “Nova” special about Ramanujan aired.

And then, lastly, as a graduate student, my adviser, who really turned me on to mathematics– there’s a difference between being good at mathematics, and then being passionate about the subject– Professor Gordon, helped me find that passion. And one of the first steps along the way it was reading the biography, “The Man Who Knew Infinity,” which came out when I was in graduate school, and that’s the book that the film is based on. And, well–

IRA FLATOW: And you’re the adviser. The man who–

KEN ONO: I’m the adviser, and I have to say, I’m an accidental associate producer. I’ll be sorry to see the theatrical end run, because it’s been two wonderful years.

IRA FLATOW: It’s hard making a movie, isn’t it?

KEN ONO: Oh, it’s unbelievable how many moving parts there are.

IRA FLATOW: Yeah, I’ve done a little of that. Where is Ramanujan stand on all of mathematicians? I mean, he died at 32.

KEN ONO: He died at 32. Right. So I actually write a chapter about this at the end of my book in the epilogue. And it’s very difficult to rank mathematicians. It’s hard to rank anything. How do rank colleges? How do you rank basketball players?

So there are many different kinds of mathematicians. You could be a theory-builder. You could be someone who’s whip-smart, able to solve problems much more quickly than anyone else. Or you could be someone who can borrow ideas from one area of science, and apply them in another. These are all ways in which you can be world-class.

But in Ramanujan, we have something completely different. We have an incomplete prophet. He died young. He left behind three notebooks that we’ve been mining 100 years after his death.

And just think about it. We have been studying his notebooks for 100 years, and we are still learning about the full potential of his ideas. So as an anticipator of the future, as someone whose ideas mean a lot for the future of science, I’m not sure Ramanujan has an equal.

IRA FLATOW: Well, and you hope now that the biopic about Ramanujan, “The Man Who Knew infinity,” which is in theaters now, you hope this will create some sort of buzz.

KEN ONO: Oh, absolutely.

IRA FLATOW: Ask anybody who is not in the field of mathematics. They’d never heard of him.

KEN ONO: That’s right. Well, I’m delighted to say that today is the opening day for the wide release of “The Man Who Knew Infinity.” So if you’re listening to me now, please go and see the film tonight. We think that Ramanujan should be a household name. Think Isaac Newton to England.

Why does Ramanujan matter? Well, we’ve talked about the science. Of course, to mathematicians like me, he matters. But what he symbolizes is much greater. What he symbolizes is that greatness can be found in the most unforgiving of circumstances.

And it’s the responsibility of teachers and mentors alike to, first, recognize that talent, and then find a way to nurture it. Why is it super-important today, and in particular, for this show? So science usually proceeds by the work of thousands, slowly adding to a body of work.

But as I’ve said just a moment ago, every once in awhile, some people come along and they propel knowledge further. They’re rare. And that’s what we have in Ramanujan

IRA FLATOW: We could go on talking with Ken Ono forever. He also has a memoir called “My Search for Ramanujan.” And as he says, the film opens today, “The Man Who Knew Infinity.” Thank you very much–

KEN ONO: Thank you very much, Ira.

IRA FLATOW: –for taking the time to be with us today.

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