Ken Ono is a professor of mathematics at Emory University in America. As a teenager he struggled both with the pedantic nature of his school work and the tall aspirations of his Japanese parents. Then his mathematician father pointed to the life and work of Srinivasa Ramanujan (1887–1920) who dropped out of two colleges early in his life and then went onto Cambridge where he was recognized as one of the greatest mathematicians of the time. With no formal training in mathematics, Ramanujan contributed many major mathematical theorems. Ono specializes in number theory, especially in integer partitions, modular forms, Umbral moonshine, and the fields of interest to Srinivasa Ramanujan. He was the Manasse Professor of Letters and Science and the Hilldale Professor of Mathematics at the University of Wisconsin–Madison and is the vice president of the American Mathematical Society. Ono was also a consultant on the Hollywood film on Ramanujan, The Man Who Knew Infinity . He spoke to Grin about the lessons he learnt from Ramanujan on the nature of failure, and success, and how to preserve talent.
- You have said the Ramanujan helped you, in a sense, find yourself and your own path in the study of mathematics. Could you explain how this happened and what is the biggest lesson you learnt from Ramanujan? Tell us a bit about your early struggle and how knowing Ramanujan changed your perspective.
I first learned about Ramanujan when I was a troubled 16-year-old. I felt a lot of pressure from my parents to aim for perfect grades. Then a letter arrived from India; it was a letter from Ramanujan’s widow. She wrote a letter to my father, one of approximately 80 mathematicians around the world who contributed for a bronze bust of Ramanujan that was given to her as a gift. That was when I first learned about Ramanujan. My father told me about the enigmatic Indian genius who had inspired the world’s leading mathematicians. Ramanujan turned out to be a two-time college dropout. I gained strength and hope from the knowledge that one did not need to be a prototypical straight A-s student to succeed.
Ramanujan also offers a glorious example of the fact that talent and potential is often found in the most unpromising of circumstances. This is a lesson that we can all learn from. What if Ramanujan had not reached out to Hardy? Or, what if Hardy ignored him? This would have resulted in a future that I would not be able to absorb. Therefore, I have come to understand the important role we have as mentors and teachers. We must locate and then nurture talent. The future of the world depends on it.
2. Of all of Ramanujan’s mathematical works, which or which ones do you think are most important and will be most important in the future, and which are the most underrated?
Ramanujan left behind thousands of formulas, and so it is extremely difficult to assemble a ‘best hits’ list. Therefore, I prefer to offer general commentary. Ramanujan gave birth to probabilistic number theory, the
subject that would later be perfected by the Hungarian genius Paul Erdos. Ramanujan’s work on theta functions offer prototypes of many fundamental themes in mathematics. These include the proof of Fermat’s Last Theorem, the Langlands Program, and the theory of Monstrous Moonshine and its applications to String Theory. Ramanujan was perhaps the most influential maestro of infinite power series. He was a wizard with the number theory of partitions, and his identities form the foundation of the theory of basic hypergeometric series. Finally, Ramanujan’s invention of the ‘circle method’ with Hardy can be thought of as the analytic number theory analog of the invention of the wheel.
3. From your own life story and your reading of Ramanujan’s life, what have you learnt about the way we look at mathematics?
Ramanujan left behind glimpses of many theories among the thousands of unproved formulas and expressions that can be found in his unpublished notebooks. We will never know his methodology. I have no idea of how he arrived at his findings. Frankly, I cannot dispute the claim that his ideas came to him as visions from his family Hindu goddess. This is how mysterious his notebooks are. I think of Ramanujan as a gift to mathematics.
We have the advantage of Ramanujan’s notes, and our task is to find the deeper theories suggested by the examples he left behind. I would love to have had his insight. Frankly, I would love to know how he looked at mathematics. The answer would probably propel mathematics decades forward.
4. Why is mathematics so alluring for some and yet so difficult even today for so many people? Is it the way people are taught mathematics? How would you do it better? How would Ramanujan have done it better?
I don’t wish to complain about the current state of education. Instead, let’s begin by noting that there are many problems with education. Teachers are overworked. Teachers are expected to prepare students for standardized tests. Teachers are underpaid. And I could continue with a litany of other problems. Students of mathematics typically come to view mathematics as the stuff of long and boring problem sets.
I don’t have a solution. I wish I did. Instead, I have to say that mathematics is a subject which really begins after the subjects which are typically taught after K-12 coursework (i.e. pre-college). Mathematics is about ideas, and I regret that most students don’t ever get to take courses where we focus on these skills. If I could, I would reorganize pre-college education so that students are introduced to ideas and core theoretical concepts. This question is particularly relevant in Ramanujan’s case. Ramanujan was almost lost to the world. He was a victim of an inelastic educational system. Frankly, it is a miracle that he was discovered. I struggle with the thought of all of the Ramanujans that we have lost because of such inelasticity.
5. From your own life story and your reading of Ramanujan’s life, what have you learnt about the way we look at the notion of success and life?
Ramanujan matters for many reasons. His ideas have powered the mathematics of his future, and his ideas have been put to use in real world applications. Ramanujan also matters because he represents the fact that talent is often found in the most unpromising of circumstances. We must take steps to locate this talent in the world, and then we must take steps to properly nurture without being encumbered by an inelastic educational system.