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Mathematician Don Zagier

23/03/2022 - Trieste

Mathematician Don Zagier, Emeritus Scientific Member and Director at the Max Planck Institute for Mathematics, has been named the first holder of ICTP's newly-established Ramanujan International Chair.

Zagier, who first visited ICTP more than 10 years ago, has built over the years strong connections with the Centre as a Distinguished Staff Associate, and collaborated on numerous research papers with ICTP scientists, both within and outside the Mathematics section. In addition to his ICTP affiliation, Zagier is a distinguished affiliated member of the Trieste-based Institute for Geometry and Physics, run jointly by ICTP and SISSA. Zagier recently gave a lecture during ICTP's Ramanujan Day celebrations (watch on ICTP's YouTube channel). Pictures are available here.

A number theorist who has also done work in topology, algebraic geometry, and mathematical physics, he has served as a professor in Germany while simultaneously holding a second chair at the University of Maryland in the United States, then at the University of Utrecht in the Netherlands, and finally at the Collège de France. An American by birth who completed his undergraduate degrees in mathematics and physics at MIT at the age of 16 and defended his doctorate in Oxford at 20, he is a truly international mathematician.

In an interview with ICTP, Professor Zagier shared his impressions regarding the nomination and his continuing and stable connection with ICTP.

**How do you feel about your nomination as the first holder of the Ramanujan chair? How is this important for your relationship with ICTP?**

This nomination has two aspects: the fact that it is a chair and the fact that it is named after Ramanujan. For the Chair part, well, I've had chairs before. The exciting part for me is the fact that it is a chair at the ICTP. I have been part of ICTP since 2014, and I already felt like a member of the ICTP family, but now I feel that I am really part of the team. So if there are things that are important to the Centre, like, for example, working with least developed countries, which has been its mission for over 50 years, I would love to be part of that. That's why I originally started collaborating with ICTP in 2014, rather than going somewhere else. When I visited the Centre the first time, I liked so much what I saw that I really wanted to join it. And now I feel that with this new position I have become part of it in some more serious sense.

**And what do you think about the fact that the chair is named after Ramanujan?**

Well, it's not quite like there has been a Ramanujan chair for centuries and I'm the most recent person who holds it, like it happens in Oxford, for example, where you can have illustrious predecessors, or terrible ones. In this case, the chair was a new one. The name of Ramanujan was partially picked, I think, because it suits me and I was to be the first holder of this mathematics chair. Ramanujan was a number theorist like me, so I think it was a good choice. In any case, he's one of my big heroes, and I have given many lectures about his work. We also have in common the fact of preferring a very particular kind of mathematics: we both love calculating complicated formulae and find them very beautiful. I'm quite good at finding nice formulae, and so was Ramanujan. But that's kind of like saying that I play the piano, and so did Mozart: Ramanujan was not just good at this, but was some kind of a Da Vinci of formulae!

As a mathematician, I feel very close to Ramanujan's spirit. I of course also do some theory after my calculations just to make other people happy, but what always makes me happiest is an unexpected and beautiful formula.

**Has Ramanujan always been a hero to you since you started studying or did you discover him later?**

I started studying mathematics at a very young age. At 14, I spent one year in England in Winchester private school. By coincidence, this was the same school which Hardy, the man who later brought Ramanujan to England, went to. But he absolutely hated it, because it was so elitist and snobbish, whereas I kind of liked it because it was such an amazing experience for an American boy to be in a school that was from the 13th century. It was like being in an Harry Potter movie!

There was a mathematical competition there and I got a first prize. This prize was one book, and that book was Hardy's "Introduction to the theory of numbers". And that's how I became a number theorist. In that book, of course, many of Ramanujan's formulas are mentioned because he had worked with Hardy and was so important to him. So Ramanujan has been huge on my horizon at least since I was a teenager, and is really meaningful to me.

**Have you "encountered" Ramanujan again later in your work?**

Yes, often. I once gave a very appreciated lecture called "From the first letter to the last", where I chose Ramanujan's first letter to Hardy, when he wrote to introduce himself, and the last one, when he was back in India and was already about to die, and I told the story in between.

In a short article of mine, called "On an approximate identity of Ramanujan", I discuss a formula from Ramanujan's famous *"Lost Notebooks"*. These notebooks were actually not lost at all, but had merely disappeared from view, and were only found many years later by George Andrews. Then he and Bruce Berndt (both friends of mine) spent years editing them, adding proofs, and publishing them. It's a mammoth work of 6 volumes, maybe 2000 pages in total. Many of the formulae in the notebooks, with no proof, were not clear to any modern mathematician, some turned out to be very difficult to prove, and a few are probably still mysterious. My article gave a formal proof of one of them.

**Are you inspired by the figure of Ramanujan in your work?**

He's like my kindred spirit. My other kindred spirit, of course just in the style, certainly not in level, is Euler. The way he did mathematics is the way I would like to do mathematics! The one I like the least from this point view is Gauss. He was an incredible snob, he would write a paper without explaining anything, knowing that only a tiny elite could read it and understand it.

On the other hand Euler, unlike Gauss but also unlike Ramanujan, was very pedagogic. He wrote a fantastic number of papers. He wrote and wrote and wrote. When he had an idea, he explained that idea. And if the idea didn't work, he would explain *why* it didn't work. He was not afraid of extra words. Even 150 years after Euler, all mathematicians in Europe still learned their mathematics from him. He explained even the wrong ideas, whilst Gauss wanted to be sure never to make a mistake. And that's certainly not my goal! As a teacher, I'd like to be like Euler and explain also the wrong things. Of course, Ramanujan never held any teaching position, so I am inspired by him as a mathematician, and by Euler as a teacher.

**Did you always want to be a mathematician?**

Actually, my first publication was in physics. I thought I could be a good physicist, because at school I had good grades and I thought that being good in mathematics would be a big advantage in physics. But I soon realized that I was cheating. Every problem I encountered, I would think how to translate it into purely mathematical terms. And my next step was to forget the physics entirely, work with pure mathematics, and at the end translate it back to physics. So I realized: "Who are you kidding, you're not a physicist, you have no feeling for the physical world. You're a theoretical mathematician." But I did love physics, and I still do.

**Do you think your new position at ICTP will bring you closer to physics?**

Yes, one of the reasons why I started collaborating with ICTP and its scientists was the "P" in the name. I really want to learn more about the many fields of theoretical physics studied at ICTP, like what I did for the paper I published with Matteo Marsili from the Quantitative Life Sciences section. Next, I want to learn more about integrable systems, for example, but also string theory, statistical mechanics, and more quantum field theory. So for me, the main excitement of this new position is going in the direction of learning more about unfamiliar fields.

*--Marina Menga*