Andrew Granville is the Canadian Research Chair in number theory at the Université de Montréal. He specializes in analytic number theory and properties of prime numbers. Granville is a graduate of Trinity College, University of Cambridge. He obtained his doctorate at Queen's University, Kingston, Ontario. In 1989-91, he was a member of the Institute for Advanced Study, Princeton. Before coming to Montreal in 2002, he was a professor at the University of Georgia.
Granville's recent research has centered on the (mathematical) notion of "pretentiousness." He has won three MAA writing awards: The 2008 Chauvenet Prize for the article "It Is Easy to Determine Whether a Given Integer is Prime," published in the January 2005 Bulletin of the American Mathematical Society; the 2007 Lester R. Ford Award (with Greg Martin) for "Prime Number Races," published in the January 2006 American Mathematical Monthly, and the 1995 Merten M. Hasse Prize for "Zaphod Beeblebrox's Brain and the Fifty-ninth Row of Pascal's Triangle," published in the April 1992 American Mathematical Monthly.
Ivars Peterson: Were you interested in mathematics at an early age?
Andrew Granville: I enjoyed playing with figures as a small child. In Britain, one of the main sports is cricket, which involves a lot of statistics. I was always interested in that—and still am. That was the starting point. At school, I did well in math.
IP: When you went to university, did you know you were going to go into math at that point?
AG: At school, I excelled at two things: mathematics and history.
IP: You ended up doing graduate school in Canada.
AG: I did a year of graduate school in England. I read a book by Paulo Ribenboim, a Brazilian number theorist who works at Queen's University in Kingston, Ontario. He's a wonderful writer, just delightful.
IP: What was your research topic?
AG: Fermat's last theorem. This was before Andrew Wiles's proof.
IP: Was the computational work you did in connection with Fermat's last theorem something new and you were learning as you went along, or was that already an interest?
AG: I had these criteria that I had proved theoretically, and I wanted to do a calculation, and it couldn't be done.
IP: After Queen's University, you did a post-doc at the University of Toronto, spent two years at the Institute for Advanced Study, then taught at the University of Georgia.
AG: I did my Ph.D., and like many people, waited a long time until I got a nibble for a job. I went to do a post-doc with John Friedlander at the University of Toronto. I was doing my Ph.D. in algebraic number theory, but John is an analytic number theorist. So that seemed like a great opportunity to somewhat change my direction.
IP: Has your move to Montreal shifted the direction of your research?
AG: Montreal is a very interesting place to do mathematics.
IP: You've won three MAA writing awards. How important is writing to you?
AG: It's developed over my career. I went to be Paulo Ribenboim's doctoral student because of the way he wrote a book. He loves to write. He has written many books, some more serious than others.
IP: You wrote a newspaper article about Andrew Wiles and his announcement of his proof of Fermat's last theorem.
AG: I was actually there when Andrew Wiles gave his famous lecture where he announced his proof.
IP: What are you focusing on now in your research?
AG: I've been having a wonderful time for the last few years with a mathematician named Soundararajan, who's at Stanford. We've been developing a notion in the theory of multiplicative functions, which we call pretentiousness.
IP: You have also shown an interest in random matrix theory and its link to the Riemann hypothesis, another case of links between seemingly unconnected pieces of mathematics.
AG: Random matrices are a wonderful subject.
IP: You seem to be continuing to work on topics such as the quadratic sieve factoring algorithm.
AG: Arjun Lenstra, who is one of the top computing people in the quadratic sieve area, ran some experiments for me.
IP: Where do you see yourself, say, 10 years from now.
AG: It's hard to know, but there are various research areas that I enjoy.
IP: Tell me about the unusual writing project—a mathematical detective story—that you’re working on.
AG: My sister is a film writer—she writes for Hollywood—and we're doing this together.