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.

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**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.

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**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.

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**IP**: What was your research topic?

**AG**: Fermat's last theorem. This was before Andrew Wiles's proof.

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**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.

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**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.

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**IP**: Has your move to Montreal shifted the direction of your research?

**AG**: Montreal is a very interesting place to do mathematics.

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**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.

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**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.

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**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.

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**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.

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**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.

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**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.

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**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.

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Read about Andrew Granville's Carriage House lecture.