Cam Stewart

The art of mathematics

Open questions in number theory have been examined over the centuries by people like Euclid, Fermat and Gauss. The community of mathematicians working in this field look for ways to push forward and make progress on proving, or refuting open questions. Number theorists like Cam Stewart study questions examining the additive and multiplicative structures of integers and the distribution of prime numbers. Recently Cam has done work on the distribution of primes.

Prime numbers are the building blocks of all integers. So every integer can be decomposed in a unique way into a product of primes. (For instance, 12=2x3x2.) There are an infinite number of primes irregularly spaced among the integers. “Primes have a distinct distribution,” explains Cam. “What one can prove is that there are long intervals with fewer primes than you’d expect if the primes were distributed randomly. Why this occurs is a basic open question and one of the puzzling facts that makes the primes special.”

Cam derives satisfaction from trying to understand these basic, important questions. In describing number theory, Cam clearly expresses his appreciation of the natural mystery and history of study. He uses words like ’powerful’, ‘deep’ and ‘elegant’ to express an admiration of the ideas contributed by other number theorists. “There’s a lot of art to it. There’s an aesthetic sense of what is beautiful mathematics that most mathematicians have, and while it’s difficult to describe what beautiful mathematics is, it’s easy to recognize.”

University of Waterloo Mathematics, Annual Report 2005