Mathematics and Statistics Colloquium
Fernando Gouvêa, Colby College
What is Number Theory?
Monday, September 23, 2019, 4:00 PM, Davis 301
Refreshments at 3:30 PM, Davis 2nd floor
The name of a part of mathematics seldom tells outsiders much about the actual nature of that subject. “Number Theory” seems particularly obscure, perhaps because most people associate all of mathematics with numbers. Even to insiders, it can be hard to explain why certain questions fit into “Number Theory” rather than into other parts of mathematics.
Rather than try to define Number Theory, this talk seeks to consider a range of examples. We will start with a very old problem about whole numbers and demonstrate several different ways to solve it. Each solution will suggest new questions, some of which will turn out to be very difficult. We may even run into some problems that remained unsolved.
This talk is aimed at students. High school algebra is enough to understand most of it.