The Stanford University Mathematical Organization recently began a speaker series. The goal of the series is to let students listen to professors discuss their backgrounds and research, as well as to let students hear some interesting problems or ideas.
"At first glance the stuff of partitions seems like child's play:
4 = 3 + 1 = 2 + 2 = 2 + 1 + 1 = 1 + 1 + 1 + 1.
Therefore, there are 5 partitions of the number 4. But (as happens in Number Theory) the seemingly simple business of counting the ways to break a number into parts leads quickly to some difficult and beautiful problems. Partitions play important roles in such diverse areas of mathematics such as Combinatorics, Lie Theory, Representation Theory, Mathematical Physics, and the theory of Special Functions, but we shall concentrate here on their role in Number Theory. We shall give an account of the impact of Leonhard Euler, Freeman Dyson and Srinivasa Ramanujan on the subject, and describe some of the recent advances in the subject."
