Somehow tonite while I was taking a bath I got to thinking about the following question: If I were invited to give a series of exactly 10 one hour talks on "The Great Ideas in Mathematics" what would be the ten individual titles? I really don't know how it came to mind, but here's my answer:

1. Mathematical Proof
2. Abstract Variables
3. Induction
4. Coordinate Geometry
5. The Calculus
6. Complex Numbers
7. Modulo Equivalence
8. Local/Global
9. Geometry as Functions
10. Category Theory

It was hard to leave out the Euler zeta function from that list, but hey, I was only invited to give 10.

It's strange just how different in kind many of those topics are from each other. One of those topics (1) is about what mathematics means. Two of them are just about advances in language (2 and 10). Two of them are connections between different branches of mathematics (4 and 9). One of them is just an object (6).

Anyway, if any of you ever want to invite me to give such a lecture series, I at least have the titles now...