We’ll start with a puzzle, taken from Hofstader’s Godel, Escher, Bach. In this puzzle, we are going to learn to speak in a restricted language. We will be talking about integers, so our variables will always stand for integers. We have available to us...

A few results 1 (Bjorner, Eidelman and Ziegler) Suppose we have a finite collection of great circles on a sphere, none of them through the north or nouth pole. Let be the set of regions in the complement of these circles, and suppose that every...

Here’s a nice little story about quantum mechanics, which surprisingly few mathematicians seem to know about. The essential idea is “quantum mechanics on the projective space looks remarkably like classical mechanics”! Everything I say here comes from...

This post is based on a conversation I had with Allan Adams at Mathcamp a few summers ago, and I was reminded of it by an aside in Mike Freedman’s talk in Scott’s backyard on Friday. As usual with blog posts based on other people’s talks, all good...

I am coming to the point in my career where I will be expected to take graduate students, and I’d like some advice about finding problems for them. How responsible am I for making sure that a problem is solvable and not already under attack elsewhere?...