I’m not sure what this post set out to be. It ended up a digression on set theory vs. category theory. In modern mathematics, there are two notions that might be truly called foundational to all the work we do. These are set theory and category theory. Both theories are living, evolving things with their specialists, constructions and interesting problems, just like any other field of math, but the core ideas are familiar and useful to nearly every mathematician.

You know the sensation where a familiar word becomes suddenly completely strange for no apparent reason? Like suddenly the scales fall away from your eyes and you see how utterly weird it is that a concept has a particular name? I’ve been having that feeling with the word graph as I use it in math. As a kid, you learn how to graph simple functions in the sense of being able to sketch them on a sheet of, say, graph paper.

Earlier this week, Marc Weidenbaum of disquiet.com wrote a paean to the blog that I found really inspiring. “Self-publishing,” he writes, “is the heart of the healthy internet.” So hello. Having been given the push I needed, I decided to move my academic website to its own URL and use it as an excuse to start blogging. Since much of the rest of this website is given over to my career as a mathematician, it’s reasonable to expect that I will talk about math here, and I expect to get technical with it when I want to.