Hello everybuddy!

My name is Paul and I will be your friend. I’ve written a few things about myself on my about page. I would like to use this space to talk about things I like — math mostly, but also books and movies and cool ideas. Though I’m not very good at it, I like to analyze songs and books and stuff and I think this will be nice practice. As I said, I’m new to blogging and so I’d imagine the look of this place will change a lot until I get settled in.

A few words about the mathematical content. I was mostly inspired to this by John Armstrong’s excellent blog, which has covered a lot of territory in explaining math to the “Generally Interested Lay Audience.” I’ll start with pretty basic stuff and work up; since he starts with groups, I think I’ll start with topology, though I’ll probably end up covering a lot of algebra as well. If you don’t like my exposition, please read his! He knows a lot more than me and is a good writer as well.

I offer you The Following Promises:

- I will have a considerably freeform approach to my math discussion. In particular, if I read a cool paper or learn a cool idea in class, I’ll consider changing tacks in order to teach my readers about it. If a reader asks me to discuss something, I will do my best to do so.
- I will also try to keep the math discussion readable. This means that I’ll start with elementary concepts and work up (and we’re going to cover some cool, higher math eventually). If you’ve done high school calculus, you should be good — and again, if you ask me to explain something, I will. Of course, the best way to learn is by doing. I am not particularly good at writing exercises, but I’ll definitely link to books with good exercises and discussion.
- Likewise, I’ll link to direct prerequisites in new posts, so you know where to go to learn what you’re missing.
- I will never call my writing here “musings.”
- Math is a very beautiful and underappreciated art, and I think of it as an art first and foremost. Even if you’re not initially interested, I hope to attract you to some part of it. This isn’t really a promise, but what the hell.
- Oh, I’ll try to end each math post with a cool example — something that made me really appreciate the theory I’m explaining. Conversely, my writing process will probably be to write until I reach a cool example. This is a good and a bad thing.
- Above all else, I want this to be a blog of ideas. This means not only the process of math but its philosophy and the reasons we think the way we do. It means not only analysis of ideas but discussion. I welcome comments and commenters and really want to hear what you all have to say.

Long first post. Tomorrow, I’ll get started!