A mathematician is like a tiny dog....

...with a huge bone in its mouth, trying to get through a tiny hole in a wall. When attempting a proof for the first time, that is. And hopefully, you try and you try, turn your head one way , then the other, hit the bone in all manner of ways against the edges of the hole, and eventually - somehow end up on the other side of the hole, but have no idea how it happened. You cannot explain it or repeat it. What you proved is true, because there you are on the other side - but why and how?

This is a story Miklos, one of my professors, told us this morning in Spectral Theory. We also had a hilarious moment (this is the inquiry-based learning class, so starting quite soon, Miklos will probably never talk at all, as we are supposed to figure stuff out and show each other at the board for the most part) when I was presenting a "proof" at the board, but a proof about graph theory. I've never heard a graph theory lecture in my life, and all I knew was what was on our homework sheet given the night before. And I understood the proof but had no idea how to write down a graph theory proof ('graphs' in this sense are dots and lines between dots. That's all. No x-y stuff, just actually a bunch of points and lines ((though we call them vertices and edges)) - they don't exist in any particular space. Just - dots and lines. Kinda hard to think of how to describe them!).

In any case, part of the point of this class is learning how to present well at the board, which is something that I've actually had a lot of practice with. But in this area, I had no idea! (In fact, my practice may prove to be not very helpful - Miklos was saying today we might have a day when you aren't allowed to speak at all while at the board, and have to make yourself understood through your writing alone. I love explaining math, so that's tricky, but I know I'll figure it out if the time comes! After all, that's what my proofs on paper are supposed to be anyway, since I can't stand there and explain it to the professor while he/she grades my exam)

So, after explaining this not really too complicated but kind of fun graph theory problem, all I had written on the board was 7*3=21, which no one could argue with, but it was hilarious that that was my entire 'proof'. We had a good laugh about it. This class should be fun.

I'm just digesting my notes from Algebraic Topology on Tuesday, getting ready for the second lecture in an hour. This hellish week is almost over. It's been hellish but also awesome - and I'm ready for a bit of sleep and calm math-ing, not dashing from place to place.

Also, my apartment got a bit of a rearrangement and now has a large, hanging pad of huge paper for me to do work on - not a whiteboard, but close enough. Pictures soon.