### math, wisdom teeth

I got my wisdom teeth removed today. I was looking forward to being put under, since I've never done that before. When they stuck the needle in my vein I concentrated intently. Nothing... nothing... and then next thing I know I'm opening my eyes and two hours have gone by. There was no intermediate stage at all; you go from alert to unconscious in seconds. I guess I was hoping it would be more like when you're falling asleep but not quite asleep yet and you have these bizarre stream-of-consciousness dreams.

My mouth's all numb but other than that, feeling pretty good. They gave me percoset, which (according to erowid) is stronger than vicodin. Ideally I won't be needing it, because what's the fun of painkillers if you *need* them?

I've been meaning to write something here about my recent obsession with math. It's unclear what's brought on this sudden mania, but here's a partial list of books I've been reading (with various degrees of comprehension):

*The Honor's Class - Hilbert's Problems and Their Solvers*

*Prime Obsession - Bernard Riemann and the Greatest Unsolved Problem in Mathematics*

*Algebraic Number Theory and Fermat's Last Theorem*

*Differential Topology: First Steps*

*Everything and More: A Compact History of Infinity*

*The Millennium Problems: The Seven Greatest Unsolved Mathematical Puzzles of Our Time*

There's an interesting article in some back issue of *The Believer* where the author discusses how often mountaineering/rock climbing metaphors are used to describe math problems. He claims that this stems from the fact that math problems and mountains are both prototypical challenges, where a challenge needs to meet some or all of the following criteria:

- The challenge is difficult
- The challenge is dangerous
- It is unambiguous whether you've succeeded in the challenge
- Personal virtues help you succeed in the challenge
- The challenge is undertaken for its own sake

The danger part is the only dicey comparison, but "in popular accounts, math is about as hazardous to the mind as a solo ascent of K2 is to the body. [The books and play]

*A Beautiful Mind*and

*Proof*both feature deranged mathematicians as main characters; in the movie

*Pi*and the novel

*Presumed Innocent*, the crazy mathematicians are explicitly made so by their mathematical frustrations." In

*Everything and More*, David Foster Wallace comments aptly on this: "The Math Melodrama's own allegorical template appears to be more classically Tragic, its hero a kind of Prometheus-Icarus figure whose high-altitude genius is also hubris and Fatal Flaw. If this sounds a bit grandiose, well, it is; but it's also a fair description of the way Math Melodramas characterize the project of pure math-- as nothing less than the mortal quest for Divine Truth."

Of all the books I've been reading, *Algebraic Number Theory* is the toughest and most purely mathematical. It's a textbook, basically, but to really dive into it you have to have an understanding of abstract algebra (groups, rings, fields, modules), which is turning out to be a hard thing to teach myself. Modern math is so unbelievably abstract. Numbers don't really have a lot to do with abstract algebra; they're just a particular case of this much broader class of objects that obey certain properties. My dim intuition is no help here, nor is recourse to memorization of definitions. I struggle on because like poetry, these formulas are a compact distillation of deep and beautiful ideas. Unlike poetry, the formulas are grounded in rigor and logic. I think for that reason I prefer them. If free verse is like "playing tennis without the net", then poetry in general is like that with respect to mathematics. I like the constraints imposed by math; the creativity that blossoms within those constraints appeals to me more than the lesser constraints of meter and rhyme. n-dimensional space, different sizes of infinity, undecidable problems... there are more things in this philosophy than are dreamt of in heaven and earth.