Music Of The Spheres

I just learned that geometrist and Field medal-winner William Thurston passed away on Tuesday. I've never really got geometry.  Not the applications, of course, which are clear, varied and important.  Nor even the attraction, I suppose - I remember clearly the first time I learned of the Pythagorean Theorem, and just being blown away by the idea that mathematics could demonstrate such a thing; everything I'd learned up to that point being either intuitively obvious or simple enough to verify.

But I never really understood why anyone would dedicate their career to it.  Of course, probability is just the most mathematically rigorous way possible to fail to predict the future, so it's not like my choice is necessarily any better.  And looking at what Thurston achieved, it's hard to fault his choice.  Anyone who gets so good in a given field that everyone else stays away from it in case he solves the whole shebang before they've gotten a chance to play is worthy of some considerable respect (though I wish "Thurston's Monster Theorem" involved fewer closed hyperbolic 3-manifolds, and more minotaurs).

Plus, on top of everything, his work was interesting enough to inspire Grigori Perelman, the charmingly lunatic Russian geometrist who solved the Poincare Conjecture - which even I'd heard of - leading to him also being awarded the Field Medal, though he refused to accept it.