Wednesday, August 22, 2012

Bill Thurston, RiP

I first met him in 1979, when he gave a talk on the proof of the Smith Conjecture somewhere on the Upper West Side. Man, oh man, was he a towering figure in those days (and for decades after that). Now melanoma got him. Here are some of his musings on mathematics.


Arelcao Akleos said...

Crud. He was not old enough to consider this so "natural".

Mr roT said...

Sad indeed. Melanoma is not easy to beat, I hear.

Arelcao Akleos said...

"And we all go with them, into the silent funeral,
Nobody's funeral, for there is no one to bury.
I said to my soul, be still, and let the dark come upon you
Which shall be the darkness of God."

Eliot, 4 Quartets.

A. Leverkuhn said...

I really enjoyed reading Thurston's beneficent note on proof and progress. At some point he makes an academic case of a view of Obama's which has (deservedly ?) taken quite a bit of heat here on FCP:

in sound and fury,
A. Leverkühn ;)

" If what we are accomplishing is advancing human
understanding of mathematics, then we would be much better off recognizing and
valuing a far broader range of activity. The people who see the way to proving the-
orems are doing it in the context of a mathematical community; they are not doing
it on their own. They depend on understanding of mathematics that they glean
from other mathematicians. Once a theorem has been proven, the mathematical
community depends on the social network to distribute the ideas to people who
might use them further—the print medium is far too obscure and cumbersome. "

Tecumseh said...

Interesting parallel, Leverkühn. But note: Thurston doesn't make the case that "you didn't prove that theorem", because you stood on the shoulders of accumulated wisdom, and pushed the boundaries a bit, or because you depended on others to provide you with pad and pen or chalk and board.

What he says is, you depend on others to appreciate that theorem, and advertise it. It's a far more subtle case, and much more accurate than the crass "you didn't build that" case.

A. Leverkuhn said...

I think he's saying the dependence goes beyond just communal appreciation and dissemination --- that, indeed, the understanding itself is 'gleaned' from society. Newton also makes this kind of confession (which I think Herr Rott is quoting every once and a while). It may well be a matter of degree, but the sentiment is still pretty close to our beloved leader's take: That individual progess of this kind is the manifestation of collective effort and zeitgeist.

A. Leverkühn

Mr roT said...

I do not know what I may appear to the world, but to myself I seem to have been only like a boy playing on the sea-shore, and diverting myself in now and then finding a smoother pebble or a prettier shell than ordinary, whilst the great ocean of truth lay all undiscovered before me.

Gots the presicunt's mind and heart all over it, eh? You didn't build those laws of motion, you colonialist sissyboy. The shiny little sequins did.

Tecumseh said...

I know Mr Rot will sneer (I can picture that in my mind!), but this is not a black and white issue, there are shades of gray. The way math (and more generally, science and technology) advances is complicated, and highly non-linear. There are steady periods of incremental advances, verification, implementation, consolidation -- heck, even steps backward, when you hit a wall, or things fall apart -- followed by sudden bursts of genius that leapfrog ahead.

I'm not at all a connoisseur of classical music, but isn't this a bit how an opera also works, or certain symphonies or concertos? You can't have all cymbals and full-throated arias all the time, you need some intermezzos and adagios along the way, no? Time for the audience to digest, sort of?

OK, OK, a strained analogy, for sure. I probably threw a softball for Mr Rot to whack it over the Green Monster.

Mr roT said...

Mutual admiration societies are nonlinear.