Comments on: The Art of Mumford

By: Jacob Freeze

Jacob Freeze — Tue, 20 Jan 2009 14:47:55 +0000

Although it may not be as useful as those inky squiggles that gave so many people their first glimmer of understanding schemes, some recent artwork by David Mumford and his collaborators, under the general title of "Indra's Pearls," is worth a detour here, here, here, and here, and there's even a whole batch of movies here.

By: James

James — Tue, 30 Dec 2008 03:32:32 +0000

Dear Sir,

With the seeming demise of the blog of Lieven Le Bruyn, I feel I am left with nowhere else to turn… I am not a mathematician - however, usually in most areas I have some clue about what is involved, what the aims may be, what the basic concepts are, the important results that are proved, and the the conjectures yet to be proved… etc

But I find this not to be the case with algebraic geometry…

If I have mis-pegged your maths area then I’m sorry. Otherwise, what the hell are schemes, ideals, motives, etc? And why do they matter?

Yours, stacked on an ideal variety of sheafs…

By: notedscholar

notedscholar — Wed, 24 Dec 2008 22:09:51 +0000

I agree that it’s confusing. Unfortunately I am also highly skeptical of the ability of 2d representationalism to explain this concept.

By: Jonathan Lubin

Jonathan Lubin — Mon, 22 Dec 2008 18:20:29 +0000

I met David when I was a senior in high school—he’s a year or two younger than me. I thought then that he was the smartest person I had ever met, and I’ve never had reason to modify that opinion. In grad school, everybody was in awe of him, thinking of him I guess as belonging to a different species from us.
Anyhow, I bought the Red Book when it came out, and had it for many years, but it’s not on the shelf here, which either means that somebody borrowed it and never returned it (good), or that I left it with the Brown Library when I retired (better).

By: Walt

Walt — Sun, 21 Dec 2008 17:41:42 +0000

I don’t think there’s any way in which it can’t seem exotic the first time you learn it. When I first understood what the scheme corresponding to R[x] looked like, it was a sensation that can only be accurately rendered in stoner patois: “Wow, that blows my mind, man.”

By: estraven

estraven — Sun, 21 Dec 2008 17:37:58 +0000

I find it kind of funny that this stuff still needs explaining and counts as “new and exotic” at age 40+. Funny and sad. I would compare the idea of schemes with the particle/wave duality; unexpected, hard to digest, but incredibly fruitful.

This said, of course (re)reading Mumford is always a good idea. Any Mumford, for whatever reason. Almost as good as (re)reading Grothendieck, that is :-).