Alexander Grothendieck
November 13, 2014 7:56 PM   Subscribe

Alexander Grothendieck, who brought much of contemporary mathematics into being with the force of his uncompromising vision, is dead at 86, some twenty-five years after leaving academic mathematics and retreating into a spiritual seclusion in the countryside. "As if summoned from the void," a two-part account of Grothendieck's life, from the Notices of the American Math Society: part I, part II.

"Most mathematicians take refuge within a specific conceptual framework, in a “Universe” which seemingly has been fixed for all time – basically the one they encountered “ready-made” at the time when they did their studies. They may be compared to the heirs of a beautiful and capacious mansion in which all the installations and interior decorating have already been done, with its living-rooms , its kitchens, its studios, its cookery and cutlery, with everything in short, one needs to make or cook whatever one wishes. How this mansion has been constructed, laboriously over generations, and how and why this or that tool has been invented (as opposed to others which were not), why the rooms are disposed in just this fashion and not another – these are the kinds of questions which the heirs don’t dream of asking . It’s their “Universe”, it’s been given once and for all! It impresses one by virtue of its greatness, (even though one rarely makes the tour of all the rooms) yet at the same time by its familiarity, and, above all, with its immutability.....

I consider myself to be in the distinguished line of mathematicians whose spontaneous and joyful vocation it has been to be ceaseless building new mansions." (quoted in a memorial blog post by Steven Landsburg.)

"A country of which nothing is known but the name": Pierre Cartier remembers Grothendieck.

"Did earlier ideas influence Grothendieck?" Frans Oort traces the origins of Grothendieck's revolutionary way of approaching mathematics, and asks: did he really never work examples? (This one is a bit more technical than the others.)

"The Grothendieck-Serre correspondence": Leila Schneps reflects on the decades-long exchange of letters between Grothendieck and Jean-Pierre Serre.

Much more Grothendieckiana can be found at The Grothendieck Circle.
posted by escabeche (33 comments total) 45 users marked this as a favorite
posted by clavdivs at 8:47 PM on November 13, 2014

posted by wjzeng at 8:54 PM on November 13, 2014

posted by Quilford at 9:02 PM on November 13, 2014 [4 favorites]

Today I am no longer, as I once was, the prisoner of interminable tasks, which so often prevented me from leaping into the unknown, mathematical or otherwise. The time of tasks for me is over. If age has brought me anything, it is lightness.

- Alexandre Grothendieck, Esquisse d’un Programme

Towards the bearable lightness of non-being...

posted by wjzeng at 9:04 PM on November 13, 2014 [4 favorites]

posted by eruonna at 9:12 PM on November 13, 2014

posted by Vibrissae at 9:20 PM on November 13, 2014

posted by solitary dancer at 9:20 PM on November 13, 2014

posted by a lungful of dragon at 9:47 PM on November 13, 2014

Much better Related Post than the ones that appear here - Who is Alexander Grothendieck?
posted by unliteral at 9:51 PM on November 13, 2014 [1 favorite]

Very few people outside mathematics have ever heard of him, but among mathematicians it is incredible the impression he left.
posted by mgalka at 10:45 PM on November 13, 2014 [2 favorites]

Lately I've been wishing there were a math appreciation class I could take, analogous to a music appreciation class.
posted by ssr_of_V at 12:04 AM on November 14, 2014 [5 favorites]

posted by chneukirchen at 12:44 AM on November 14, 2014

Lately I've been wishing there were a math appreciation class I could take, analogous to a music appreciation class.

Grothendieckiana is kind of like a mathematical version of 12-tone music, with attendant aesthetico-political problems. it takes a certain discipline to appreciate it.
posted by at 12:50 AM on November 14, 2014 [1 favorite]

posted by Wordshore at 1:14 AM on November 14, 2014

Interesting quotations in the y-combinator obit thread on Grothendieck.
posted by jeffburdges at 1:16 AM on November 14, 2014

posted by Anything at 2:48 AM on November 14, 2014

This is why I love MetaFilter: on which other site would you find an obituary of Grothendieck in between a mashup of the Wu-Tang Clan and Final Fantasy and a discussion of surgery and tailoring?

posted by narain at 2:49 AM on November 14, 2014

There is an interesting 2012 article (in French) on his evolution since the 1970's.

He was still doing mathematics in the early 1990's, although he did not publish anything at that time.
posted by Phersu at 3:05 AM on November 14, 2014

posted by madcaptenor at 5:15 AM on November 14, 2014 [2 favorites]

posted by LizBoBiz at 6:38 AM on November 14, 2014

Grothendieck was a shibboleth when studying math and mentioned in hushed, almost religious terms. A person with his passion, uncompromising ethics, and tragic personal life seems too mythical to exist in this generation.

When reading about his contributions, it wavers from handwavy ("the relative point of view", "pre-Socratic thinking") to technically forbidding definitions ("etale cohomology", "motives"). The Bourbaki style of thousands of pages of category theory are very austere.

Algebraic geometers of Metafilter, is there a way to explain Grothendieck's philosophy to, say, a first-year level graduate student in pure math? Can/Does such a book exist or is the level of background knowledge/abstraction too high?
posted by bodywithoutorgans at 8:40 AM on November 14, 2014

posted by JoeXIII007 at 9:31 AM on November 14, 2014


> is there a way to explain Grothendieck's philosophy to, say, a first-year level graduate student in pure math? Can/Does such a book exist or is the level of background knowledge/abstraction too high?

From escabeche's (@JSEllenberg) twitter feed, a link to his own explanation:
For non-mathematicians: my attempt to give some sense of (a tiny part) of Grothendieck's work is in sec 3 of
posted by Westringia F. at 9:59 AM on November 14, 2014 [2 favorites]

There's an illuminating passage in the Frans Oort article (escabeche's third link):
(1.2).6. See [10], p. 203. Grothendieck wrote on 3-5.10.1964: “...est-il connu si la fonction ζ de Riemann a une infinité de zéros?”
On which Serre later made the comment: “... Grothendieck ne s’est jamais intéressé à la
théories analytiques des nombres.” See [10], p. 277.
Interest in the "fonction ζ de Riemann" in 1964 wasn't what it is now, but perhaps this example indicates just how minimal (yet crucial, according to Oort) the dependence of Grothendieck's work on ground-level mathematical facts is, and certainly provides context for the delightful 'Grothendieck prime' story.
posted by jamjam at 12:49 PM on November 14, 2014

□ → □
↓   ↓
□ → ■
posted by Wolfdog at 1:27 PM on November 14, 2014 [5 favorites]

Algebraic geometers of Metafilter, is there a way to explain Grothendieck's philosophy to, say, a first-year level graduate student in pure math? Can/Does such a book exist or is the level of background knowledge/abstraction too high?

For whatever it's worth (I'm not an algebraic geometer), my entire exposure to EGA was my second year of grad school and found it fairly readable or at least sometimes rather illuminating relative to Hartshorne. (I think there are some exercises in Hartshorne that require you to find (or invent) some lemma from EGA, so there's a big "Ohhh... so that's what's going on" component to my experience of EGA.)
posted by hoyland at 6:06 AM on November 15, 2014 [1 favorite]

posted by Tau Wedel at 1:35 PM on November 15, 2014

I'm the son of an Algebraic Geometer. While I must say that while Grothendieck's NY Times obit caught my interest, I don't recall my father mentioning his name. My father's thesis advisor Mumford is mentioned in this excerpt from the Grothendieck-Serre correspondence, though.
posted by larrybob at 10:11 PM on November 15, 2014

posted by LobsterMitten at 12:07 AM on November 16, 2014

I'm the son of an Algebraic Geometer.
"What is... Jimmy Buffet's least-loved song, Alex?"

posted by Wolfdog at 8:37 AM on November 16, 2014 [3 favorites]

huh, despite comparisons with perelman...
The curriculum vitae Grothendieck submitted plainly showed that he intended to give up mathematics to focus on tasks he believed to be far more urgent: “the imperatives of survival and the promotion of a stable and humane order on our planet.” (pp. 1201-1202)
maybe grothendieck is kinda a bit more like baez then (or perhaps more accurately vice versa ;) who gave up concentrating on quantum gravity [at least exclusively: 0,1,2,3 :] to work on helping save the planet using category theory?

like survivre et vivre looks interesting; have they been translated? and i wonder what he'd have thought of the azimuth project?

speaking of which, here's baez on the stacks project :P
Starting in the 1950s, Alexander Grothendieck revolutionized math by introducing many new concepts: schemes, stacks, motives, topoi and more. He wrote over 6000 pages! And then, after many quarrels with the mathematical establishment of France, he disappeared into the Pyrenees, where he now lives in seclusion.

The Stacks Project is an open-source reference book with many authors which aims to explain a lot of the math Grothendieck and his collaborators created. It's currently 4000 pages long! You can download it as a single huge PDF file... but much better, you can read it on the web, and see how each result relies on previous ones!
also btw...
-Letter from Grothendieck
-A mad day's work from Grothendieck to Connes and Kontsevich: The evolution of concepts of space and symmetry
-John Baez on Research Tactics
Grothendieck came along and gave us a new dream of what homotopy types might actually be. Very roughly, he realized that they should show up naturally if we think of “equality” as a process—the process of proving two thing are the same—rather than a static relationship.

I’m being pretty vague here, but I want to emphasize that this was a very fundamental discovery with widespread consequences, not a narrow technical thing.

For a long time people have struggled to make Grothendieck’s dream precise. I was involved in that myself for a while. But in the last 5 years or so, a guy named Voevodsky made a lot of progress by showing us how to redo the foundations of mathematics so that instead of treating equality as a mere relationship, it’s a kind of process. This new approach gives an alternative to set theory, where we use homotopy types right from the start as the basic objects of mathematics, instead of sets. It will take about a century for the effects of this discovery to percolate through all of math.

So, you see, by taking something important but rather technical, like algebraic topology, and refusing to be content with treating it as a bunch of recipes to be memorized, you can dig down into deep truths. But it takes great persistence. Even if you don’t discover these truths yourself, but merely learn them, you have to keep simplifying and unifying.
-Advice for the Young Scientist: "As Grothendieck put it..."
In our acquisition of knowledge of the Universe (whether mathematical or otherwise) that which renovates the quest is nothing more nor less than complete innocence. It is in this state of complete innocence that we receive everything from the moment of our birth. Although so often the object of our contempt and of our private fears, it is always in us. It alone can unite humility with boldness so as to allow us to penetrate to the heart of things, or allow things to enter us and taken possession of us.

This unique power is in no way a privilege given to "exceptional talents" - persons of incredible brain power (for example), who are better able to manipulate, with dexterity and ease, an enormous mass of data, ideas and specialized skills. Such gifts are undeniably valuable, and certainly worthy of envy from those who (like myself) were not so "endowed at birth, far beyond the ordinary".

Yet it is not these gifts, nor the most determined ambition combined with irresistible will-power, that enables one to surmount the "invisible yet formidable boundaries" that encircle our universe. Only innocence can surmount them, which mere knowledge doesn't even take into account, in those moments when we find ourselves able to listen to things, totally and intensely absorbed in child's play.
-Dessins d'enfants
-"While Grothendieck may seem a bit like Neal Cassidy figure, he was also an incredible workhorse in his prime. Even later, his 600-page letter to Daniel Quillen in 1972 helped trigger what's likely to be the biggest revolution in 21st-century mathematics - the theory of n-categories."
posted by kliuless at 9:41 AM on November 16, 2014 [3 favorites]

posted by klausness at 2:43 PM on November 23, 2014

Interesting kliuless, thanks for that perspective. And the analogy with John Baez. I've some reading to do now. :)
posted by jeffburdges at 2:19 AM on November 25, 2014

« Older The 3-6 Chambers   |   The craft of surgery Newer »

This thread has been archived and is closed to new comments