[HN Gopher] Alexander Grothendieck
___________________________________________________________________
Alexander Grothendieck
Author : cyberlimerence
Score : 77 points
Date : 2024-08-31 10:24 UTC (12 hours ago)
(HTM) web link (www.theguardian.com)
(TXT) w3m dump (www.theguardian.com)
| FrankWilhoit wrote:
| Suppose he were both. Then do we need to distinguish between
| them? If so, would it be possible to make that distinction? If
| not, can we afford to need to make it? This applies to all
| incomprehensibly gifted persons.
| effed3 wrote:
| agree, forgotten genius AND lonely madman, there is no
| contradiction.. In mathematics, and science, these people are
| not uncommon.
| ValentinA23 wrote:
| The root cause for his departure from mathematics was his
| categorical refusal to let the military-industrial complex
| invest in his research at Bures-sur-Yvette.
|
| Source: https://www.jp-petit.org/Nouvelles/Grothendieck.htm
|
| - I know the story. He was a man viscerally opposed to
| militarism. He once said "he'd rather be shot than wear a
| uniform." One day a letter arrived at IHES in Bures, where
| the army's scientific services, called DRET at the time
| (Direction of Research and Technical Studies), now DGA
| (Delegation for Armament Applications), offered a grant of
| four thousand francs (650 euros). When he came across this
| paper, he flushed red, saying "No way we're accepting a penny
| from these people!" His colleagues tried to change his mind:
| "Listen, Alexandre, don't be so rigid. It'll pay for
| photocopies..."
|
| - And then?
|
| - He said, "It's not difficult, we'll put it to a vote. The
| IHES scientific council will decide whether or not to accept
| money from the soldiery. But if you accept this grant, I
| solemnly warn you: you'll have my resignation in your hands
| within the minute that follows."
|
| - And what happened?
|
| - They didn't take his threat seriously. The vote took place
| and the four thousand francs were accepted by a majority of
| one vote. His face then turned grey, hard as marble. He took
| a letterhead paper and simply wrote: "I have the honor to
| tender my resignation" then handed it to the council members
| and turned on his heel. The next day he didn't show up at his
| office, nor the day after. Paperwork began to pile up. There
| were letters from all over the world.
|
| - He was a Fields Medal winner.
|
| - His reputation was such that he attracted the greatest
| mathematicians on the planet to the Institute. For everyone,
| he was the beacon of Algebraic Geometry, illuminating the
| entire planet with all its light. At first, people thought it
| was depression or a disappearance. At IHES, he occupied an
| official apartment. After a week, they ended up calling a
| locksmith to open the door. The apartment was empty. Masses
| of his papers were found in a trash can. He had thrown
| everything away, his notes, his books, his reports, his
| correspondence.
|
| - Incredible! ...
|
| - Wait, weeks and months passed without anyone knowing where
| he had gone. You can't imagine the panic at the Institute.
| Scientists started calling from all corners of the world.
| They had to answer and admit that he had resigned. People
| wanted to know why he had acted this way, under what
| circumstances this had happened, where he had gone, what he
| was doing now. The most unbelievable rumors were circulating.
| At one point, they thought he had committed suicide, but as
| some people had met him, they had to face the facts: he was
| apparently still alive. We have a letter from him dated two
| years after his resignation from IHES addressed to a company
| providing organic fertilizers, where he complains that these
| do not meet the specified standards. It was indeed his
| signature and, it must be said, his style.
|
| - And since then?
|
| - Since then, nothing. The world's greatest mathematician
| simply vanished one fine day. He simply let the scientific
| community know that he wanted nothing more to do with this
| environment. He announced, through a letter he addressed to
| one of his former students, his decision to withdraw
| completely. As people had finally located him in this small
| village near Carpentras where he had rented a small farm,
| they hoped to flush him out by offering him a new prize, the
| Crafoord Foundation prize. This must have been in the early
| eighties. The amount was around forty million francs.
| af78 wrote:
| This text is a short story ("nouvelle" in French).
| ilya_m wrote:
| That's correct! The text is presented on the source web
| page as a story, and it does not claim to be factual.
|
| Alexander Grothendieck was indeed awarded the Crafoord
| Prize, which he rejected. (It was never worth 40 mil
| francs as the translation above claims. The original
| French put it at "40 briques" = 400,000, currency not
| specified, which is much closer to the more accurate 800K
| SEK ~ 800K FFr that he would have received. The fact that
| the full amount, 1,6M SEK, would be split between him and
| Pierre Deligne, whom Grothendieck had denounced, might
| have contributed to his decision.) Grothendieck's
| rejection letter was remarkably lucid and articulate:
| https://www.fermentmagazine.org/quest88.
| webdoodle wrote:
| Fantastic! In this money driven world, he had the courage
| to stand up for what he believed in. Also, I seriously
| doubt he was considered crazy, that was the war time
| propaganda trying to break him down and make an example of
| him, so that others wouldn't stand up. It's the same thing
| we see today with the coercion and censorship that plaques
| social and old school media.
| karmakurtisaani wrote:
| I feel like it was more like his experiences from WW2
| formed a very rigid world view about militaries. Arguing
| for pacificism is difficult as the Ukraine war rages on.
| FrankWilhoit wrote:
| The background of this particular case is interesting, but
| the larger point is that what we call "genius" is a matter
| of priorities. From some angle, every gifted person appears
| mad.
| ballooney wrote:
| I shall choose to remember him in his prime.
| bifftastic wrote:
| 57
| ysofunny wrote:
| sorry, that's not a prime because 3*19
| cyberlimerence wrote:
| It's a joke.
|
| "Although fifty-seven is not prime, it is jokingly known as
| the Grothendieck prime after a legend according to which
| the mathematician Alexander Grothendieck supposedly gave it
| as an example of a particular prime number." [1]
|
| [1]
| https://en.wikipedia.org/wiki/57_(number)#In_mathematics
| ysofunny wrote:
| it's surrounded by 53 and 59 which is a twin with 61 then
| 67
|
| but the fun part is how the same happens to these four
| numbers -30
|
| so 23, 29 twin with 31 then 37
|
| my problem is that I don't know why this would be
| important
| Jevon23 wrote:
| Nothing forgotten about him. His work is foundational to modern
| algebraic geometry and there's no mathematician who doesn't know
| who he is.
| mjd wrote:
| Right? It's baffling.
| seanhunter wrote:
| The title is specifically referring to a possible
| reassessment of his later, quasi-mystical writings, post
| retirement from mathematics in 1970.
|
| It's a bit too long for the HN title submission but the
| actual article title in the Guardian is
|
| " 'He was in mystic delirium': was this hermit mathematician
| a forgotten genius whose ideas could transform AI - or a
| lonely madman?"
| Yeul wrote:
| Why not both? Crazy people can be smart. As for mystic
| delirium well that's our modern sensibilities talking. Hell
| there are people today who believe in Marian apparitions.
| wslh wrote:
| Wasn't Newton a mystic too? Yes, he was [1].
|
| [1] https://en.wikipedia.org/wiki/Isaac_Newton%27s_occult_s
| tudie...
| AIorNot wrote:
| ' And there is growing academic and corporate attention to how
| Grothendieckian concepts could be practically applied for
| technological ends. Chinese telecoms giant Huawei believes his
| esoteric concept of the topos could be key to building the next
| generation of AI, and has hired Fields medal-winner Laurent
| Lafforgue to explore this subject. But Grothendieck's motivations
| were not worldly ones, as his former colleague Pierre Cartier
| understood. "Even in his mathematical milieu, he wasn't quite a
| member of the family," writes Cartier. "He pursued a kind of
| monologue, or rather a dialogue with mathematics and God, which
| to him were one and the same."
|
| Never heard of him before, RIP but this reads like the beginning
| of neal stephenson novel... interesting
| ValentinA23 wrote:
| There is nothing esoteric about topos theory, it is a formally
| defined concept: https://en.wikipedia.org/wiki/Topos
|
| Thought it was important to state this, as Grothendieck also
| wrote rather esoteric texts, Recoltes et Semailles as well as
| La Cle des Songes, which haven't been translated or even
| published.
| hackandthink wrote:
| Recoltes et Semailles is translated, e.g. the mathematical
| stuff:
|
| https://tongchow.github.io/ReSII.pdf
| soVeryTired wrote:
| The AI angle is weird, and a red herring. I'll happily give 100
| to 1 odds that something as abstract as topos theory isn't useful
| to machine learning. As far as I know, the full weight of topos
| theory isn't even needed for algebraic geometry.
|
| The story of Grothendieck is a tragedy about a generational
| genius, not unlike Godel's story. It's deep and far reaching
| enough to stand on its own without AI hype making it appear more
| relevant.
| gremgoth wrote:
| The folks at Symbolica are also applying topos theory, category
| theory, etc to AI, backed by serious folks such as Khosla and
| Wolfram. https://finance.yahoo.com/news/vinod-khosla-betting-
| former-t...
| bubblyworld wrote:
| I was sure this was going to be a case of spraying jargon at
| investors, but they've actually produced an interesting paper
| in this direction (in collaboration with some DeepMind
| people): https://arxiv.org/abs/2402.15332
| cc-color wrote:
| this paper is not good: it's easy to describe things in a
| categorical language (which this paper does), but not as
| easy to draw insights from that framework (which this paper
| does not do)
| whatshisface wrote:
| It is rarely within reach to draw new insights from
| applied category theory, in particular because of the
| Yoneda lemma and the greater familiarity of sets and
| functions, and also because as algebraic objects
| categories have very few properties.
| karmakurtisaani wrote:
| Classic application of abstract math in something sexy at
| the time. I once saw a paper describing a trading
| strategy using stochastic calculus. Turns out it boiled
| down to buying when price went under some indicator
| variable, selling when above another.
| whatshisface wrote:
| Stochastic calculus is the only available tool for
| proving things about continuous-time stochastic
| processes. There aren't any alternatives, save guessing
| at criteria and backtesting them.
| karmakurtisaani wrote:
| Yes, for sure useful for the appropriate mathematics. My
| point is, the trading strategy was a simple heuristic
| wrapped into overly complicated definitions and proofs.
| The complicated mathematics added exactly nothing to the
| application.
| catgary wrote:
| I think the point was they (probably) used the abstract
| math to prove some desirable properties about the trading
| strategy?
| karmakurtisaani wrote:
| Yes, it was something like that. But "desirable" here
| means something very different for mathematicians and
| traders actually applying the strategy (I.e., they don't
| care at all, and neither does anyone else working in
| finance).
| downvotetruth wrote:
| <Doob rolls over in his grave>ugh</s>
| catgary wrote:
| I was definitely on a group chat of ML/category theory
| people roasting this paper when it came out, I'm sure I
| wasn't the only one.
| catgary wrote:
| Ehh, I'm an ML scientist with a PhD in category theory and
| I really don't see it going anywhere. The comparison to
| geometric deep learning is especially misplaced, because I
| think you'll find that Bronstein's school sets things us as
| a group action, etc, but then does a lot of really hard
| math to actually tease out properties of how information
| flows through a gnn. Here they just do the Applied Category
| Thing and say they've drawn a picture so QED.
| catgary wrote:
| "A new kind of deep learning."
|
| Edit: I need to think more before I comment, "A new kind of
| data science" was right there.
| fjdjshsh wrote:
| Wolfram is serious about his software, but, to my mind, has
| been closer to a crackpot scientist than a real researcher
| the last few decades. Him backing something up diminishes my
| subjective probability that this is something "serious"
| enlightenedfool wrote:
| " he rarely made use of specific equations to grasp at
| mathematical truths, instead intuiting the broader conceptual
| structure around them to make them surrender their solutions all
| at once."
|
| Something that caught my attention recalling Arthur
| Schopenhauer's philosophy on the need for conceptual or apriori
| knowledge based proofs than empirical or derived in math.
| frereubu wrote:
| This is, in my view, a better article about Grothendieck that's
| less sensationalist (particularly the guff about AI):
| https://planetofstorms.wordpress.com/2021/03/30/the-man-of-t...
| romankolpak wrote:
| The stories of geniuses suffering from depression and other
| mental illnesses sure make remarkably interesting reads. It's a
| pity he didn't get psychiatric help, this could have been a
| boring story of an aging scientist taking care of his plants.
| toomuchtodo wrote:
| https://en.wikipedia.org/wiki/Alexander_Grothendieck
| lapinot wrote:
| Always infuriating to see that people always focus on the his
| pre-70s (hardcore math) or post-80s period (borderline mysticism
| ramp up). In the 70s he was most politically active and
| _definitely_ not delirious in any sense of the word and in fact
| according to Leila Schneps this is one of the few periods of his
| life he described as happy, the "sunday of his life" [1]. I
| translated the '72 CERN talk, its baffling how relevant it is, to
| this day [2].
|
| [1] french, https://www.youtube.com/watch?v=V8BbFTEyvIw
|
| [2] https://github.com/Lapin0t/grothendieck-cern
___________________________________________________________________
(page generated 2024-08-31 23:02 UTC)