7 ms·

Alexander Grothendieck

FrankWilhoit 2y ago
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.
- deleted 2y ago
  [deleted]
- effed3 2y ago
  agree, forgotten genius AND lonely madman, there is no contradiction.. In mathematics, and science, these people are not uncommon.
  - ValentinA23 2y ago
    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 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 2y ago
      This text is a short story ("nouvelle" in French).
      - ilya_m 2y ago
        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 https://www.fermentmagazine.org/quest88.
    - webdoodle 2y ago
      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 2y ago
        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 2y ago
      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.
    - amy-petrik-214 2y ago
ballooney 2y ago
I shall choose to remember him in his prime.
- bifftastic 2y ago
  57
  - ysofunny 2y ago
    sorry, that's not a prime because 3*19
    - cyberlimerence 2y ago
      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 https://en.wikipedia.org/wiki/57_(number)#In_mathematics
      - ysofunny 2y ago
        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
        deleted 2y ago
        [deleted]
Jevon23 2y ago
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 2y ago
  Right? It's baffling.
  - seanhunter 2y ago
    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 2y ago
      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 2y ago
      Wasn't Newton a mystic too? Yes, he was [1]. [1] https://en.wikipedia.org/wiki/Isaac_Newton%27s_occult_studies https://en.wikipedia.org/wiki/Isaac_Newton%27s_occult_studie...
    - throwaway81523 2y ago
      He left IHÉS around 1970 but he stayed active in math, and he kept working as a math professor and later at the CNRS (French research institute). https://en.wikipedia.org/wiki/Alexander_Grothendieck#Manuscripts_written_in_the_1980s https://en.wikipedia.org/wiki/Alexander_Grothendieck#Manuscr...
AIorNot 2y ago
‘ 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 2y ago
  There is nothing esoteric about topos theory, it is a formally defined concept: https://en.wikipedia.org/wiki/Topos https://en.wikipedia.org/wiki/Topos Thought it was important to state this, as Grothendieck also wrote rather esoteric texts, Récoltes et Semailles as well as La Clé des Songes, which haven't been translated or even published.
  - hackandthink 2y ago
    Récoltes et Semailles is translated, e.g. the mathematical stuff: https://tongchow.github.io/ReSII.pdf https://tongchow.github.io/ReSII.pdf
- deleted 2y ago
  [deleted]
soVeryTired 2y ago
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 2y ago
  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-tesla-130000001.html https://finance.yahoo.com/news/vinod-khosla-betting-former-t...
  - bubblyworld 2y ago
    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 https://arxiv.org/abs/2402.15332
    - cc-color 2y ago
      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 2y ago
        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.
        2y ago
enlightenedfool 2y ago
“ 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 2y ago
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-the-circular-ruins/ https://planetofstorms.wordpress.com/2021/03/30/the-man-of-t...
romankolpak 2y ago
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 2y ago
https://en.wikipedia.org/wiki/Alexander_Grothendieck https://en.wikipedia.org/wiki/Alexander_Grothendieck
lapinot 2y ago
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 https://www.youtube.com/watch?v=V8BbFTEyvIw [2] https://github.com/Lapin0t/grothendieck-cern https://github.com/Lapin0t/grothendieck-cern

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.

deleted 2y ago
[deleted]
effed3 2y ago
agree, forgotten genius AND lonely madman, there is no contradiction.. In mathematics, and science, these people are not uncommon.
- ValentinA23 2y ago
  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 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 2y ago
    This text is a short story ("nouvelle" in French).
    - ilya_m 2y ago
      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 https://www.fermentmagazine.org/quest88.
  - webdoodle 2y ago
    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 2y ago
      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 2y ago
    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.
  - amy-petrik-214 2y ago

ballooney 2y ago

I shall choose to remember him in his prime.

bifftastic 2y ago
57
- ysofunny 2y ago
  sorry, that's not a prime because 3*19
  - cyberlimerence 2y ago
    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 https://en.wikipedia.org/wiki/57_(number)#In_mathematics
    - ysofunny 2y ago
      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
      - deleted 2y ago
        [deleted]

Jevon23 2y ago

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 2y ago
Right? It's baffling.
- seanhunter 2y ago
  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 2y ago
    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 2y ago
    Wasn't Newton a mystic too? Yes, he was [1]. [1] https://en.wikipedia.org/wiki/Isaac_Newton%27s_occult_studies https://en.wikipedia.org/wiki/Isaac_Newton%27s_occult_studie...
  - throwaway81523 2y ago
    He left IHÉS around 1970 but he stayed active in math, and he kept working as a math professor and later at the CNRS (French research institute). https://en.wikipedia.org/wiki/Alexander_Grothendieck#Manuscripts_written_in_the_1980s https://en.wikipedia.org/wiki/Alexander_Grothendieck#Manuscr...

AIorNot 2y ago

‘ 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 2y ago
There is nothing esoteric about topos theory, it is a formally defined concept: https://en.wikipedia.org/wiki/Topos https://en.wikipedia.org/wiki/Topos Thought it was important to state this, as Grothendieck also wrote rather esoteric texts, Récoltes et Semailles as well as La Clé des Songes, which haven't been translated or even published.
- hackandthink 2y ago
  Récoltes et Semailles is translated, e.g. the mathematical stuff: https://tongchow.github.io/ReSII.pdf https://tongchow.github.io/ReSII.pdf
deleted 2y ago
[deleted]

soVeryTired 2y ago

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 2y ago
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-tesla-130000001.html https://finance.yahoo.com/news/vinod-khosla-betting-former-t...
- bubblyworld 2y ago
  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 https://arxiv.org/abs/2402.15332
  - cc-color 2y ago
    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 2y ago
      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.
      - 2y ago

enlightenedfool 2y ago

“ 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 2y ago

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-the-circular-ruins/ https://planetofstorms.wordpress.com/2021/03/30/the-man-of-t...

romankolpak 2y ago

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 2y ago

https://en.wikipedia.org/wiki/Alexander_Grothendieck https://en.wikipedia.org/wiki/Alexander_Grothendieck

lapinot 2y ago

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 https://www.youtube.com/watch?v=V8BbFTEyvIw [2] https://github.com/Lapin0t/grothendieck-cern https://github.com/Lapin0t/grothendieck-cern