8 ms·

The Anarchist Abstractionist – Who Was Alexander Grothendieck?

141 points by jorgenveisdal 7y ago

einpoklum 7y ago
Quick point: His parents were Anarchists - in the workers'-movement, anti-Capitalist, revolutionary sense, Groethendieck wasn't. Or rather, his activities did not involve Anarchist organizing/politics. Also, in the summary, where it says "discovered a proof of the Lebesgue measure" - that's obviously nonsensical, he (re-)developed the Lebesgue measure himself, without being aware of Lebesgue's work. Or so it says; I don't know whether he actually focused on non-Riemann-measurable sets etc.
- mikorym 7y ago
  I also think one should be careful not to make it seem like he was part of any kind of political scene. He did write some texts outside of mathematics that could be seen as anarchist in the apolitical sense, for example the "Survivre" text. It's in French, so I don't know the exact contents, but I think it's like a sort of survival guide. But hey, we all have hobbies; one shouldn't read to much into the pasttimes of people, especially of people who rose to prominence not based on their pasttimes.
  - wfn 7y ago
    > anarchist in the apolitical sense Hm. But how is the founding of Survivre (a political group publishing antimilitary etc. texts) and serving as its editor apolitical?
    - Melting_Harps 7y ago
      It isn't, and this is the vocal anti-anarchist contingent voicing their POV as fact when in reality he had stepped down from IHES after he realized his work was being funded by the French Military [1] in some Academic-Military collusion and couldn't continue any longer--not unlike DARPA has with MIT in modern times. He had a greater regard and estimation in his colleagues and Academia as a whole that turned out to be false as none followed him in protest and he then dedicated his Life to Environmentalism. He even shunned his Field's medal and rejected all the awards that followed. He, like many other Anarchists, felt that the State's continual and expansionist military activity needlessly contributes to the haphazard and headlong demise of the World's Ecology--which threatens all of Life on Earth--and wrote at great length about it. And sees the State as an imminent threat to Humanity as it accelerates our demise as a Species. I learned about Grothendieck's amazing Life and his work upon his death in 2014 (a month or 2 after Hal Finney died) in a very defining period of my Life, not just as an anarchist myself but as a Human and this article's final paragraph summed up what I think he wanted to be remembered the most as it was a Life well lived.: The man who had advanced mathematics in the most profound ways did not believe that math was the answer to everything. He taught us that life is more valuable than any equation. 1: https://www.nytimes.com/2014/11/25/science/the-lives-of-alexander-grothendieck-a-mathematical-visionary.html https://www.nytimes.com/2014/11/25/science/the-lives-of-alex...
      - wfn 7y ago
        Thanks for the comment. ...yeah. All this also reminded me of the story when he gave lectures on category theory in the forests near Hanoi when it was being bombed...
    - mikorym 7y ago
      I don't regard being antimilitary as being political at all. Maybe the working definition of politics is different, but if you are not involved in a political party that tries to exercise influence and prescription to others, then I would call one apolitical. In the same way, many Soviet intellectuals that were against their government still referred to themselves as apolitical.
      - wfn 7y ago
        Hm, that seems to be a rather peculiar and particular interpretation of the term. Grassroots organisations, political activist movements of all kinds would then fall outside your criterion. I mean... Women's suffrage movement (which changed the definition of who can vote in the first place), civil rights movement, etc. would also fall outwith your definition of the notion. (edit) The political processes which culminated in the French, the 1917 communist revolutions, etc... I don't see a point in defining the term in that way at all.
        bmelton 7y ago
        I'm sort of down for it. "I don't like cats" is a fairly apolitical statement, that is until such point as political parties start taking stances on cats and arguing in favor of who subsidizes what kinds of feline activities. I have many beliefs that I regard as accidentally political - which is to say that I believe these things regardless of whether or which politicians happen to agree, or what their political affiliations are, or how closely tied their affiliations are to mine. It doesn't particularly matter to me whether others regard those beliefs as political or not, but it seems that we're approaching an era in which anything and everything can be deemed 'political' in some way merely because parties choose to take positions on them, and that may be completely at odds with how an individual may have come to conclusions on their own.
        wfn 7y ago
        I think I see what you mean, maybe there is a need to differentiate (individual conclusions "on their own", though there'd be arguments in favour of viewing those as political as well, etc.) But perhaps not at the expense of the term "political" (but rather introduction of some other term). Because it's simply not the case that something is necessarily apolitical "until such point as political parties start taking stances on cats". Some revolutions, changes in political regime, etc. happened not via the process of already existing political establishment systems (of which parliamentary parties is a mere (and not necessary (being descriptive here, not prescriptive)) subset of) accepting / incorporating / etc. some views at all (rather the exact opposite, say). Also, "I don't like cats" is a sort of easy example to use here, but if you take e.g. "domestic violence should not happen", where do you draw the line in terms of when it becomes political (let's say you start a grassroots network where victims of domestic violence can support each other, and gradually build political capital, and so on)... That said, differentiation along your lines is maybe useful, but severely redefining the scope of the term "political" seems a weird way to go about it.
- EthanHeilman 7y ago
  >His parents were Anarchists - in the workers'-movement, anti-Capitalist, revolutionary sense, Groethendieck wasn't. I'm not a Groethendieck scholar but I did read a short biography of him and it definitely left me with the impression that he was an anarchist or left-libertarian in the anti-Capitalist, liberty, revolutionary sense. What are your sources to back up the claim that he wasn't? >is activities did not involve Anarchist organizing/politics. In Groethendieck's "The Responsibility of the Scientist Today [0] he writes: "Thus the proliferation of military power and stocks of weapons throughout the world poses an ever-increasing danger not only to our species, but also to life in general. This predicament, unparalleled in the long history of biological evolution, must be met with immediate radical action." He directly calls for political organization and radical action. Edit: I don't object to getting voted down, but I would encourage anyone downvoting a comment on hackernews to provide their rational. This helps improve the quality of the discussion. [0] "The Responsibility of the Scientist Today" (translated from French) http://ccnr.org/grothendieck.pdf" http://ccnr.org/grothendieck.pdf"
  - Melting_Harps 7y ago
    I'm not sure why you're being downvoted, thanks for the link, I've bookmarked it for later reading. Was that short bio 'La Clef des Songes,' I heard it was translated into Spanish, but never looked to deep for it. People really should be forced to refute before they can downvote. Even if you disagree with his points, he gives substance for what and why he said what he did.
    - EthanHeilman 7y ago
      The short biography was "The Artist and the Mathematician: The Story of Nicolas Bourbaki, the Genius Mathematician Who Never Existed" [0]. It dedicates a good chunk of the book to the life of Grothendieck. Grothendieck was a member of the group that used the Nicolas Bourbaki pseudonym. It's a fun read you can finish in an afternoon. Not sure how accurate it is. [0]: https://www.goodreads.com/book/show/208933.The_Artist_and_the_Mathematician https://www.goodreads.com/book/show/208933.The_Artist_and_th...
  - sudosysgen 7y ago
- danharaj 7y ago
  You think he went to lecture in Hanoi in the middle of the Vietnam war for shiggles?
  - einpoklum 7y ago
    Being against the Vietnam war doesn't make you an Anarchist (although naturally anti-Imperialism is in line with Anarchism). I didn't say Grohtendiek didn't have any political opinions.
stareatgoats 7y ago
An interesting, and sad story: that such a beautiful mind ended up with paranoia. It seems to be a real danger that many geniuses run, maybe in part (pardon the speculation) because they tend to work too hard: "Grothendieck was working on the foundations of algebraic geometry seven days a week, twelve hours a day, for ten years". That has to take a toll.
- ur-whale 7y ago
  > that such a beautiful mind ended up with paranoia. there's certainly a pattern here, that people that walk the edge of what a human brain can do often drift to paranoia and/or extremism. I'm thinking: Bobby Fischer, Grigory Perelman, Évariste Galois, and to a certain extent, Isaac Newton. I suspect the list is a lot longer.
  - jorgenveisdal 7y ago
    Galois - shot in duel. Turing - committed suicide by cyanide-laced apple. Boltzmann - committed suicide while on vacation. Gödel - died from starvation and exhaustion. Cantor - died from starvation in an insane asylum. Ramanujan - died from malnutrition. de Moivre - predicted the day of his death by calculating his sleep cycle. Lie - became insane and attacked his friends. Erdös - did amphetamines all his life. Nash - was legally insane for 30 years. Perelman - refuses contact with anyone except his mother. Grothendieck - refused contact with anyone. Kaczynski - serving a life sentence in maximum security prison.
    - selimthegrim 7y ago
      Rananujan had a digestive issue IIRC
      - selimthegrim 7y ago
        *Ramanujan
    - hope-striker 7y ago
colinhb 7y ago
This biographical sketch is well-written, concise, and complete (or at least it appears to be). It includes many quotes and photos that I hadn’t seen before. But I can imagine that some readers will be left wondering what was so remarkable about this guy’s work. Unfortunately, it’s hard to explain without some exposure to pure mathematics. David Mumford, who pops up in this article, has a lengthy blog post[1] on this exact problem, stemming from his experience writing Grothendieck’s obituary for Nature. It’s an interesting read if you have some math background. In any case, I think the New York Times obituary by Edward Frenkel[2] does a nice job of giving a taste of his work to a lay audience (by tackling the problem of defining Grothendieck’s schemes, just like Mumford did). [1] http://www.dam.brown.edu/people/mumford/blog/2014/Grothendieck.html http://www.dam.brown.edu/people/mumford/blog/2014/Grothendie... [2] https://www.nytimes.com/2014/11/25/science/the-lives-of-alexander-grothendieck-a-mathematical-visionary.html https://www.nytimes.com/2014/11/25/science/the-lives-of-alex...
- mikorym 7y ago
  And for the more nonlay audience, Grothendieck's real pull is the persistence with which he applied category theoretic techniques successfully. Usually one would qualify this to algebraic geometry, but I think his approach can be followed in any of the many extensive fields in mathematics. I would contrast this to what often happens in the physics community, albeit not in a condescending manner, where techniques diverge rather than converge. In fact, I would guess this is the role that Einstein played a hundred years ago: to encourage sensible connections between researchers' work.
  - nabla9 7y ago
    Grothendieck's relative point of view https://en.wikipedia.org/wiki/Grothendieck%27s_relative_point_of_view https://en.wikipedia.org/wiki/Grothendieck%27s_relative_poin...
    - mikorym 7y ago
      Linked to via two degrees is this: https://en.wikipedia.org/wiki/Grothendieck%E2%80%93Riemann%E2%80%93Roch_theorem#/media/File:Grothendieck-Riemann-Roch.jpg https://en.wikipedia.org/wiki/Grothendieck%E2%80%93Riemann%E.... I don't know German, but it would be really interesting to know what the text says.
mathandpoop 7y ago
You seem to have put quite an extensive amount of biographical research into this. I have never seen these photos in this high quality on the internet before. As a maths person and a bit of a Grothendieck fan, thanks!
- jorgenveisdal 7y ago
  Thanks a lot! Indeed, high res photos of Grothendieck are quite hard to come by
papeda 7y ago
I read a few articles about Grothendieck when he died, but I still learned a lot from this one. Those articles usually skipped over his early years as some version of anarchy. This one better fills in those gaps. For example, I didn't realize how haphazard Grothendieck's early professional progress was, or that it depended on an interview with a French education official who recognized unorthodox talent: > “Instead of a meeting of twenty minutes, he went on for two hours explaining to me how he had reconstructed, ‘with the tools available’, theories that had taken decades to construct. He showed an extraordinary sagacity.” It reminds me of Ramanujan, another exceptionally gifted and devoted mathematician who acquired most of his education on his own, and was very nearly lost to history but for the efforts of a few well-connected officials who could see his potential. Conversely, what a bummer it is to think of similar talents who didn't get so lucky. It also gets at just how much the culture of math education matters to math students, even ones like Grothendieck: > [Grothendieck] felt free to ask questions, but also found himself “struggling to learn things that those around him seemed to grasp instantly […] like they had known them from the cradle”. The contrast lead Grothendieck to eventually leave Paris, in October of 1949 on the advice of Cartan and Weil who recommended he instead travel to Nancy to work with Schwartz and Dieudonné on functional analysis. And this was a guy whose internal mathematical drive was strong enough to independently discover measure theory as a teenager! Then there are all the other "failures" absent from a short biographical blurb: he finished his PhD "with few prospects for employment after his graduation in 1953", then "planned to write a book on topological vector spaces, but it never materialized", spent a year failing to solve the "approximation problem", despaired that the field of his thesis was "dead", pivoted away from analysis, rest is history, etc.
drummer 7y ago
The name grothendieck sounds a lot like big dick. Like bigus dickus in monthy pythons life of brian. Groot means big in dutch.
_hardwaregeek 7y ago
A few months ago, I stumbled upon an antique store in Paris where the owner had thousands of notes taken from Grothendieck's house after he died. Apparently he was in charge of appraising them. Which is pretty stunning since Grothendieck didn't publish anything for the last few decades of his life, so it's quite possible there's new math there. Anyways the guy described how Grothendieck's house didn't have a roof and was pretty decrepit. Which made me pretty sad. One of the greatest mathematicians of the 20th century dying alone in a house with no roof. Part of me wonders if maybe, had he gotten proper mental health care, Grothendieck could have enjoyed a longer, more healthy career. Or career aside, could he have just had a better life? In the mathematical community it feels like there's a bit of an acceptance of idiosyncrasies bordering on potential mental health issues. Well I say acceptance but really it's bordering on willful ignorance. How many advisors give their doctoral students advice on mental health? How many advisors themselves received training on mental health? It's worth analyzing.
- jorgenveisdal 7y ago
  Absolutely. Check out my essays on Wiener and Oppenheimer. Many of the same tendencies, though with better outcomes
mhartl 7y ago
I recently enjoyed listening to this interview with someone who knew Grothendieck. It takes a while to get going, but some of the stories are quite gripping. https://youtu.be/L--9bJApz_A https://youtu.be/L--9bJApz_A
- mhartl 7y ago
  The article mentions Jean-Pierre Serre, with whom Grothendieck corresponded extensively, and Pierre Deligne, widely regarded as Grothendieck’s greatest student. While investigating Grothendieck recently (inspired by the interview linked in the parent comment), I came across this astonishing anecdote, relating a comment by Serre about Deligne [1]: “Look, I can take on anyone in Math.” — don’t forget, this guy [Serre] is the youngest Fields medal winner ever, the first Abel prize laureate, etc. — “I can understand the reasoning of the greats, handle them new ideas, you name it.” “Except for Deligne.” (WHAT ?) “Deligne is totally out of my league. Above my head.” “The difference between Deligne and me, is the same difference between me and an average good mathematician.” I found this anecdote especially astonishing considering that at the time I had never even heard of Deligne. (And most people, of course, haven’t even heard of Grothendieck.) [1]: https://www.quora.com/What-is-the-height-of-confidence/answer/Thomas-Cayne-1?share=1 https://www.quora.com/What-is-the-height-of-confidence/answe...

141 points by jorgenveisdal 7y ago

Quick point: His parents were Anarchists - in the workers'-movement, anti-Capitalist, revolutionary sense, Groethendieck wasn't. Or rather, his activities did not involve Anarchist organizing/politics. Also, in the summary, where it says "discovered a proof of the Lebesgue measure" - that's obviously nonsensical, he (re-)developed the Lebesgue measure himself, without being aware of Lebesgue's work. Or so it says; I don't know whether he actually focused on non-Riemann-measurable sets etc.

mikorym 7y ago
I also think one should be careful not to make it seem like he was part of any kind of political scene. He did write some texts outside of mathematics that could be seen as anarchist in the apolitical sense, for example the "Survivre" text. It's in French, so I don't know the exact contents, but I think it's like a sort of survival guide. But hey, we all have hobbies; one shouldn't read to much into the pasttimes of people, especially of people who rose to prominence not based on their pasttimes.
- wfn 7y ago
  > anarchist in the apolitical sense Hm. But how is the founding of Survivre (a political group publishing antimilitary etc. texts) and serving as its editor apolitical?
  - Melting_Harps 7y ago
    It isn't, and this is the vocal anti-anarchist contingent voicing their POV as fact when in reality he had stepped down from IHES after he realized his work was being funded by the French Military [1] in some Academic-Military collusion and couldn't continue any longer--not unlike DARPA has with MIT in modern times. He had a greater regard and estimation in his colleagues and Academia as a whole that turned out to be false as none followed him in protest and he then dedicated his Life to Environmentalism. He even shunned his Field's medal and rejected all the awards that followed. He, like many other Anarchists, felt that the State's continual and expansionist military activity needlessly contributes to the haphazard and headlong demise of the World's Ecology--which threatens all of Life on Earth--and wrote at great length about it. And sees the State as an imminent threat to Humanity as it accelerates our demise as a Species. I learned about Grothendieck's amazing Life and his work upon his death in 2014 (a month or 2 after Hal Finney died) in a very defining period of my Life, not just as an anarchist myself but as a Human and this article's final paragraph summed up what I think he wanted to be remembered the most as it was a Life well lived.: The man who had advanced mathematics in the most profound ways did not believe that math was the answer to everything. He taught us that life is more valuable than any equation. 1: https://www.nytimes.com/2014/11/25/science/the-lives-of-alexander-grothendieck-a-mathematical-visionary.html https://www.nytimes.com/2014/11/25/science/the-lives-of-alex...
    - wfn 7y ago
      Thanks for the comment. ...yeah. All this also reminded me of the story when he gave lectures on category theory in the forests near Hanoi when it was being bombed...
  - mikorym 7y ago
    I don't regard being antimilitary as being political at all. Maybe the working definition of politics is different, but if you are not involved in a political party that tries to exercise influence and prescription to others, then I would call one apolitical. In the same way, many Soviet intellectuals that were against their government still referred to themselves as apolitical.
    - wfn 7y ago
      Hm, that seems to be a rather peculiar and particular interpretation of the term. Grassroots organisations, political activist movements of all kinds would then fall outside your criterion. I mean... Women's suffrage movement (which changed the definition of who can vote in the first place), civil rights movement, etc. would also fall outwith your definition of the notion. (edit) The political processes which culminated in the French, the 1917 communist revolutions, etc... I don't see a point in defining the term in that way at all.
      - bmelton 7y ago
        I'm sort of down for it. "I don't like cats" is a fairly apolitical statement, that is until such point as political parties start taking stances on cats and arguing in favor of who subsidizes what kinds of feline activities. I have many beliefs that I regard as accidentally political - which is to say that I believe these things regardless of whether or which politicians happen to agree, or what their political affiliations are, or how closely tied their affiliations are to mine. It doesn't particularly matter to me whether others regard those beliefs as political or not, but it seems that we're approaching an era in which anything and everything can be deemed 'political' in some way merely because parties choose to take positions on them, and that may be completely at odds with how an individual may have come to conclusions on their own.
        wfn 7y ago
        I think I see what you mean, maybe there is a need to differentiate (individual conclusions "on their own", though there'd be arguments in favour of viewing those as political as well, etc.) But perhaps not at the expense of the term "political" (but rather introduction of some other term). Because it's simply not the case that something is necessarily apolitical "until such point as political parties start taking stances on cats". Some revolutions, changes in political regime, etc. happened not via the process of already existing political establishment systems (of which parliamentary parties is a mere (and not necessary (being descriptive here, not prescriptive)) subset of) accepting / incorporating / etc. some views at all (rather the exact opposite, say). Also, "I don't like cats" is a sort of easy example to use here, but if you take e.g. "domestic violence should not happen", where do you draw the line in terms of when it becomes political (let's say you start a grassroots network where victims of domestic violence can support each other, and gradually build political capital, and so on)... That said, differentiation along your lines is maybe useful, but severely redefining the scope of the term "political" seems a weird way to go about it.
EthanHeilman 7y ago
>His parents were Anarchists - in the workers'-movement, anti-Capitalist, revolutionary sense, Groethendieck wasn't. I'm not a Groethendieck scholar but I did read a short biography of him and it definitely left me with the impression that he was an anarchist or left-libertarian in the anti-Capitalist, liberty, revolutionary sense. What are your sources to back up the claim that he wasn't? >is activities did not involve Anarchist organizing/politics. In Groethendieck's "The Responsibility of the Scientist Today [0] he writes: "Thus the proliferation of military power and stocks of weapons throughout the world poses an ever-increasing danger not only to our species, but also to life in general. This predicament, unparalleled in the long history of biological evolution, must be met with immediate radical action." He directly calls for political organization and radical action. Edit: I don't object to getting voted down, but I would encourage anyone downvoting a comment on hackernews to provide their rational. This helps improve the quality of the discussion. [0] "The Responsibility of the Scientist Today" (translated from French) http://ccnr.org/grothendieck.pdf" http://ccnr.org/grothendieck.pdf"
- Melting_Harps 7y ago
  I'm not sure why you're being downvoted, thanks for the link, I've bookmarked it for later reading. Was that short bio 'La Clef des Songes,' I heard it was translated into Spanish, but never looked to deep for it. People really should be forced to refute before they can downvote. Even if you disagree with his points, he gives substance for what and why he said what he did.
  - EthanHeilman 7y ago
    The short biography was "The Artist and the Mathematician: The Story of Nicolas Bourbaki, the Genius Mathematician Who Never Existed" [0]. It dedicates a good chunk of the book to the life of Grothendieck. Grothendieck was a member of the group that used the Nicolas Bourbaki pseudonym. It's a fun read you can finish in an afternoon. Not sure how accurate it is. [0]: https://www.goodreads.com/book/show/208933.The_Artist_and_the_Mathematician https://www.goodreads.com/book/show/208933.The_Artist_and_th...
- sudosysgen 7y ago
danharaj 7y ago
You think he went to lecture in Hanoi in the middle of the Vietnam war for shiggles?
- einpoklum 7y ago
  Being against the Vietnam war doesn't make you an Anarchist (although naturally anti-Imperialism is in line with Anarchism). I didn't say Grohtendiek didn't have any political opinions.

stareatgoats 7y ago

An interesting, and sad story: that such a beautiful mind ended up with paranoia. It seems to be a real danger that many geniuses run, maybe in part (pardon the speculation) because they tend to work too hard: "Grothendieck was working on the foundations of algebraic geometry seven days a week, twelve hours a day, for ten years". That has to take a toll.

ur-whale 7y ago
> that such a beautiful mind ended up with paranoia. there's certainly a pattern here, that people that walk the edge of what a human brain can do often drift to paranoia and/or extremism. I'm thinking: Bobby Fischer, Grigory Perelman, Évariste Galois, and to a certain extent, Isaac Newton. I suspect the list is a lot longer.
- jorgenveisdal 7y ago
  Galois - shot in duel. Turing - committed suicide by cyanide-laced apple. Boltzmann - committed suicide while on vacation. Gödel - died from starvation and exhaustion. Cantor - died from starvation in an insane asylum. Ramanujan - died from malnutrition. de Moivre - predicted the day of his death by calculating his sleep cycle. Lie - became insane and attacked his friends. Erdös - did amphetamines all his life. Nash - was legally insane for 30 years. Perelman - refuses contact with anyone except his mother. Grothendieck - refused contact with anyone. Kaczynski - serving a life sentence in maximum security prison.
  - selimthegrim 7y ago
    Rananujan had a digestive issue IIRC
    - selimthegrim 7y ago
      *Ramanujan
  - hope-striker 7y ago

colinhb 7y ago

This biographical sketch is well-written, concise, and complete (or at least it appears to be). It includes many quotes and photos that I hadn’t seen before. But I can imagine that some readers will be left wondering what was so remarkable about this guy’s work. Unfortunately, it’s hard to explain without some exposure to pure mathematics. David Mumford, who pops up in this article, has a lengthy blog post[1] on this exact problem, stemming from his experience writing Grothendieck’s obituary for Nature. It’s an interesting read if you have some math background. In any case, I think the New York Times obituary by Edward Frenkel[2] does a nice job of giving a taste of his work to a lay audience (by tackling the problem of defining Grothendieck’s schemes, just like Mumford did). [1] http://www.dam.brown.edu/people/mumford/blog/2014/Grothendieck.html http://www.dam.brown.edu/people/mumford/blog/2014/Grothendie... [2] https://www.nytimes.com/2014/11/25/science/the-lives-of-alexander-grothendieck-a-mathematical-visionary.html https://www.nytimes.com/2014/11/25/science/the-lives-of-alex...

mikorym 7y ago
And for the more nonlay audience, Grothendieck's real pull is the persistence with which he applied category theoretic techniques successfully. Usually one would qualify this to algebraic geometry, but I think his approach can be followed in any of the many extensive fields in mathematics. I would contrast this to what often happens in the physics community, albeit not in a condescending manner, where techniques diverge rather than converge. In fact, I would guess this is the role that Einstein played a hundred years ago: to encourage sensible connections between researchers' work.
- nabla9 7y ago
  Grothendieck's relative point of view https://en.wikipedia.org/wiki/Grothendieck%27s_relative_point_of_view https://en.wikipedia.org/wiki/Grothendieck%27s_relative_poin...
  - mikorym 7y ago
    Linked to via two degrees is this: https://en.wikipedia.org/wiki/Grothendieck%E2%80%93Riemann%E2%80%93Roch_theorem#/media/File:Grothendieck-Riemann-Roch.jpg https://en.wikipedia.org/wiki/Grothendieck%E2%80%93Riemann%E.... I don't know German, but it would be really interesting to know what the text says.

mathandpoop 7y ago

You seem to have put quite an extensive amount of biographical research into this. I have never seen these photos in this high quality on the internet before. As a maths person and a bit of a Grothendieck fan, thanks!

jorgenveisdal 7y ago
Thanks a lot! Indeed, high res photos of Grothendieck are quite hard to come by

papeda 7y ago

I read a few articles about Grothendieck when he died, but I still learned a lot from this one. Those articles usually skipped over his early years as some version of anarchy. This one better fills in those gaps. For example, I didn't realize how haphazard Grothendieck's early professional progress was, or that it depended on an interview with a French education official who recognized unorthodox talent: > “Instead of a meeting of twenty minutes, he went on for two hours explaining to me how he had reconstructed, ‘with the tools available’, theories that had taken decades to construct. He showed an extraordinary sagacity.” It reminds me of Ramanujan, another exceptionally gifted and devoted mathematician who acquired most of his education on his own, and was very nearly lost to history but for the efforts of a few well-connected officials who could see his potential. Conversely, what a bummer it is to think of similar talents who didn't get so lucky. It also gets at just how much the culture of math education matters to math students, even ones like Grothendieck: > [Grothendieck] felt free to ask questions, but also found himself “struggling to learn things that those around him seemed to grasp instantly […] like they had known them from the cradle”. The contrast lead Grothendieck to eventually leave Paris, in October of 1949 on the advice of Cartan and Weil who recommended he instead travel to Nancy to work with Schwartz and Dieudonné on functional analysis. And this was a guy whose internal mathematical drive was strong enough to independently discover measure theory as a teenager! Then there are all the other "failures" absent from a short biographical blurb: he finished his PhD "with few prospects for employment after his graduation in 1953", then "planned to write a book on topological vector spaces, but it never materialized", spent a year failing to solve the "approximation problem", despaired that the field of his thesis was "dead", pivoted away from analysis, rest is history, etc.

drummer 7y ago

The name grothendieck sounds a lot like big dick. Like bigus dickus in monthy pythons life of brian. Groot means big in dutch.

_hardwaregeek 7y ago

A few months ago, I stumbled upon an antique store in Paris where the owner had thousands of notes taken from Grothendieck's house after he died. Apparently he was in charge of appraising them. Which is pretty stunning since Grothendieck didn't publish anything for the last few decades of his life, so it's quite possible there's new math there. Anyways the guy described how Grothendieck's house didn't have a roof and was pretty decrepit. Which made me pretty sad. One of the greatest mathematicians of the 20th century dying alone in a house with no roof. Part of me wonders if maybe, had he gotten proper mental health care, Grothendieck could have enjoyed a longer, more healthy career. Or career aside, could he have just had a better life? In the mathematical community it feels like there's a bit of an acceptance of idiosyncrasies bordering on potential mental health issues. Well I say acceptance but really it's bordering on willful ignorance. How many advisors give their doctoral students advice on mental health? How many advisors themselves received training on mental health? It's worth analyzing.

jorgenveisdal 7y ago
Absolutely. Check out my essays on Wiener and Oppenheimer. Many of the same tendencies, though with better outcomes

mhartl 7y ago

I recently enjoyed listening to this interview with someone who knew Grothendieck. It takes a while to get going, but some of the stories are quite gripping. https://youtu.be/L--9bJApz_A https://youtu.be/L--9bJApz_A

mhartl 7y ago
The article mentions Jean-Pierre Serre, with whom Grothendieck corresponded extensively, and Pierre Deligne, widely regarded as Grothendieck’s greatest student. While investigating Grothendieck recently (inspired by the interview linked in the parent comment), I came across this astonishing anecdote, relating a comment by Serre about Deligne [1]: “Look, I can take on anyone in Math.” — don’t forget, this guy [Serre] is the youngest Fields medal winner ever, the first Abel prize laureate, etc. — “I can understand the reasoning of the greats, handle them new ideas, you name it.” “Except for Deligne.” (WHAT ?) “Deligne is totally out of my league. Above my head.” “The difference between Deligne and me, is the same difference between me and an average good mathematician.” I found this anecdote especially astonishing considering that at the time I had never even heard of Deligne. (And most people, of course, haven’t even heard of Grothendieck.) [1]: https://www.quora.com/What-is-the-height-of-confidence/answer/Thomas-Cayne-1?share=1 https://www.quora.com/What-is-the-height-of-confidence/answe...