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).
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.
rough translation (it's kinda tricky to preserve the tone. Question marks are words I'm not sure the translation works):
> Riemann-Roch theorem: the last trend(?): the diagram(?) <formula> is commutative!
To give this statement over f:x->y an approximative sense I had try the patience of the listeners for almost 2 hours. Black-on-white (in Springer's Lecture Notes) its about 400, 500 pages. A fitting example how our drive to knowledge and discovery more and more realizes itself in a far-from-life logical delirium, while the life itself is ruined in a thousand ways - and is threatened by total destruction. High time to change our path!
I wonder if he means what I think he means, which is that a concept that is for some field all-encompassing in your mind takes 400 pages to write down in a way that translates your ideas. University group theory is like that, when the real objective may just be to show that you can't circle the square.
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.
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.
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.
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.
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.
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.
> 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.
Then I don't think you understand what anarchism is at all, here is a working definition from his Biography [1] portion titled Anarchism; it helps elucidate what it is that anarchism is, and what it seeks to achieve (note that no actual Political affiliation is ascribed or required to adhere to these principals, as anarchism carries within it a breadth of sub-types in its mode of operation but carries within it core principals and values):
The first part of this book describes the life of an anarchist, und perhaps it would not be completely superfluous to make a short statement about what Anarchism is:
Anarchism is a world view whose basis lies in the conviction that the domination of people over each other, and every form of hierarchy, leads to the suppression of individual and collective freedom; that it is unjustified, repressive, and results in violence. Anarchism propagates the dissolving of hierarchical state structures. It places individual freedom, equality and collective self-determination at the center of its effort to create a social organization entirely free of coercion.
If you're interested, as you clearly shown that you are to some degree, you can take the the time to read for yourself how he viewed the World with his other Work [2] outside of mathematics and what his aims were from the links below for yourself. The Grothendieck Circle is also another great source for reading his works, it could use some sprucing up as it looks like an 90s Angelfire site, but the links work.
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.
I think the discussion is becoming complicated, but I think my key points are this:
1. One can be apolitical by being socially apathetic towards the influences of other people. This describes myself: I am alabellist and as a general courtesy to other mathematicians (as a group in particular) allow them the benefit of the doubt that they would prefer me to not label them either. This is my approach to Grothendieck: I think it's perfectly consistent to have complicated views on politics, but to still remain apolitical in the sense that you don't try to propagate your views other than their inherent merits. Going to live as a hermit in the mountains is the evidence that I use for this; I haven't heard that he tried to lure other people into the mountains or forced an agenda on other people from his stay there.
2. Mathematicians are often an oppressed group of people, as are all scientists, sometimes become oppressive themselves and often have serious mental health issues or other social risks. For this reason one should approach other mathematicians with empathy. It also suggests to not judge people by their worst, but by their best. For me, the best of Grothendieck is not a political environmental crusader, it is a great mathematician with certain idiosyncratic tendencies for isolation and statements on politics. That does not mean that his actions have a political undertone in the sense that they try to exert influence without permission. Such actions to me are apolitical by nature; Youtubers are not all political, but I would have called them so if we were all forced to watch their channels.
"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.
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.
I think the best way to understand this reality is that when it comes down to it, a lot more things are political than one would think.
For example, "I don't like cats" is apolitical because it doesn't take into consideration anyone but you. But as soon as you say, "we like cats too much", that's political.
An example I would give is someone that's debating which feature an open-source project should work on. That's inherently political. The only difference between that and whether or not we should fund smartphones for homeless people, for example, is a matter of scale.
An issue I see right off the bat, how do you deal with the reality that politics can and does exist without and within, not just between political parties?
I think the best definition of politics is anything that relates to the making of decisions that concern a group of people. If whatever you are doing or talking about concerns how we should make decisions, then it is political. And I don't think that's an issue. To try to limit politics to what happens in an electoral party state is pretty sad and reductive, and contributes to political apathy.
Political - (defn) relating to the ideas or strategies of a particular party or group in politics
Whereas in within the context of this discussion, i.e. is Grothendieck an Anarchist?, political is being used to mean:
Political - (defn) an ethical philosophy of society and government.
However Grothendieck is political under both definitions:
(1). he formed and participated in a political group which attempted to advance policies (defn 1), (2). and those policies were based on an ethical philosophy of society which he believed in (defn 2).
Political—Promoting the influence of a group of people x on some group of people y, often in an insistent manner and often without the critical evaluation of subject matter.
Apolitical—Being opposed, for most x and y, to the influence of some group of people x on some group of people y. When in some unfortunate cases in life, some influence of x on y is tolerated, it is only tolerated because of the subject matter, and not tolerated because of the particular humans that comprise x (promoting them) or the set y (subjecting them).
>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.
I honestly don't see the issue with this argument. How is it that this doesn't contribute to the discussion? I don't think it does. It also doesn't make any argument in bad faith or that is egregiously wrong, so I see absolutely no reason for it to be downvoted, unless the only objection is of the order of "I don't agree" or "I don't want to agree". Which is by itself a bad faith reason to downvote a post.
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.
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.
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!
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.
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.
I'm not sure it was paranoia, he became disillusioned with humanity.
It is important to be careful to not define activities that deviate from normal human behavior as mental illness. We should not expect average human behavior to represent a ceiling on virtue, wisdom, or rationality.
Hey, 'not sure' is supposed to my guiding star! I may have lapsed here, and absolutely agree that we should not define activities that deviate from normal human behavior as mental illness. On the other hand one should not romanticize and define as normal or unproblematic that which is a mental illness either.
Granted I could have dug further. To my defense I just echoed a quote in the article, which states he held a resentment that "eventually metamorphosed into a paranoia which is evident in the pages of Récoltes et Semailles. - Excerpt, "The IHÉS at Forty" by Allyn Jackson (1999)".
I did however do some digging in order to produce this response to your comment, and I found an interesting article about Grothendieck on Psychology Today [0]. It also mentions an apparent trend among some mathematical geniuses to develop mental illness, and it expresses hope that a connection may be found thanks to "advances in the nascent field of creativity-psychopathology neuroscience", of which I know nothing. But I stick to my original speculation: that overworking might be part of it (until I'm convinced otherwise).
As for Grothendieck the author has this to say about the later stages of his life: "He believed himself to be in communication with Plato and Descartes, and even with God himself. The belief in signal transmission is a signature psychotic delusion".
Thats interesting, I've heard mathematicians remark that "the study of the theory of infinity sets can lead to madness". I didn't realize that there was actual science behind that.
Thanks for finding those details. I didn't know that Grothendieck was hearing voices.
I became disillusioned with humanity long ago, that still doesn't have anything to do with burning 25000 pages I could have wrote or writing 300-page manuscript about how god exists and talks to us through our dreams.
At least in Grothendieck's case, the boundary between "visionary" and "madman" is not so clear. This is a guy who spent decades pursuing targets nobody else could see, and convincing other people to join him, and the end result was a resounding success for mathematics. The combination of 1. the truth-seeking confidence that comes from pulling that off, and 2. what sounds like a deeply traumatizing childhood at the hands of various governments is a...complicated mixture.
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.
Erdős took amphetamine in the second half of his life, and apparently it helped him a lot to stay productive. There is a story about it.
Erdős’s friends worried about his drug use, and in 1979 Graham bet Erdős $500 that he couldn’t stop taking amphetamines for a month. Erdős accepted, and went cold turkey for a complete month. Erdős’s comment at the end of the month was “You’ve showed me I’m not an addict. But I didn’t get any work done. I’d get up in the morning and stare at a blank piece of paper. I’d have no ideas, just like an ordinary person. You’ve set mathematics back a month.” He then immediately started taking amphetamines again.
His biography “The Man Who Loved Only Numbers” is a very good interesting book.
Turing committed suicide to escape government persecution for being gay. That's not the same as a case like Grothendieck or Nash; it can't fairly be called paranoia when someone really is out to get you.
More exactly turing was suffering due chemical castration mandated by the government, I don't want to imagine what such procedure does to one's mental health.
Given that the regimen at that time involved high doses of some of the same hormones used in MtF HRT today, I suspect it'd be not totally unakin to being forced into severe gender dysphoria, with gynecomastia and permanent sterility as just a couple of the side effects.
I'm afraid Kaczynski is probably more famous than most of them among those not interested in mathematics. And he was an assistant professor of mathematics at UCB when he turned, after all.
Gödel's story is certainly a fascinating one. However, he did
have a paranoid fear of being poisoned most of his life and weighed 30kg when he died - of malnutrition.
I think there's an issue with saying that extremism is necessarily an issue. For most theoretical thinkers, extremism is a necessary result of theory. And there is nothing wrong with that, if extremism in an ideology is an issue it's generally that the ideology itself is problematic.
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.
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.)
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/Grothendie...
[2] https://www.nytimes.com/2014/11/25/science/the-lives-of-alex...