7 ms·

Alexander Grothendieck has died

356 points by hokkos 12y ago

neworder 12y ago
There is a fundraising effort to fund the translation of Grothendieck's biography, written by Winfried Scharlau: http://www.gofundme.com/7ldiwo http://www.gofundme.com/7ldiwo I've read the 1st volume of the biography and fully recommend it, so if you find AG's life interesting, you can consider donating a few bucks.
- deleted 12y ago
  [deleted]
- another_user 12y ago
  Are there any fundraising efforts on recoltes et semalles?
fermigier 12y ago
Some of the best papers about his life and his work: From the notices of the AMS: http://www.ams.org/notices/200409/fea-grothendieck-part1.pdf http://www.ams.org/notices/200409/fea-grothendieck-part1.pdf http://www.ams.org/notices/200410/fea-grothendieck-part2.pdf http://www.ams.org/notices/200410/fea-grothendieck-part2.pdf By Pierre Cartier: http://xahlee.info/math/i/Alexander_Grothendieck_cartier.pdf http://xahlee.info/math/i/Alexander_Grothendieck_cartier.pdf By Pierre Deligne (in French): http://www.emis.de/journals/SC/1998/3/pdf/smf_sem-cong_3_11-19.pdf http://www.emis.de/journals/SC/1998/3/pdf/smf_sem-cong_3_11-...
nabla9 12y ago
Too much dandelion soup?
jordigh 12y ago
Wow, I swear I was just wondering last night if he was still alive or not, as I was reading about him in Serge Lang's Algebra. Personal coincidence for me. May we never forget the Grothendieck prime, 57.
- davmre 12y ago
  For those unfamiliar with the reference (from http://www.ams.org/notices/200410/fea-grothendieck-part2.pdf http://www.ams.org/notices/200410/fea-grothendieck-part2.pdf): One striking characteristic of Grothendieck’s mode of thinking is that it seemed to rely so little on examples. This can be seen in the legend of the so-called “Grothendieck prime”. In a mathematical conversation, someone suggested to Grothendieck that they should consider a particular prime number. “You mean an actual number?” Grothendieck asked. The other person replied, yes, an actual prime number. Grothendieck suggested, “All right, take 57." But Grothendieck must have known that 57 is not prime, right? Absolutely not, said David Mumford of Brown University. “He doesn’t think concretely.”
  - deleted 12y ago
    [deleted]
  - Igglyboo 12y ago
    I'm not sure I understand what Mumford is alluding to, care to explain?
    - deleted 12y ago
      [deleted]
    - billforsternz 12y ago
      You or I might try to understand some mathematics by mapping it onto some kind of real-world analog, for example a model or graph or specific example case. This guy was a genius who didn't need to do that.
    - masklinn 12y ago
      He was a very abstract mathematician, he built and worked with concepts and neither used nor needed numbers much.
    - wires 12y ago
      His style of thinking seems very categorical, where one does not focus on structure of the objects in question (say prime numbers), rather on the mappings between/from/to them. In fact, from the cat. perspective you need to put extra effort to point out particular objects in your collection (http://ncatlab.org/nlab/show/generalized+element http://ncatlab.org/nlab/show/generalized+element). Grothendieck certainly knew what it means for p to be prime. I don't know, but maybe his thoughts went along the line of "primes are some substructure of the natural numbers and such and such changes happen in the functions that we can build on them". So he was obviously able to speak about some collection of primes, yet whether an actual number is prime he probably doesn't think much about.
michael_nielsen 12y ago
Grothendieck's comments on creativity have been very important in my life, especially the following quote (in translation from the French): "To state it in slightly different terms: in those critical years [roughly from age 17 to 20] I learned how to be alone." "This formulation doesn't really capture my meaning. I didn't, in any literal sense learn to be alone, for the simple reason that this knowledge had never been unlearned during my childhood. It is a basic capacity in all of us from the day of our birth. However these 3 years of work in isolation, when I was thrown onto my own resources, following guidelines which I myself had spontaneously invented, instilled in me a strong degree of confidence, unassuming yet enduring, in my ability to do mathematics, which owes nothing to any consensus or to the fashions which pass as law...." "By this I mean to say: to reach out in my own way to the things I wished to learn, rather than relying on the notions of the consensus, overt or tacit, coming from a more or less extended clan of which I found myself a member, or which for any other reason laid claim to be taken as an authority. This silent consensus had informed me, both at the lyé and at the university, that one shouldn't bother worrying about what was really meant when using a term like "volume", which was "obviously self-evident", "generally known", "unproblematic", etc. I'd gone over their heads, almost as a matter of course, even as Lesbesgue himself had, several decades before, gone over their heads. It is in this gesture of "going beyond", to be something in oneself rather than the pawn of a consensus, the refusal to stay within a rigid circle that others have drawn around one - it is in this solitary act that one finds true creativity. All others things follow as a matter of course." Very late in his life, Grothendieck asked for people to cease re-publishing his work, even brief excerpts. (See: http://sbseminar.wordpress.com/2010/02/09/grothendiecks-letter/ http://sbseminar.wordpress.com/2010/02/09/grothendiecks-lett... ) So I have mixed feelings about quoting the above. But I do so in the hope that it can help others as it has helped me.
- StandardFuture 12y ago
  > Later in life, Grothendieck asked for people to cease re-publishing his work, even brief excerpts. I think Grothendeick used Mathematics as a way to rebel against/escape from the world he grew up in. It was a formal discipline that could provide concrete results, unlike the mundance political arguing and nonsense that he commonly saw elsewhere controlling the world. But, I bet as he grew older he noticed that even his very own mathematical work could be used in mundane academic political nonsense. Thus, a disenchantment with everything ensued leading to a total isolationist viewpoint.
StandardFuture 12y ago
The aspects that struck me the most about this article was how passionately political his parents were. Moving around Europe in an effort to outright escape/support various political factions. In fact, much of their apparent political views and the people they were supporting seemed to be one vast pool of contradictions (as most European politics were in those days -- thus World War II). And it gave me a possible picture of why Alexandre may have used mathematics as an escape from the ferocious world he grew up around until maybe he became disenchanted with the idea of having any part of this same world at all? I also remember reading about him partaking in anti-nuclear rallies a while back. Idk, just my small take away. :)
joaorico 12y ago
Here's one of his staggering quotes [1], worth reading through: "In those critical years I learned how to be alone. [But even] this formulation doesn't really capture my meaning. I didn't, in any literal sense learn to be alone, for the simple reason that this knowledge had never been unlearned during my childhood. It is a basic capacity in all of us from the day of our birth. However these three years of work in isolation [1945–1948], when I was thrown onto my own resources, following guidelines which I myself had spontaneously invented, instilled in me a strong degree of confidence, unassuming yet enduring, in my ability to do mathematics, which owes nothing to any consensus or to the fashions which pass as law....By this I mean to say: to reach out in my own way to the things I wished to learn, rather than relying on the notions of the consensus, overt or tacit, coming from a more or less extended clan of which I found myself a member, or which for any other reason laid claim to be taken as an authority. This silent consensus had informed me, both at the lycée and at the university, that one shouldn't bother worrying about what was really meant when using a term like "volume," which was "obviously self-evident," "generally known," "unproblematic," etc....It is in this gesture of "going beyond," to be something in oneself rather than the pawn of a consensus, the refusal to stay within a rigid circle that others have drawn around one—it is in this solitary act that one finds true creativity. All others things follow as a matter of course. Since then I've had the chance, in the world of mathematics that bid me welcome, to meet quite a number of people, both among my "elders" and among young people in my general age group, who were much more brilliant, much more "gifted" than I was. I admired the facility with which they picked up, as if at play, new ideas, juggling them as if familiar with them from the cradle—while for myself I felt clumsy, even oafish, wandering painfully up an arduous track, like a dumb ox faced with an amorphous mountain of things that I had to learn (so I was assured), things I felt incapable of understanding the essentials or following through to the end. Indeed, there was little about me that identified the kind of bright student who wins at prestigious competitions or assimilates, almost by sleight of hand, the most forbidding subjects. In fact, most of these comrades who I gauged to be more brilliant than I have gone on to become distinguished mathematicians. Still, from the perspective of thirty or thirty-five years, I can state that their imprint upon the mathematics of our time has not been very profound. They've all done things, often beautiful things, in a context that was already set out before them, which they had no inclination to disturb. Without being aware of it, they've remained prisoners of those invisible and despotic circles which delimit the universe of a certain milieu in a given era. To have broken these bounds they would have had to rediscover in themselves that capability which was their birthright, as it was mine: the capacity to be alone." [1] Quote translation found in [2] from Alexander Grothendieck, Récoltes et Semailles, 1986, English translation by Roy Lisker, www.grothendieck-circle.org, chapter 2. [2] Smolin, Lee - The Trouble with Physics
j2kun 12y ago
For those who don't know, Alexander[1] Grothendieck revolutionized algebraic geometry, which is (in a very rough sense) the study of solutions of systems of polynomial equations as both algebraic and geometric objects. Grothendieck gave a totally new foundation for the subject via category theory, and one could argue that he is a primary reason why categories are so central in modern mathematics. [1]: He spelled his own name different from the French spelling, apparently.
thebear 12y ago
I believe that Grothendieck always insisted on spelling his first name "Alexander" rather than the French "Alexandre." If this is true, as I believe it is, let's make an effort to respect his wish.
- dang 12y ago
  Ok, we'll take your word for that and change the HN title.
  - thebear 12y ago
    Thanks, I checked the Wikipedia article at http://en.wikipedia.org/wiki/Alexander_Grothendieck http://en.wikipedia.org/wiki/Alexander_Grothendieck. It says in the first paragraph: 'He consistently spelt his first name "Alexander" rather than the French "Alexandre"', and they give a reference for that.
    - hokkos 12y ago
      The french wikipedia says he cared a lot about the spelling "Alexander", but signed his french work as "Alexadre".
- fermigier 12y ago
  Interestingly, it seems that on what might be the last autographed document publicly available from him, he signed "Alexandre" and not "Alexander": https://ztfnews.files.wordpress.com/2014/11/grothendiecks-declaration-original.png https://ztfnews.files.wordpress.com/2014/11/grothendiecks-de...
kiba 12y ago
Who is this guy? Why is he important?
- defen 12y ago
  Arguably the most important mathematician of the second half of the 20th century
auntienomen 12y ago
It's difficult to understate Grothendieck's impact on modern mathematics. His work touches everything from stochastic PDE to number theory. In algebraic geometry, where he had the most impact, it is difficult to so much as think about the subject without using his ideas. His personal story is also interesting and unique. Pierre Cartier recently published an appreciation of his life and work -- Alexander Grothendieck: A Country Known Only By Name -- which is well worth the read even if you aren't a mathematician. http://inference-review.com/article/a-country-known-only-by-name http://inference-review.com/article/a-country-known-only-by-...
dil8 12y ago
Translation here: https://www.reddit.com/r/math/comments/2m82zw/reports_are_coming_in_of_the_death_of_alexandre/cm1wt6u https://www.reddit.com/r/math/comments/2m82zw/reports_are_co...
myg204 12y ago
Sad news, such an original individual and truly a giant of Mathematics. To imagine he invented Lebesgue measure theory on his own in his late teens. I remember reading that when he was sent to study under Schwartz and Dieudonne in Nancy (if i remember correctly), he solved the equivalent of seven phd thesis problems in nine months. His work with radical ecology is also highlighted in the article.
lkesteloot 12y ago
A good eulogy here from economist Steve Landsburg: http://www.thebigquestions.com/2014/11/13/the-rising-sea/ http://www.thebigquestions.com/2014/11/13/the-rising-sea/ "... the greatest of all modern mathematicians and arguably the greatest mathematician of all time ..."
pfortuny 12y ago
May he rest in peace. His honest fight against war (teaching in Hanoi while bombings were going on, leaving the IHES after learning that NATO supported it, etc.) are an example of honesty. One may disagree with his positions (as I do) but we shall always be impressed by his acts. I am obviously leaving the maths apart: we hope to stand on his shoulders, we and many future generations.
conformal 12y ago
while i am generally loathe to comment on HN, i consider it truly sad to see the passing of grothendieck. he was a truly revolutionary mathematician and his contribution to the (hard) science of mathematics cannot be overstated. people who live on principle are rare, and those willing to go without salary as part of that protest are even rarer [1]. [1] - http://www.fermentmagazine.org/Quest88.html http://www.fermentmagazine.org/Quest88.html
hokkos 12y ago
Grothendieck has been a point of interest in me since I read many years ago about his work about generalization of theories, his genius, his hermit life and that he chose to be stateless. Just last Sunday I saw an issue of a scientific magazine about him in a friend's house, and said I loved this guy, it is so strange and sad to learn about his death a few days after.
205guy 12y ago
I am both surprised as how successful he was at remaining obscure, and yet how many on HN were familiar with his work and writings. I was briefly a math major at the university, I studied at a technical school in France, I read a lot on technical forums such as HN where some people seem to know his work, like many I am fascinated by geniuses and their eccentricities, I browse Wikipedia for fun, and yet I was totally unaware of his life and work. Maybe I'd heard his name in passing, but no mention of his talent or writings, or his eccentric life because then I would've remembered his name. I find it sad that he is so obscure, though I see that it was his wish. On the one hand, you want to respect someone who obviously had his own reasons for withdrawal, on the other it seems like a madman's wish to be erased from the history books and even from the annals of science. That's not how science works, and that he thought he could be the exception shows a disjunction. I don't want to imply it was a mental illness, but I'd like to read more to try to understand his state of mind. Now that he lived and died in (relative) obscurity, it won't hurt to learn about him and learn from him.
- Bahamut 12y ago
  In mathematics, he is far from obscure though. His name is all over algebraic geometry. Any graduate student who has taken an algebraic geometry class would absolutely know of him, and most should have heard of his name from various algebra or topology courses.
- omaranto 12y ago
  He's as famous as posible for a mathematician: every mathematician knows about him, even probably most undergraduate math majors, but only a few non-math people have heard of him.
malaporte 12y ago
Wow. I've never heard about him, but reading the article I realized he used to live not 500 meters away from my house (a long time ago).
barbudorojo 12y ago
I wonder if there is some hidden factor in the minds of those mathematicians that allows them to think so easily in abstract terms. I have always needed to begin with simple examples and from them to go to generalities. Perhaps they learned all the easy stuff when they were children and all those years of their adolescence were employed to enrich their minds with more and more general and powerful concepts and frameworks. Then, when they mature they no longer needs to think about the concrete, for then those abstracts ideas are as concrete like a tree for a child. That vision is only achievable for those able to live alone, to wander with their thoughts, to lose themselves in the island of their inner world. Their inner world and ideas are more real and concrete than what we see with our eyes. They don't see a prime number, a prime ideal is only point in the spectrum of a ring, their math ideas are so colorful that nobody can reach that peak without forgetting where we come from and that the earth is our planet. They live in a different math heaven always climbing to reach the book (Erdos ideal).
toreoft 12y ago
Rest in peace. - A great matematician and even also a great philosopher.
toreoft 12y ago
Rest in peace. A great matematician and even also a great philosopher.
toreoft 12y ago
Rest in peace. A great matematician and even also a great philosopher.

356 points by hokkos 12y ago

There is a fundraising effort to fund the translation of Grothendieck's biography, written by Winfried Scharlau: http://www.gofundme.com/7ldiwo http://www.gofundme.com/7ldiwo I've read the 1st volume of the biography and fully recommend it, so if you find AG's life interesting, you can consider donating a few bucks.

deleted 12y ago
[deleted]
another_user 12y ago
Are there any fundraising efforts on recoltes et semalles?

fermigier 12y ago

Some of the best papers about his life and his work: From the notices of the AMS: http://www.ams.org/notices/200409/fea-grothendieck-part1.pdf http://www.ams.org/notices/200409/fea-grothendieck-part1.pdf http://www.ams.org/notices/200410/fea-grothendieck-part2.pdf http://www.ams.org/notices/200410/fea-grothendieck-part2.pdf By Pierre Cartier: http://xahlee.info/math/i/Alexander_Grothendieck_cartier.pdf http://xahlee.info/math/i/Alexander_Grothendieck_cartier.pdf By Pierre Deligne (in French): http://www.emis.de/journals/SC/1998/3/pdf/smf_sem-cong_3_11-19.pdf http://www.emis.de/journals/SC/1998/3/pdf/smf_sem-cong_3_11-...

nabla9 12y ago

Too much dandelion soup?

jordigh 12y ago

Wow, I swear I was just wondering last night if he was still alive or not, as I was reading about him in Serge Lang's Algebra. Personal coincidence for me. May we never forget the Grothendieck prime, 57.

davmre 12y ago
For those unfamiliar with the reference (from http://www.ams.org/notices/200410/fea-grothendieck-part2.pdf http://www.ams.org/notices/200410/fea-grothendieck-part2.pdf): One striking characteristic of Grothendieck’s mode of thinking is that it seemed to rely so little on examples. This can be seen in the legend of the so-called “Grothendieck prime”. In a mathematical conversation, someone suggested to Grothendieck that they should consider a particular prime number. “You mean an actual number?” Grothendieck asked. The other person replied, yes, an actual prime number. Grothendieck suggested, “All right, take 57." But Grothendieck must have known that 57 is not prime, right? Absolutely not, said David Mumford of Brown University. “He doesn’t think concretely.”
- deleted 12y ago
  [deleted]
- Igglyboo 12y ago
  I'm not sure I understand what Mumford is alluding to, care to explain?
  - deleted 12y ago
    [deleted]
  - billforsternz 12y ago
    You or I might try to understand some mathematics by mapping it onto some kind of real-world analog, for example a model or graph or specific example case. This guy was a genius who didn't need to do that.
  - masklinn 12y ago
    He was a very abstract mathematician, he built and worked with concepts and neither used nor needed numbers much.
  - wires 12y ago
    His style of thinking seems very categorical, where one does not focus on structure of the objects in question (say prime numbers), rather on the mappings between/from/to them. In fact, from the cat. perspective you need to put extra effort to point out particular objects in your collection (http://ncatlab.org/nlab/show/generalized+element http://ncatlab.org/nlab/show/generalized+element). Grothendieck certainly knew what it means for p to be prime. I don't know, but maybe his thoughts went along the line of "primes are some substructure of the natural numbers and such and such changes happen in the functions that we can build on them". So he was obviously able to speak about some collection of primes, yet whether an actual number is prime he probably doesn't think much about.

michael_nielsen 12y ago

Grothendieck's comments on creativity have been very important in my life, especially the following quote (in translation from the French): "To state it in slightly different terms: in those critical years [roughly from age 17 to 20] I learned how to be alone." "This formulation doesn't really capture my meaning. I didn't, in any literal sense learn to be alone, for the simple reason that this knowledge had never been unlearned during my childhood. It is a basic capacity in all of us from the day of our birth. However these 3 years of work in isolation, when I was thrown onto my own resources, following guidelines which I myself had spontaneously invented, instilled in me a strong degree of confidence, unassuming yet enduring, in my ability to do mathematics, which owes nothing to any consensus or to the fashions which pass as law...." "By this I mean to say: to reach out in my own way to the things I wished to learn, rather than relying on the notions of the consensus, overt or tacit, coming from a more or less extended clan of which I found myself a member, or which for any other reason laid claim to be taken as an authority. This silent consensus had informed me, both at the lyé and at the university, that one shouldn't bother worrying about what was really meant when using a term like "volume", which was "obviously self-evident", "generally known", "unproblematic", etc. I'd gone over their heads, almost as a matter of course, even as Lesbesgue himself had, several decades before, gone over their heads. It is in this gesture of "going beyond", to be something in oneself rather than the pawn of a consensus, the refusal to stay within a rigid circle that others have drawn around one - it is in this solitary act that one finds true creativity. All others things follow as a matter of course." Very late in his life, Grothendieck asked for people to cease re-publishing his work, even brief excerpts. (See: http://sbseminar.wordpress.com/2010/02/09/grothendiecks-letter/ http://sbseminar.wordpress.com/2010/02/09/grothendiecks-lett... ) So I have mixed feelings about quoting the above. But I do so in the hope that it can help others as it has helped me.

StandardFuture 12y ago
> Later in life, Grothendieck asked for people to cease re-publishing his work, even brief excerpts. I think Grothendeick used Mathematics as a way to rebel against/escape from the world he grew up in. It was a formal discipline that could provide concrete results, unlike the mundance political arguing and nonsense that he commonly saw elsewhere controlling the world. But, I bet as he grew older he noticed that even his very own mathematical work could be used in mundane academic political nonsense. Thus, a disenchantment with everything ensued leading to a total isolationist viewpoint.

StandardFuture 12y ago

The aspects that struck me the most about this article was how passionately political his parents were. Moving around Europe in an effort to outright escape/support various political factions. In fact, much of their apparent political views and the people they were supporting seemed to be one vast pool of contradictions (as most European politics were in those days -- thus World War II). And it gave me a possible picture of why Alexandre may have used mathematics as an escape from the ferocious world he grew up around until maybe he became disenchanted with the idea of having any part of this same world at all? I also remember reading about him partaking in anti-nuclear rallies a while back. Idk, just my small take away. :)

joaorico 12y ago

Here's one of his staggering quotes [1], worth reading through: "In those critical years I learned how to be alone. [But even] this formulation doesn't really capture my meaning. I didn't, in any literal sense learn to be alone, for the simple reason that this knowledge had never been unlearned during my childhood. It is a basic capacity in all of us from the day of our birth. However these three years of work in isolation [1945–1948], when I was thrown onto my own resources, following guidelines which I myself had spontaneously invented, instilled in me a strong degree of confidence, unassuming yet enduring, in my ability to do mathematics, which owes nothing to any consensus or to the fashions which pass as law....By this I mean to say: to reach out in my own way to the things I wished to learn, rather than relying on the notions of the consensus, overt or tacit, coming from a more or less extended clan of which I found myself a member, or which for any other reason laid claim to be taken as an authority. This silent consensus had informed me, both at the lycée and at the university, that one shouldn't bother worrying about what was really meant when using a term like "volume," which was "obviously self-evident," "generally known," "unproblematic," etc....It is in this gesture of "going beyond," to be something in oneself rather than the pawn of a consensus, the refusal to stay within a rigid circle that others have drawn around one—it is in this solitary act that one finds true creativity. All others things follow as a matter of course. Since then I've had the chance, in the world of mathematics that bid me welcome, to meet quite a number of people, both among my "elders" and among young people in my general age group, who were much more brilliant, much more "gifted" than I was. I admired the facility with which they picked up, as if at play, new ideas, juggling them as if familiar with them from the cradle—while for myself I felt clumsy, even oafish, wandering painfully up an arduous track, like a dumb ox faced with an amorphous mountain of things that I had to learn (so I was assured), things I felt incapable of understanding the essentials or following through to the end. Indeed, there was little about me that identified the kind of bright student who wins at prestigious competitions or assimilates, almost by sleight of hand, the most forbidding subjects. In fact, most of these comrades who I gauged to be more brilliant than I have gone on to become distinguished mathematicians. Still, from the perspective of thirty or thirty-five years, I can state that their imprint upon the mathematics of our time has not been very profound. They've all done things, often beautiful things, in a context that was already set out before them, which they had no inclination to disturb. Without being aware of it, they've remained prisoners of those invisible and despotic circles which delimit the universe of a certain milieu in a given era. To have broken these bounds they would have had to rediscover in themselves that capability which was their birthright, as it was mine: the capacity to be alone." [1] Quote translation found in [2] from Alexander Grothendieck, Récoltes et Semailles, 1986, English translation by Roy Lisker, www.grothendieck-circle.org, chapter 2. [2] Smolin, Lee - The Trouble with Physics

j2kun 12y ago

For those who don't know, Alexander[1] Grothendieck revolutionized algebraic geometry, which is (in a very rough sense) the study of solutions of systems of polynomial equations as both algebraic and geometric objects. Grothendieck gave a totally new foundation for the subject via category theory, and one could argue that he is a primary reason why categories are so central in modern mathematics. [1]: He spelled his own name different from the French spelling, apparently.

thebear 12y ago

I believe that Grothendieck always insisted on spelling his first name "Alexander" rather than the French "Alexandre." If this is true, as I believe it is, let's make an effort to respect his wish.

dang 12y ago
Ok, we'll take your word for that and change the HN title.
- thebear 12y ago
  Thanks, I checked the Wikipedia article at http://en.wikipedia.org/wiki/Alexander_Grothendieck http://en.wikipedia.org/wiki/Alexander_Grothendieck. It says in the first paragraph: 'He consistently spelt his first name "Alexander" rather than the French "Alexandre"', and they give a reference for that.
  - hokkos 12y ago
    The french wikipedia says he cared a lot about the spelling "Alexander", but signed his french work as "Alexadre".
fermigier 12y ago
Interestingly, it seems that on what might be the last autographed document publicly available from him, he signed "Alexandre" and not "Alexander": https://ztfnews.files.wordpress.com/2014/11/grothendiecks-declaration-original.png https://ztfnews.files.wordpress.com/2014/11/grothendiecks-de...

kiba 12y ago

Who is this guy? Why is he important?

defen 12y ago
Arguably the most important mathematician of the second half of the 20th century

auntienomen 12y ago

It's difficult to understate Grothendieck's impact on modern mathematics. His work touches everything from stochastic PDE to number theory. In algebraic geometry, where he had the most impact, it is difficult to so much as think about the subject without using his ideas. His personal story is also interesting and unique. Pierre Cartier recently published an appreciation of his life and work -- Alexander Grothendieck: A Country Known Only By Name -- which is well worth the read even if you aren't a mathematician. http://inference-review.com/article/a-country-known-only-by-name http://inference-review.com/article/a-country-known-only-by-...

dil8 12y ago

Translation here: https://www.reddit.com/r/math/comments/2m82zw/reports_are_coming_in_of_the_death_of_alexandre/cm1wt6u https://www.reddit.com/r/math/comments/2m82zw/reports_are_co...

myg204 12y ago

Sad news, such an original individual and truly a giant of Mathematics. To imagine he invented Lebesgue measure theory on his own in his late teens. I remember reading that when he was sent to study under Schwartz and Dieudonne in Nancy (if i remember correctly), he solved the equivalent of seven phd thesis problems in nine months. His work with radical ecology is also highlighted in the article.

lkesteloot 12y ago

A good eulogy here from economist Steve Landsburg: http://www.thebigquestions.com/2014/11/13/the-rising-sea/ http://www.thebigquestions.com/2014/11/13/the-rising-sea/ "... the greatest of all modern mathematicians and arguably the greatest mathematician of all time ..."

pfortuny 12y ago

May he rest in peace. His honest fight against war (teaching in Hanoi while bombings were going on, leaving the IHES after learning that NATO supported it, etc.) are an example of honesty. One may disagree with his positions (as I do) but we shall always be impressed by his acts. I am obviously leaving the maths apart: we hope to stand on his shoulders, we and many future generations.

conformal 12y ago

while i am generally loathe to comment on HN, i consider it truly sad to see the passing of grothendieck. he was a truly revolutionary mathematician and his contribution to the (hard) science of mathematics cannot be overstated. people who live on principle are rare, and those willing to go without salary as part of that protest are even rarer [1]. [1] - http://www.fermentmagazine.org/Quest88.html http://www.fermentmagazine.org/Quest88.html

hokkos 12y ago

Grothendieck has been a point of interest in me since I read many years ago about his work about generalization of theories, his genius, his hermit life and that he chose to be stateless. Just last Sunday I saw an issue of a scientific magazine about him in a friend's house, and said I loved this guy, it is so strange and sad to learn about his death a few days after.

205guy 12y ago

I am both surprised as how successful he was at remaining obscure, and yet how many on HN were familiar with his work and writings. I was briefly a math major at the university, I studied at a technical school in France, I read a lot on technical forums such as HN where some people seem to know his work, like many I am fascinated by geniuses and their eccentricities, I browse Wikipedia for fun, and yet I was totally unaware of his life and work. Maybe I'd heard his name in passing, but no mention of his talent or writings, or his eccentric life because then I would've remembered his name. I find it sad that he is so obscure, though I see that it was his wish. On the one hand, you want to respect someone who obviously had his own reasons for withdrawal, on the other it seems like a madman's wish to be erased from the history books and even from the annals of science. That's not how science works, and that he thought he could be the exception shows a disjunction. I don't want to imply it was a mental illness, but I'd like to read more to try to understand his state of mind. Now that he lived and died in (relative) obscurity, it won't hurt to learn about him and learn from him.

Bahamut 12y ago
In mathematics, he is far from obscure though. His name is all over algebraic geometry. Any graduate student who has taken an algebraic geometry class would absolutely know of him, and most should have heard of his name from various algebra or topology courses.
omaranto 12y ago
He's as famous as posible for a mathematician: every mathematician knows about him, even probably most undergraduate math majors, but only a few non-math people have heard of him.

malaporte 12y ago

Wow. I've never heard about him, but reading the article I realized he used to live not 500 meters away from my house (a long time ago).

barbudorojo 12y ago

I wonder if there is some hidden factor in the minds of those mathematicians that allows them to think so easily in abstract terms. I have always needed to begin with simple examples and from them to go to generalities. Perhaps they learned all the easy stuff when they were children and all those years of their adolescence were employed to enrich their minds with more and more general and powerful concepts and frameworks. Then, when they mature they no longer needs to think about the concrete, for then those abstracts ideas are as concrete like a tree for a child. That vision is only achievable for those able to live alone, to wander with their thoughts, to lose themselves in the island of their inner world. Their inner world and ideas are more real and concrete than what we see with our eyes. They don't see a prime number, a prime ideal is only point in the spectrum of a ring, their math ideas are so colorful that nobody can reach that peak without forgetting where we come from and that the earth is our planet. They live in a different math heaven always climbing to reach the book (Erdos ideal).

toreoft 12y ago

Rest in peace. - A great matematician and even also a great philosopher.

toreoft 12y ago

Rest in peace. A great matematician and even also a great philosopher.

toreoft 12y ago

Rest in peace. A great matematician and even also a great philosopher.