7 ms·

Who Is Alexander Grothendieck? (2008) [pdf]

74 points by benbreen 6y ago

MaxBarraclough 6y ago
This PDF weighs 11MB, for no good reason (there are few images in the document but nothing to justify 11MB). The web server is pitifully slow. Curiously, curl tells me the HTTPS cert has expired, but Firefox doesn't. Unfortunately I wasn't able to find a decent mirror.
- deleted 6y ago
  [deleted]
- yesenadam 6y ago
  This 500KB version is the first result on google scholar searching by title. https://www.jeanpierrevarlenge.com/app/download/826854410/WhoIsAGrothendieck.pdf https://www.jeanpierrevarlenge.com/app/download/826854410/Wh... Also I think it should say (2006) not 2008: > This article is a translation of the article “Wer ist Alexander Grothendieck?”, which originally appeared in German in the Annual Report 2006 of the Mathematics Research Institute in Oberwolfach, Germany
  - MaxBarraclough 6y ago
    That's much better, thanks. (I overthought it and tried googling for a short extract from the article, should have done the obvious thing.)
- leoh 6y ago
  Becuase curl uses system certs as opposed to ones bundled with the browser. Also this is off-topic, read the article, he was an incredible human being.
- generationP 6y ago
  AMS Notices have gone crazy with their file size; not sure why. Are they generating them from PS?
m4lvin 6y ago
If you read German or just want more pictures, here are slides and handouts from a talk about Grothendieck https://jonathanweinberger.wordpress.com/2014/08/27/alexander-grothendieck-necessary-solitude/ https://jonathanweinberger.wordpress.com/2014/08/27/alexande...
seesawtron 6y ago
>> Alexander Grothendieck was a mathematician who became the leading figure in the creation of modern algebraic geometry. His research extended the scope of the field and added elements of commutative algebra, homological algebra, sheaf theory and category theory to its foundations, while his so-called "relative" perspective led to revolutionary advances in many areas of pure mathematics. He is considered by many to be the greatest mathematician of the 20th century. Wiki: https://en.wikipedia.org/wiki/Alexander_Grothendieck https://en.wikipedia.org/wiki/Alexander_Grothendieck
- throwgeorge 6y ago
  what is the point of this? usually this type of comment is when there's something inscrutable in the title of a post but the title of this post is literally "Who Is Alexander Grothendieck?"; if you didn't know who he was before clicking you certainly know afterwards.
  - seesawtron 6y ago
    When the link doesn't load and yet you are stuck with this boiling question in the title, you start to look for answers in the comments to decide how long you are willing to wait for the said link.
bollu 6y ago
I am currently learning modern algebraic geometry (scheme theory) from Ravi Vakil's algebraic geometry in the time of COVID: https://math216.wordpress.com/agittoc-2020/ https://math216.wordpress.com/agittoc-2020/. It's a great ongoing course that offers amazing intuition into scheme theory. We're divided into "working group(oid)s" where we discuss the mathematics and solve the weekly homework assigned by Ravi. Best of all, anyone [all over the world] can join in on the fun! You get added to a discord and a zulip group, where all the discussion happens. My favourite article about Grothendieck is the one titled "The Grothendieck-Serre Correspondence": https://webusers.imj-prg.fr/~leila.schneps/corr.pdf https://webusers.imj-prg.fr/~leila.schneps/corr.pdf This article describes both the mathematics, and the lives of Grothendieck and Serre through their exchange of letters. It's powerfully written, and provides great insight into both the mathematics and the two as people. The last line of the article is absolutely beautiful.
- markhollis 6y ago
  I'm also learning some algebraic geometry at the moment: Some resources I have used are: * video lectures by Richard Borcherds * Lecture notes by Andreas Gathmann (https://www.mathematik.uni-kl.de/~gathmann/class/alggeom-2002/alggeom-2002.pdf https://www.mathematik.uni-kl.de/~gathmann/class/alggeom-200...) * This blog: https://rigtriv.wordpress.com/ag-from-the-beginning/ https://rigtriv.wordpress.com/ag-from-the-beginning/ * An infinite large napkin, by Evan Chen (https://venhance.github.io/napkin/Napkin.pdf https://venhance.github.io/napkin/Napkin.pdf) It also found it helpful to learn some (algebraic) number theory, to get a sense of where some of the motivation comes from (e.g. elliptic curves, modular forms). Grothendieck's work is abstract, but he was always motivated by concrete problems (e.g. Weil conjectures).
- yeellow 6y ago
  Thanks for sharing, it looks really interesting, too bad I did not know about it earlier (but I will still try to watch the lectures). Are there more initiatives like that one? I know Terry Tao had open lectures online, so it is probably popular nowadays.
ur-whale 6y ago
Grothendieck's work is, for me, a rather perfect example of what's happened in the 20th century to mathematics, where the boundaries of knowledge have been pushed so hard and so far that there is almost no hope for anyone to even begin to understand the substance of the work outside a very tiny circle of people who pretty much dedicated life to that arcane corner of the field. I really wish vulgarization was an actual scientific disciple rather than being done in an ad-hoc fashion by people who happen to be good at it. I also really wish I could read a vulgarized summary of Grothendieck's body of work, and specifically: . why everyone is so excited about the work . what potential practical application do (or will) exist.
- impendia 6y ago
  As another commenter mentioned, currently Ravi Vakil is teaching a course in modern algbraic geometry. The course is largely based on Vakil's book in progress, which he titled The Rising Sea, after a quote from Grothendieck: > I can illustrate the ... approach with the ... image of a nut to be opened. The first analogy that came to my mind is of immersing the nut in some softening liquid, and why not simply water? From time to time you rub so the liquid penetrates better, and otherwise you let time pass. The shell becomes more flexible through weeks and months — when the time is ripe, hand pressure is enough, the shell opens like a perfectly ripened avocado! . . . > A different image came to me a few weeks ago. The unknown thing to be known appeared to me as some stretch of earth or hard marl, resisting penetration ... the sea advances insensibly in silence, nothing seems to happen, nothing moves, the water is so far off you hardly hear it ... yet finally it surrounds the resistant substance. Here is, roughly speaking, a theorem that illustrates what modern algebraic geometry is good for. Theorem. If you have two conic sections in the plane, which don't share a common component, then they intersect in exactly four points. Here a "conic section" is just any quadratic equation in two variables, e.g. x^2 + y^2 + 3xy + 4x = 1. "Common component" means that the conic sections are identical or overlap in an entire line. Now, here are some "examples". Concentric circles, e.g. x^2 + y^2 = 1 and x^2 + y^2 = 4. They don't intersect at all, right? Ah, except you forgot to count points over the complex numbers, where they do. Tangency, e.g. y = x^2 and x^2 + (y - 1)^2 = 1. These curves are tangent at (0, 0), so you have to count this point with multiplicity. One major goal of modern algebraic geometry is to wrap these sorts of considerations into the foundations. So you have to work a lot harder to even say what a conic section is, or what it means for two of them to intersect. But, once you've laid the foundations in this manner, there are no special cases.
bhopballooo 6y ago
Stories like these suggest to me that genius level creativity equals intrinsic motivation plus time. They also demonstrate that such motivation cannot be adjusted at will. It amounts to one's deepest understanding of where personal progress or best direction lies. Thus when Grothendieck or Swedenborg had religious experiences later in life their technical output ceased because their motivations had changed irrevocably.
- ChrisLomont 6y ago
  > their technical output ceased I think Grothendieck was still writing multi-1000-page mathematical manuscripts up until he died. I know there are such unpublished manuscripts floating around the mathematical community. As Wikipedia states " he lived secluded, still working tirelessly on mathematics until his death in 2014". https://en.wikipedia.org/wiki/Alexander_Grothendieck https://en.wikipedia.org/wiki/Alexander_Grothendieck
  - tangue 6y ago
    Some of his manuscripts can be downloaded here https://grothendieck.umontpellier.fr/archives-grothendieck/# https://grothendieck.umontpellier.fr/archives-grothendieck/# but according to this (reliable) radio program [1] he was fascinated by the devil and only wrote about this at the end of his life [1] https://www.franceculture.fr/emissions/la-conversation-scientifique/alexandre-grothendieck-un-mathematicien-qui-prit-la-tangente https://www.franceculture.fr/emissions/la-conversation-scien...
  - bhopballooo 6y ago
    Good point and it's not cut and dried but the character of his output had changed to the extent that it was not published in technical journals as it had been: >Relatively little of his work after 1960 was published by the conventional route of the learned journal, circulating initially in duplicated volumes of seminar notes; his influence was to a considerable extent personal. His influence spilled over into many other branches of mathematics, for example the contemporary theory of D-modules. (It also provoked adverse reactions, with many mathematicians seeking out more concrete areas and problems.) My guess would be that he was working on himself rather than on the mathematics. Mathematics was merely the means and the medium. But I haven't read the material...!
throwawaymanbot 6y ago
He really shouldnt be Grothen anybodys dieck.

74 points by benbreen 6y ago

This PDF weighs 11MB, for no good reason (there are few images in the document but nothing to justify 11MB). The web server is pitifully slow. Curiously, curl tells me the HTTPS cert has expired, but Firefox doesn't. Unfortunately I wasn't able to find a decent mirror.

deleted 6y ago
[deleted]
yesenadam 6y ago
This 500KB version is the first result on google scholar searching by title. https://www.jeanpierrevarlenge.com/app/download/826854410/WhoIsAGrothendieck.pdf https://www.jeanpierrevarlenge.com/app/download/826854410/Wh... Also I think it should say (2006) not 2008: > This article is a translation of the article “Wer ist Alexander Grothendieck?”, which originally appeared in German in the Annual Report 2006 of the Mathematics Research Institute in Oberwolfach, Germany
- MaxBarraclough 6y ago
  That's much better, thanks. (I overthought it and tried googling for a short extract from the article, should have done the obvious thing.)
leoh 6y ago
Becuase curl uses system certs as opposed to ones bundled with the browser. Also this is off-topic, read the article, he was an incredible human being.
generationP 6y ago
AMS Notices have gone crazy with their file size; not sure why. Are they generating them from PS?

m4lvin 6y ago

If you read German or just want more pictures, here are slides and handouts from a talk about Grothendieck https://jonathanweinberger.wordpress.com/2014/08/27/alexander-grothendieck-necessary-solitude/ https://jonathanweinberger.wordpress.com/2014/08/27/alexande...

seesawtron 6y ago

>> Alexander Grothendieck was a mathematician who became the leading figure in the creation of modern algebraic geometry. His research extended the scope of the field and added elements of commutative algebra, homological algebra, sheaf theory and category theory to its foundations, while his so-called "relative" perspective led to revolutionary advances in many areas of pure mathematics. He is considered by many to be the greatest mathematician of the 20th century. Wiki: https://en.wikipedia.org/wiki/Alexander_Grothendieck https://en.wikipedia.org/wiki/Alexander_Grothendieck

throwgeorge 6y ago
what is the point of this? usually this type of comment is when there's something inscrutable in the title of a post but the title of this post is literally "Who Is Alexander Grothendieck?"; if you didn't know who he was before clicking you certainly know afterwards.
- seesawtron 6y ago
  When the link doesn't load and yet you are stuck with this boiling question in the title, you start to look for answers in the comments to decide how long you are willing to wait for the said link.

bollu 6y ago

I am currently learning modern algebraic geometry (scheme theory) from Ravi Vakil's algebraic geometry in the time of COVID: https://math216.wordpress.com/agittoc-2020/ https://math216.wordpress.com/agittoc-2020/. It's a great ongoing course that offers amazing intuition into scheme theory. We're divided into "working group(oid)s" where we discuss the mathematics and solve the weekly homework assigned by Ravi. Best of all, anyone [all over the world] can join in on the fun! You get added to a discord and a zulip group, where all the discussion happens. My favourite article about Grothendieck is the one titled "The Grothendieck-Serre Correspondence": https://webusers.imj-prg.fr/~leila.schneps/corr.pdf https://webusers.imj-prg.fr/~leila.schneps/corr.pdf This article describes both the mathematics, and the lives of Grothendieck and Serre through their exchange of letters. It's powerfully written, and provides great insight into both the mathematics and the two as people. The last line of the article is absolutely beautiful.

markhollis 6y ago
I'm also learning some algebraic geometry at the moment: Some resources I have used are: * video lectures by Richard Borcherds * Lecture notes by Andreas Gathmann (https://www.mathematik.uni-kl.de/~gathmann/class/alggeom-2002/alggeom-2002.pdf https://www.mathematik.uni-kl.de/~gathmann/class/alggeom-200...) * This blog: https://rigtriv.wordpress.com/ag-from-the-beginning/ https://rigtriv.wordpress.com/ag-from-the-beginning/ * An infinite large napkin, by Evan Chen (https://venhance.github.io/napkin/Napkin.pdf https://venhance.github.io/napkin/Napkin.pdf) It also found it helpful to learn some (algebraic) number theory, to get a sense of where some of the motivation comes from (e.g. elliptic curves, modular forms). Grothendieck's work is abstract, but he was always motivated by concrete problems (e.g. Weil conjectures).
yeellow 6y ago
Thanks for sharing, it looks really interesting, too bad I did not know about it earlier (but I will still try to watch the lectures). Are there more initiatives like that one? I know Terry Tao had open lectures online, so it is probably popular nowadays.

ur-whale 6y ago

Grothendieck's work is, for me, a rather perfect example of what's happened in the 20th century to mathematics, where the boundaries of knowledge have been pushed so hard and so far that there is almost no hope for anyone to even begin to understand the substance of the work outside a very tiny circle of people who pretty much dedicated life to that arcane corner of the field. I really wish vulgarization was an actual scientific disciple rather than being done in an ad-hoc fashion by people who happen to be good at it. I also really wish I could read a vulgarized summary of Grothendieck's body of work, and specifically: . why everyone is so excited about the work . what potential practical application do (or will) exist.

impendia 6y ago
As another commenter mentioned, currently Ravi Vakil is teaching a course in modern algbraic geometry. The course is largely based on Vakil's book in progress, which he titled The Rising Sea, after a quote from Grothendieck: > I can illustrate the ... approach with the ... image of a nut to be opened. The first analogy that came to my mind is of immersing the nut in some softening liquid, and why not simply water? From time to time you rub so the liquid penetrates better, and otherwise you let time pass. The shell becomes more flexible through weeks and months — when the time is ripe, hand pressure is enough, the shell opens like a perfectly ripened avocado! . . . > A different image came to me a few weeks ago. The unknown thing to be known appeared to me as some stretch of earth or hard marl, resisting penetration ... the sea advances insensibly in silence, nothing seems to happen, nothing moves, the water is so far off you hardly hear it ... yet finally it surrounds the resistant substance. Here is, roughly speaking, a theorem that illustrates what modern algebraic geometry is good for. Theorem. If you have two conic sections in the plane, which don't share a common component, then they intersect in exactly four points. Here a "conic section" is just any quadratic equation in two variables, e.g. x^2 + y^2 + 3xy + 4x = 1. "Common component" means that the conic sections are identical or overlap in an entire line. Now, here are some "examples". Concentric circles, e.g. x^2 + y^2 = 1 and x^2 + y^2 = 4. They don't intersect at all, right? Ah, except you forgot to count points over the complex numbers, where they do. Tangency, e.g. y = x^2 and x^2 + (y - 1)^2 = 1. These curves are tangent at (0, 0), so you have to count this point with multiplicity. One major goal of modern algebraic geometry is to wrap these sorts of considerations into the foundations. So you have to work a lot harder to even say what a conic section is, or what it means for two of them to intersect. But, once you've laid the foundations in this manner, there are no special cases.

bhopballooo 6y ago

Stories like these suggest to me that genius level creativity equals intrinsic motivation plus time. They also demonstrate that such motivation cannot be adjusted at will. It amounts to one's deepest understanding of where personal progress or best direction lies. Thus when Grothendieck or Swedenborg had religious experiences later in life their technical output ceased because their motivations had changed irrevocably.

ChrisLomont 6y ago
> their technical output ceased I think Grothendieck was still writing multi-1000-page mathematical manuscripts up until he died. I know there are such unpublished manuscripts floating around the mathematical community. As Wikipedia states " he lived secluded, still working tirelessly on mathematics until his death in 2014". https://en.wikipedia.org/wiki/Alexander_Grothendieck https://en.wikipedia.org/wiki/Alexander_Grothendieck
- tangue 6y ago
  Some of his manuscripts can be downloaded here https://grothendieck.umontpellier.fr/archives-grothendieck/# https://grothendieck.umontpellier.fr/archives-grothendieck/# but according to this (reliable) radio program [1] he was fascinated by the devil and only wrote about this at the end of his life [1] https://www.franceculture.fr/emissions/la-conversation-scientifique/alexandre-grothendieck-un-mathematicien-qui-prit-la-tangente https://www.franceculture.fr/emissions/la-conversation-scien...
- bhopballooo 6y ago
  Good point and it's not cut and dried but the character of his output had changed to the extent that it was not published in technical journals as it had been: >Relatively little of his work after 1960 was published by the conventional route of the learned journal, circulating initially in duplicated volumes of seminar notes; his influence was to a considerable extent personal. His influence spilled over into many other branches of mathematics, for example the contemporary theory of D-modules. (It also provoked adverse reactions, with many mathematicians seeking out more concrete areas and problems.) My guess would be that he was working on himself rather than on the mathematics. Mathematics was merely the means and the medium. But I haven't read the material...!

throwawaymanbot 6y ago

He really shouldnt be Grothen anybodys dieck.