4 ms·

Alexander Grothendieck, the secret genius of mathematics

95 points by ar7hur 12y ago

ar7hur 12y ago
Here is the original work "Récoltes et Semailles" from Grothendieck (PDF, French): http://lipn.univ-paris13.fr/~duchamp/Books&more/Grothendieck/RS/pdf/RetS.pdf http://lipn.univ-paris13.fr/~duchamp/Books&more/Grothendieck... Brace yourself, it's about 1000 thousand pages, sometimes very technical. The post I translated is a very short summary.
- ZoF 12y ago
  1000 thousand pages
myg204 12y ago
The CERN talk referred to in the article is also available as an mp3 audio here: https://archive.org/details/AlexandreGrothendieck-UneVieDigneDtreVcue https://archive.org/details/AlexandreGrothendieck-UneVieDign... It's in French, but very touching to hear A. Grothendieck's voice.
tel 12y ago
I don't yet know how to say it, but I quit my PhD for the same reasons expressed by Grothendieck here. I'm not yet interested in talking about it; I feel confident and confused about it. Instead, more, I just felt the need to confess some small sympathy with the ideas expressed in these quotes.
- mietek 12y ago
  I am one-quarter into "Disciplined Minds", a book by John Pilger. It looks like the author may be addressing similar issues. Have you perhaps read this book?
  - tel 12y ago
    I haven't. I will take a look.
  - calibraxis 12y ago
    Minor correction: Jeff Schmidt was the author. (http://disciplined-minds.com/ http://disciplined-minds.com/) (Just in case someone loses a couple minutes searching. :)
    - mietek 12y ago
      Oops. My bad for posting while sleep-deprived. Thanks.
Punoxysm 12y ago
How can someone be a "secret" genius if they are one of the most famous mathematicians of the 20th century and received the field's highest honor? I do not think that word means what you think it means.
- Kabukks 12y ago
  I guess it's because he isn't as widely known to the public as other 'geniuses'. Or at least the people that label him as such feel that he isn't.
ctchocula 12y ago
"In our knowledge of the things of the universe (whether mathematical or otherwise), the power to innovate that lies within us is really nothing but innocence. It is the original innocence that we were all endowed with at birth, that lives inside all of us, but is often the object of our contempt and of our most secret fears. This innocence is what brings together the humility and the audacity that make it possible for us to get to the heart of things, but also allows things to deeply affect us and get under our skin so that they leave a lasting imprint on our minds and souls." Grothendieck's writing is beautifully translated and is a beacon of moral courage.
andyrj 12y ago
Sounds like quite an amazing and brave individual. We need more of his caliber. Is there a translation of his writing available in English? I would be very interested in reading more of his "Crops and Seeds"
cafebeen 12y ago
David Mumford did a great job summarizing his contributions: http://www.dam.brown.edu/people/mumford/blog/2014/Grothendieck.html http://www.dam.brown.edu/people/mumford/blog/2014/Grothendie... On a side note, this was an obituary invited by Nature that was surprisingly rejected for being too technical!
- ddumas 12y ago
  The obituary was too technical for Nature.
- clebio 12y ago
  Thanks for that link. The discussion and comments at the end are fascinating. Sad that STEM is getting dumbed down along with general education. I've been self-learning analysis and differential geometry for a while now, and feel that the way math is taught at the secondary and post-seconardy level -- and just the way the framing of the subject -- does actual damage to our chances of learning it. What I mean is, a lot of so-called higher-level or advanced math is concerned with unifying generalities. Starting with the most limited, simplest instance of sets -- integers -- makes each iteration into more general terrain seem 'difficult'. Whereas, if math education started with the abstract generality (topologies and abstract algebra), any particular constriction to a domain (complex, reals, functions, etc.) wouldn't seem isolated or unique. Anyway, thanks for the reference!

95 points by ar7hur 12y ago

Here is the original work "Récoltes et Semailles" from Grothendieck (PDF, French): http://lipn.univ-paris13.fr/~duchamp/Books&more/Grothendieck/RS/pdf/RetS.pdf http://lipn.univ-paris13.fr/~duchamp/Books&more/Grothendieck... Brace yourself, it's about 1000 thousand pages, sometimes very technical. The post I translated is a very short summary.

ZoF 12y ago
1000 thousand pages

myg204 12y ago

The CERN talk referred to in the article is also available as an mp3 audio here: https://archive.org/details/AlexandreGrothendieck-UneVieDigneDtreVcue https://archive.org/details/AlexandreGrothendieck-UneVieDign... It's in French, but very touching to hear A. Grothendieck's voice.

tel 12y ago

I don't yet know how to say it, but I quit my PhD for the same reasons expressed by Grothendieck here. I'm not yet interested in talking about it; I feel confident and confused about it. Instead, more, I just felt the need to confess some small sympathy with the ideas expressed in these quotes.

mietek 12y ago
I am one-quarter into "Disciplined Minds", a book by John Pilger. It looks like the author may be addressing similar issues. Have you perhaps read this book?
- tel 12y ago
  I haven't. I will take a look.
- calibraxis 12y ago
  Minor correction: Jeff Schmidt was the author. (http://disciplined-minds.com/ http://disciplined-minds.com/) (Just in case someone loses a couple minutes searching. :)
  - mietek 12y ago
    Oops. My bad for posting while sleep-deprived. Thanks.

Punoxysm 12y ago

How can someone be a "secret" genius if they are one of the most famous mathematicians of the 20th century and received the field's highest honor? I do not think that word means what you think it means.

Kabukks 12y ago
I guess it's because he isn't as widely known to the public as other 'geniuses'. Or at least the people that label him as such feel that he isn't.

ctchocula 12y ago

"In our knowledge of the things of the universe (whether mathematical or otherwise), the power to innovate that lies within us is really nothing but innocence. It is the original innocence that we were all endowed with at birth, that lives inside all of us, but is often the object of our contempt and of our most secret fears. This innocence is what brings together the humility and the audacity that make it possible for us to get to the heart of things, but also allows things to deeply affect us and get under our skin so that they leave a lasting imprint on our minds and souls." Grothendieck's writing is beautifully translated and is a beacon of moral courage.

andyrj 12y ago

Sounds like quite an amazing and brave individual. We need more of his caliber. Is there a translation of his writing available in English? I would be very interested in reading more of his "Crops and Seeds"

cafebeen 12y ago

David Mumford did a great job summarizing his contributions: http://www.dam.brown.edu/people/mumford/blog/2014/Grothendieck.html http://www.dam.brown.edu/people/mumford/blog/2014/Grothendie... On a side note, this was an obituary invited by Nature that was surprisingly rejected for being too technical!

ddumas 12y ago
The obituary was too technical for Nature.
clebio 12y ago
Thanks for that link. The discussion and comments at the end are fascinating. Sad that STEM is getting dumbed down along with general education. I've been self-learning analysis and differential geometry for a while now, and feel that the way math is taught at the secondary and post-seconardy level -- and just the way the framing of the subject -- does actual damage to our chances of learning it. What I mean is, a lot of so-called higher-level or advanced math is concerned with unifying generalities. Starting with the most limited, simplest instance of sets -- integers -- makes each iteration into more general terrain seem 'difficult'. Whereas, if math education started with the abstract generality (topologies and abstract algebra), any particular constriction to a domain (complex, reals, functions, etc.) wouldn't seem isolated or unique. Anyway, thanks for the reference!