22
votes
Why are étale morphisms called "étale"?
From Milne's site:
There are two different words in French, "étaler", which means spread out or displayed and is used in
"éspace étalé", and "étale", which is rare ...
- 221
17
votes
Accepted
Did Grothendieck really say that he felt "clumsy, even oafish, wandering painfully up an arduous track"?
Yes, the quote is essentially authentic. This is from a typeset version "Récoltes et Semailles", specfically from "2.2 L’importance d’être seul." (To find the document online should be possible ...
- 1,481
16
votes
Accepted
How did Grothendieck encounter and adopt the categorical language?
Grothendieck's familiarity with the categories predates Kansas. In 1948-1949 he attended Séminaire Cartan at École Normale Supérieure, where he "took the liberty of speaking to Cartan, as if to ...
- 78.4k
14
votes
Accepted
Alexander Grothendieck's "stolen" correspondence in 1985?
The Grothendieck Circle site suggests a more innocent explanation for the loss these letters.
Having left Montpellier in 1984....
In May of that year [1985] a
secretary informed him that his ...
- 7,119
13
votes
Accepted
Who were the attendees to the SGA3 seminar?
Only one left (of those visible) to be identified. The man in the middle of C. Chevalley and P. Samuel.
The seminar is not very likely to be SGA 5 but SGA 3 ("Schémas en groupes") by M. ...
- 146
9
votes
Accepted
Why are étale morphisms called "étale"?
The use of étale predates SGA, and "spread out" fits Grothendieck’s idea of all-encompassing topos, "vast" and "slack", better than usual, as these things go. The name of étale morphisms derives from ...
- 78.4k
7
votes
Accepted
Where can I find Grothendieck's letter of resignation from Bourbaki?
Here is an English translation of Grothendieck's letter dated October 9, 1960.
Here is the letter in its original French.
May also be of interest, Grothendieck's stolen correspondence of 1985.
- 7,119
6
votes
What is known about Grothendieck's capacity of work?
"At the time, he had the capacity to be able to sleep when he wanted to, and for the number of hours he wanted to, in order to take up his work all the better afterward. In fact this capacity for work ...
- 602
5
votes
Why are étale morphisms called "étale"?
The mathematical terminology "étalé" [spread out] was used by Grothendieck in his 1957 Tohoku paper, and was preexisting at that time.
Grothendieck, A. (1959). Technique de descente et théorèmes d'...
- 151
5
votes
Grothendieck's approach to solving problems
"The way to understand a mathematical problem is to express it in the mathematical world natural to it -that is, in the topos natural to it. Each topos has a natural cohomology, simply taking the ...
- 53
4
votes
Accepted
What is the history of the Scheme theory before Grothendieck?
I don't think I can give any substantive answer but here are relevant places to study this topic at least for historical traces of development:
Séminaire Henri Cartan - Many contributions here can be ...
- 1,781
3
votes
How did Grothendieck encounter and adopt the categorical language?
In the "Esquisse Thématique des Principaux Travaux Mathématique 4.a Algèbre catégorique", Grothendieck says:
En fait, de facon continuelle depuis 1953, je me suis senti dans l'obligation, ...
- 402
3
votes
Did Grothendieck have any thoughts on foundations of mathematics?
I don't know about what you read, but in practice Grothendieck expressed thoughful concerns about foundations.
See for example the concept of a Grothendieck universe, invented by Grothendieck to avoid ...
- 189
2
votes
Where can I find Grothendieck's letter of resignation from Bourbaki?
I have since found the original source. It appeared in the second part of a two-part obituary published in 2016 for the Notices of the AMS: Vol 63, No.4. Though I believe the link provided by @NWR is ...
- 113
1
vote
Who thinks Grothendieck was the greatest?
Peter Scholze previously said in an interview with a German newspaper that Grothendieck was his role model. Pierre René Deligne, a disciple of Grothendieck, also said Grothendieck was his role model ...
- 11
1
vote
Grothendieck and the Gaussian integral
It is an apocraphal story, so it's difficult to know just how much credence one should place on it. There is a similar story of when Grothendieck was asked to give a prime number, he suggested 57 - ...
- 3,788
1
vote
Grothendieck and elementary topos
The main evidence of this seems to be that whenever Grothendieck says topos, he means Grothendieck topos (unless someone can find a contradicting reference). However, it doesn't seem to be the case ...
- 189
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