Questions tagged [ho.history-overview]
History and philosophy of mathematics, biographies of mathematicians, mathematics education, recreational mathematics, communication of mathematics.
212 questions with no upvoted or accepted answers
36
votes
0
answers
2k
views
History of the Proj construction in algebraic geometry
Projective geometry was introduced by fifteenth century Renaissance painters (like Alberti, da Vinci and Dürer) in the guise of perspective theory, although one could argue that Pappus was already ...
- 48.5k
35
votes
0
answers
2k
views
Next steps on formal proof of classification of finite simple groups
While people are steaming ahead on finessing the proof of the classification of finite simple groups (CFSG), we have a formal proof in Coq of one of the first major components: the Feit-Thompson odd-...
- 37.2k
23
votes
0
answers
3k
views
Origins of the Nerve Theorem
Recently, I've read two papers which have cited the Nerve Theorem, one crediting Borsuk with the result and another Leray. Here is the question:
Who was the first to prove the Nerve Theorem?
- 16k
22
votes
0
answers
754
views
What was the "stormy discussion" about differential Galois theory at IHES?
In Kazuo Okamoto and Yousuke Ohyama's paper "Mathematical works of Hiroshi Umemura", Annales de la faculté des sciences de Toulouse Mathématiques, XXIX, no. 5 (2020) pp. 1053-1062, there is ...
- 2,476
19
votes
0
answers
800
views
Eckmann-Hilton argument / Grothendieck
In terse terms, the “Eckmann-Hilton argument” says that a monoid in the category of monoids is commutative. It is essentially used, for example, to prove that homotopy groups of topological groups are ...
- 13.2k
18
votes
0
answers
654
views
Who first noticed the duality for finite groups?
A.A.Kirillov in section 12.3 of his "Elements of the Theory of Representations" writes that the first "symmetric" duality theory for non-commutative groups was the theory for finite groups. In short ...
- 7,476
18
votes
0
answers
2k
views
History of the functor of points
Until now, I thought the functor of points approach was introduced by Grothendieck at the 1973 Buffalo seminar.
However, in this note by Lawvere the author writes:
"I myself had learned the ...
- 10.8k
17
votes
0
answers
1k
views
Jets of sections of vector bundles expressed by symmetrized iterated covariant derivatives - who did it first?
The (non-unique) bundle isomorphism between the bundle $J^r E$ of $r$-th order jets of sections of a vector bundle $\pi:E\rightarrow M$ and the direct sum $$\bigoplus^r_{k=0}\vee^kT^*M\otimes E\...
- 9,248
16
votes
0
answers
493
views
What was Gill and Ladner’s joke about P=NP?
Comments on this question point out that John Gill (of the famous Baker–Gill–Solovay paper) lists a joke on his online CV:
A Joke about P =?NP
Gill, J., T., Ladner, R.
1973
Googling, I can’t find ...
- 23.9k
16
votes
0
answers
619
views
Reference request for Grothendieck's work on "Integration with values in a topological group"
Disclaimer. This question was already asked in Mathematics Stack Exchange (see the link here). I wanted the question to be migrated here but I was told by a moderator that a question that old is ...
user57432
16
votes
0
answers
2k
views
Why did Bourbaki not use universal algebra?
I have seen a discussion about Bourbaki’s usage of categories before. So let me ask a different question: why did he not use universal algebra?
Well, universal algebra is not much older than category ...
16
votes
0
answers
1k
views
Galois theory timeline (II)
This question is a sequel. I structured the previous one around Emil Artin's classic treatment of Galois theory from the 1940s, though making clear some reservations of my own about whether Artin ...
- 12.8k
14
votes
0
answers
735
views
Who stated and proved the "Hopf lemma" on bilinear maps?
If $A\otimes B\rightarrow C$ is a nondegenerate linear map, where $A, B, C$ are vector spaces over an algebraically closed field, then $\dim C\ge \dim A + \dim B -1$.
Nondegenerate here means that ...
- 1,881
13
votes
0
answers
378
views
What is known about G. A. Croes
G. A. Croes is the author of the first description of the 2-opt moves heuristic for improving non-optimal traveling salesman tours:
Croes, G. A. “A Method for Solving Traveling-Salesman Problems.” ...
- 14.3k
13
votes
0
answers
3k
views
Is there any correspondence between Gödel and Kreisel that supports Kreisel's observation that Gödel changed his mind about his 1938 set theory note?
At a conference in 1965 there were some interesting comments made by Kreisel and Mostowski asserting that Gödel later changed his mind regarding his1938 note on his set theory results (see Problems in ...
- 481