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Results tagged with ho.history-overview
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History and philosophy of mathematics, biographies of mathematicians, mathematics education, recreational mathematics, communication of mathematics.
33
votes
Is there another controversial statement by Grothendieck apart from 57 being prime?
Yes, he did.
In his Récoltes et semailles, volume I posthumously edited by Gallimard in 2022 he reminisces (in footnote 68, page 522) about his first encounter with $\pi$ as a child:
"La valeur appro …
- 47.5k
80
votes
Examples of conjectures that were widely believed to be true but later proved false
In 1908 Steinitz and Tietze formulated the Hauptvermutung ("principal conjecture"), according to which, given two triangulations of a simplicial complex, there exists a triangulation which is a common …
- 4,713
110
votes
Did Bourbaki write a text on algebraic geometry?
Wrong!
Here is Bourbaki document on algebraic geometry, taken from the now available Master's Archives: click on Autres rédactions, then on Chap.I Théorie globale élémentaire (91 p.)
This prelimina …
- 47.5k
53
votes
Pseudonyms of famous mathematicians
Rainich=Rabinowitsch (of trick fame : cf. Nullstellensatz).
Here is an anecdote related by Bruce P. Palka, Editor of American Mathematical Monthly
in Vol.111 (2004) of that journal (page460).
Rai …
- 119
14
votes
Fundamental Examples
In the theory of holomorphic functions of several variables, Hartogs's theorem that any holomorphic function on a punctured open set of $\mathbb C^n$ ($n\geqslant 2$) can holomorphically be continued …
- 6,210
5
votes
Accepted
Two implicit references in Serre's *Groupes de Galois : le cas abélien*
I certainly don't claim that I can answer your questions authoritatively , but here are two small remarks.
1) Samuel's book is certainly an excellent guess: it is actually the only textbook in Fr …
- 47.5k
14
votes
Why and how did preschemes become schemes?
Dear Charles, Dieudonné and Grothendieck themselves changed their terminology in the second edition of EGA I, published by Springer Verlag in 1971. At the end of their Avant-propos, on page 3, they wr …
- 47.5k
170
votes
Most memorable titles
The flattering lie You Could Have Invented Spectral Sequences by Timothy Y. Chow.
- 47.5k
14
votes
Accepted
A mathematical idea "abstract enough to be useless for physics"
Dear Jérôme, I doubt that Grothendieck ever said that.
However, in an analogous vein, Jean Leray, a brilliant French mathematician, was taken prisoner by the Germans in 1940 and sent to Oflag XVIIA …
- 47.5k
6
votes
Accepted
Why did the word "exterior" get chosen for the idea of "exterior derivative"?
I) The term exterior multiplication ("äussere Multiplication") is due to Grassmann, who introduced the term in his book (written in 1844)
Die Wissenschaft der extensiven Grösse oder die Ausdehnungsl …
- 47.5k
88
votes
Widely accepted mathematical results that were later shown to be wrong?
In 1882 Kronecker proved that every algebraic subset in $\mathbb P^n$ can be cut out by $n+1$ polynomial equations.
In 1891 Vahlen asserted that the result was best possible by exhibiting
a curve in …
- 47.5k