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Results tagged with ho.history-overview
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user 19276
History and philosophy of mathematics, biographies of mathematicians, mathematics education, recreational mathematics, communication of mathematics.
26
votes
What is the oldest open math problem outside of number theory?
Stability of the Solar System ?
(Question often attributed to Newton in Opticks, 1717 or 1730.)
To further specify as requested by Timothy Chow, make it a few ($3\leqslant N\leqslant 8$) planets under …
- 31.5k
13
votes
The orders of the exceptional Weyl groups
My guess: these orders were first computed by Coxeter in his thesis
The polytopes with regular-prismatic vertex figures, Philos. Transactions (A) 229, 329–425 (1930). ZBL56.1119.03,
$E_l$ as $(\math …
- 31.5k
14
votes
Whence “uniform distribution”?
It’s far from true. For one thing, Crofton in his famous paper (1869, p. 198) speaks of points
“distributed with uniform density over the plane” (my bold). Moreover he refers to prior discussion in Th …
- 31.5k
34
votes
Accepted
Serre’s comment on Hurwitz: connecting FLT to points of finite order on elliptic curves
On page 322 of
Serre, Jean-Pierre, The works of Wiles (and Taylor,(\dots)). I., Séminaire Bourbaki. Volume 1994/95. Exposés 790-804. Paris: Société Mathématique de France, Astérisque. 237, 319-332, Ex …
- 31.5k
13
votes
Accepted
Why are distributions "tempered"?
Can someone explain, why in English the name "tempered" wins?
Presumably because that’s how the inventor himself translated it (French past participle to English past participle), on e.g. p. 188 of
…
- 31.5k
23
votes
First use of term "Hilbert's Nullstellensatz"
I think it is indeed van der Waerden, but in the earlier paper [1926], where he sounds just like one does when introducing terminology: translated from p. 143,
the proposition in question is an almos …
- 31.5k
17
votes
Accepted
Why are faithful actions called faithful and who first called them faithful?
The German word is treu, and I would look to papers by Hermann Weyl for its introduction. E.g. Quantenmechanik und Gruppentheorie (1927, p. 16):
Da das Gruppenschema aus der Darstellung abstrahiert w …
- 31.5k
9
votes
Accepted
Élie Cartan's paper "Les groupes réels simples, finis et continus" of 1914
The paper and its progeny are discussed at length in Helgason (1978, p. 537):
In his paper [2] Cartan classifies the simple Lie algebras over R. His method, which required formidable computations, us …
- 31.5k
5
votes
Mathematicians with both “very abstract” and “very applied” achievements
Mikhail L. Zeitlin, or Gel’fand-Zeitlin basis fame (1950), later switched to “game theory, the theory of automata, computer science, physiology, and mathematical methods of biology”.
8
votes
Unknown work of Nöbeling on topological/Hausdorff dimension
It seems to be:
Nöbeling, G., Hausdorffsche und mengentheoretische Dimension, Ergebnisse math. Kolloquium Wien 3, 24-25 (1931). ZBL57.0749.02.
Google shows the first and sporadically the second pa …
- 31.5k
13
votes
Accepted
Origin of the term 'index of a subgroup'
The short answer is Cauchy, with only justification: “for short”. Burnside’s Theory of groups of finite order (1897) has a useful glossary stating, p. 382 (my bold):
The ratio of the order of a su …
- 31.5k
6
votes
History of the notion of irreducible representation
I convert my comments to an answer per Abdelmalek’s request:
Dieudonné attributes the classification of irreducible $sl_2$-modules to Cayley (1856).
Also the theory of spherical and cylindrical harm …
- 31.5k
16
votes
Why are parabolic subgroups called "parabolic subgroups"?
The naming (attributed by Borel as quoted by @GjergjiZaimi) happened quite publicly, in Roger Godement : Groupes linéaires algébriques sur un corps parfait, Sémin. Bourbaki 13 (1960/61), Exp. No. 206, …
- 31.5k
5
votes
Mathematicians with both “very abstract” and “very applied” achievements
Just came across a page of 25+ of Mark Goresky’s Engineering publications.
2
votes
Tweetable Mathematics
If $S^n$ x $S^n$ minus diag & antidiag self deforms and each (x,y) → (y,x) then n = 1, 3, 7, 15, 31, 63 or 127 (Kervaire invariant).
(Stolen from the epigraph of I. M. James, The topology of Stiefel …