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4 votes

Group theory with grep?

As Derek Holt suggested in a comment, it seems Thurston was indeed thinking of word acceptors that returned normal forms for elements of automatic groups. From a 1989 research report of his titled ...
  • 365
0 votes

Where can I find that Weil suggested a cohomology theory for characteristic $p>0$?

As already mentioned in the comments it is very likely that Weil's heuristics appear in "Numbers of solutions of equations in finite fields", Bull. Amer. Math. Soc. 55(5): 497--508 (May 1949)...
17 votes

Where are Serre’s lectures at Collège de France to be found?

Most of my lectures have been taken down (hand written) and copies are available from Inst. Henri Poincaré. See Numdam CJP Serre. JPS
  • 171
2 votes
Accepted

Terminology associated with mathematical induction

Not really an answer (too long for a comment) but I hope that this will be helpful: In Jeff Miller's "Earliest Uses of Some Words of Mathematics" (https://mathshistory.st-andrews.ac.uk/...
  • 14.5k
2 votes

Birth of a mathematical journal: a question inspired in a letter by Gösta Mittag-Leffer

For best practices, you can consult the list at the Free Journal Network, which at present includes 36 journals in mathematics that offer diamond open access, meaning that they are free for authors ...
9 votes

Is the number of "breakthroughs" in mathematics decreasing, as it is claimed to be in other sciences?

I think that the picture is complex, and I'm sure that the two (currently) top comments by David Roberts and Brendan McKay, although providing arguments in apparently opposite directions, are both ...
3 votes

Is the number of "breakthroughs" in mathematics decreasing, as it is claimed to be in other sciences?

If it all, I would say that the number of breakthroughs is increasing. Here is more anecdotal evidence that supports the graph posted by Carlo Beenakker. On 23rd November 2022 Terence Tao posted on ...
3 votes

Origin of tropical mathematics

I asked Christian Choffrut and Dominique Perrin this question today. They essentially told me the following: certainly, the name tropical comes in honour of the Brazilian mathematician Imre Simon; and ...
13 votes

Is the number of "breakthroughs" in mathematics decreasing, as it is claimed to be in other sciences?

Quanta Magazine has an article on 2022's Biggest Breakthroughs in Math: "In 2022, mathematicians solved a centuries-old geometry question, proved the best way to minimize the surface area of ...
19 votes
Accepted

Is the number of "breakthroughs" in mathematics decreasing, as it is claimed to be in other sciences?

Q: Is the number of "breakthroughs" in mathematics decreasing? To get some quantitative feel for the question I considered the Timeline of mathematics on Wikipedia. Not all entries are "...
1 vote

Is the number of "breakthroughs" in mathematics decreasing, as it is claimed to be in other sciences?

It is quite easy to see why innovation is slowing down in many academic fields, as compared, say to the sixties. The sixties were a time where the population of students increased a lot in many ...
1 vote

Algebraic graph invariant $\mu(G)$ which links Four-Color-Theorem with Schrödinger operators: further topological characterizations of graphs?

The following embeddability characterization for $\mu(G)\le 5$ is merely a conjecture, but I think it fits the question: Conjecture (van der Holst, [1]): $\mu(G)\le 5$ if and only if $G$ is 4-flat. ...
  • 11.2k
11 votes
Accepted

Reference request for recurrence relation of division polynomials

These recurrences are stated explicitly in Weber's Lehrbuch der Algebra (published in 1908). See volume 3, section 58, page 200. Weber doesn't give a citation to them, so it's hard to know if they ...
  • 19.1k
2 votes

Reference request for recurrence relation of division polynomials

An early reference is Morgan Ward, Memoir on elliptic divisibility sequences (1948). (See equations 4.5 and 4.6.)
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 ...
5 votes

Is "Cartan's magic formula" due to Élie or Henri?

Actually it seems that this formula was proved by Théophile De Donder in 1911, as you can see in his paper in Bulletins de la Classe des Sciences de l'Académie Royale de Belgique : https://www....

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