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It's an interesting question. Conservatism about negative numbers as such continued indeed into the early decades of the 19th century. But that was mainly a philosophical position. Pedagogic conservat …

I think it is Auguste Aubry. The L'Enseignement Mathématique volume is on archive.org, and there is an earlier paper in it on hyperbolic functions by Aubry. The material and location suggests a school …

Quotation from Gauss: "...the greatest thing is purely mathematical thinking: this is worth much more than the application of mathematics." In conversation in 1854, a few months before his death, th …

For Weil, the Mordell-Weil theorem; for Siegel, the theorem on integral points on curves (genus at least 1). Think about the use of abelian varieties here. Mordell-Weil is sort of about making Mordell …

Post-Artin, you could read about it in English! No, that's not fair, but few authors writing in English on the "theory of equations" handled it. An exception would be L. E. Dickson, and I looked at on …

At some point between Harald Bohr's foundation of the theory of almost periodic functions, and the major paper of van der Corput that J. E. Littlewood regarded as the most technical paper in the whole …

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 shou …

There was a recent question on intuitions about sheaf cohomology, and I answered in part by suggesting the "genetic" approach (how did cohomology in general arise?). For historical material specific t …

In 1974, also, Pierre Deligne had a Fields Medal "withheld", after his proof of the Weil conjectures. That was hypothesised to be prejudice against non-peer reviewed aspects of the proof. I wouldn't r …

If you Google for "diagramme du serpent" it becomes plausible that it was a diagram in Cartan-Eilenberg first of all, before a lemma. Interesting example of how Bourbaki became the standard grad stude …

http://en.wikipedia.org/wiki/Hilbert%27s_fifth_problem is a decent survey. In general in the discussion of "status" of the Hilbert problems, there are at least two recognisable routes. Route A is the …

One can contrast Hilbert's 7th problem (http://en.wikipedia.org/wiki/Hilbert%27s_seventh_problem) on transcendence with his views on Fermat's last theorem. These are reported somewhere, namely that th …

My version, quickly, would be that he envisaged "points" that were abstractions. Whence "logical space" as came in first around 1900 (long discussion) as implied by Boolean algebra, which he also anti …

Edited: One point is that Hodge's original version of the conjecture was wrong, and in a couple of ways. You do need rational coefficients (integral is too much to ask for, see ref below). Also a mor …

It's a tendentious question, certainly. It might mean, if Bourbaki, let us say, had had more of an interest in lattice theory, that the French word for "lattice" of this kind would be more familiar at …