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The Wikipedia article Odd order theorem is worth reading.

Armand Borel's Bourbaki Seminar 121 Groupes algébriques is from 1955, and uses "drapeau" (page 7). (It's online at archive.numdam.org.) This may not be the earliest occurrence, but there is a good rea …

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 …

A recent question on the history of Galois theory wasn't the most satisfactory. But the historical issues do seem quite attractive. They relate to innovation, and to exposition. There is a perspective …

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 …

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 …

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 …

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 …

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 …

I feel the answer is obviously "yes", and indeed that much of 19th century mathematics was lost, in a serious sense, for much of the 20th century. I was struck recently by discovering that Henry Fox T …

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 …

It seems clear enough to me that Grothendieck was (perhaps is) sui generis as a mathematician, something that can be said of a few other mathematicians in each of the 19th and 20th centuries (e.g. Ram …

Interesting take, but a bit hard to make into proper history, I should think. Start with the idea that, post-Gauss, 19th century mathematics was mainly not about number theory. This could be hard to …

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 …

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 …