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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 …

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 …

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 …

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 …

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 …

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 …

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 …

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 …

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 …

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 …

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 …

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 …

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 …

If a definition can be tentative, it can also be wrong. Lakatos has been mentioned already. This is actually a fairly basic issue in understanding how "formal" mathematics advances. Something as funda …

The Wikipedia article Odd order theorem is worth reading.