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Here is a proof based on the well-ordering of the positive integers rather than the FTA: To begin with, we observe that if $\sqrt{2}$ is rational, then there is some positive integer q such that q × …

One nice example (from topology) is Tychonoff's Theorem (that a product of compact spaces is compact). No matter how many times I see it, I find the classic proof based on the (Alexandre Subbase Lemma …

Élie for sure. The formula is derived in Les systèmes differentiels extérieurs et leur applications géométriques which was probably written before Henri was born. BTW, here is a very short proof that …

Here is a suggestion, to get the idea across in an informal way---it is what I always tell the students when I introduce the triangle inequality: I tell them that its essential content, and the way it …

The OP says: " ...Recently, Palais wrote about it in the Notices but he only treats the old story from the 1950s and seems not to be aware of Olver’s facts." Actually, I am aware of Olver's work and …

Spivak's five volume "Comprehensive Introduction to Differential Geometry" still gets a lot of use---particularly the first two volumes.

I have been involved with an online Mathematical Museum (called unsurprisingly The Virtual Math Museum, and located at http://VirtualMathMuseum.org). There is also an interactive version in the form o …

The talk in question was given as part of a celebration (this past weekend) of the 80th anniversary of the founding of the Institute for Advanced Study in Princeton. As you might guess there were quit …

Well, it bears a copyright date of 1902, but I think Eduoard Goursat's Cours D'Analyse is such an excellent text that it should be mentioned. I have the English translation, Mathematical Analysis, tra …

As is well-known, in the 1820s both Bolyai and Lobachevsky showed, at long last, the independence of the Parallel Postulate from the rest of the axioms of Euclidean geometry by developing what we now …

I hope it is OK to mention "A Disorienting Look at Euler's Theorem on the Axis of a Rotation" even if I am a joint author, particularly if I admit that none of the authors thought up the cute title--- …