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The anecdote is about Polya, and it is in his contribution, Two incidents, to the book, Scientists at Work: Festschrift in Honour of Herman Wold, edited by T Dalenius, G Karlsson, and S Malmquist, pub …

This one happened - I was there (as an observer, not a principal). Only the names have been changed. X was Professor A's first doctoral student, and their relations weren't good. Rumor had it that t …

I have no idea whether this one is true - I heard it at Harvard, around 1970. The story goes that a PhD student was so sure no one would ever read his dissertation that he stuck in the middle of it an …

I suppose plenty of people could have developed non-Euclidean geometry, had they not been so intent on proving that no such thing existed.

Eric Temple Bell, The Development of Mathematics, page 76: "Like Euclid in his explicit statement of the parallel postulate, Archimedes had the true mathematician's caution in the presence of the obvi …

When Kepler was trying to work out the orbits of the planets, he wrote something to the effect of, "If only they were ellipses!" as he knew the Greeks had worked that theory out 1500 years earlier. Of …

There is a website, Earliest Known Uses of Some of the Words of Mathematics. Some entries are, DIOPHANTINE ANALYSIS (named for Diophantus of Alexandria) occurs in French in a letter of March 1770 fr …

Albert Gloden's book, Mehrgradige Gleichungen, was published in Groningen in 1944. Some of it is out of date, but it's still a good place to start the study of multigrade equations (equations in integ …

I don't have an answer, but another example. Number theorists will be familiar with "Lehmer's conjecture," but Lehmer made no conjecture; he confined himself to reporting the facts as he knew them. Al …

"Has anybody quoted that passage in this meaning later?" Does this qualify? Jennifer Geldard - Torch songs: Ambition, distraction, uglification, and derision

Bruce Berndt writes, Most of Ramanujan's mistakes arise from his claims in analytic number theory, where his unrigorous methods led him astray. In particular, Ramanujan thought his approximations an …

I think the number of examples is roughly half the number of published theorems, so this could be a very long list, indeed. But that won't stop me from making a contribution or two. The Cauchy-Daven …

In 1983, at the request of a referee, I added to a paper of mine a proof that (under certain hypotheses which need not detain us here) a certain norm could be given as a certain resultant. Since then …

You may want to look into the history of the de Branges proof of the Bieberbach conjecture. Reader's Digest version: his original proof was over 100 pages, but others studying his proof got it down to …

Nowadays, no one looks at Lambert's proof of the irrationality of $\pi$. Mostly you will see (variations of) the far nicer proof by Niven.