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History and philosophy of mathematics, biographies of mathematicians, mathematics education, recreational mathematics, communication of mathematics.
12
votes
Accepted
Random Walk anecdote.
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 …
61
votes
Mathematical "urban legends"
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 …
55
votes
Mathematical "urban legends"
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 …
19
votes
Mathematicians failing to solve problems despite having all methods required
I suppose plenty of people could have developed non-Euclidean geometry, had they not been so intent on proving that no such thing existed.
15
votes
Attribution of the quote "a mathematician is someone who is cautious in the presence of the ...
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 …
18
votes
In "splendid isolation"
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 …
11
votes
Accepted
Origin of the term "Diophantine equation"
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 …
0
votes
Notable mathematics during World War II
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 Some of it is out of date, but it's still a good place to start the study of multigrade equations (equations in integ …
4
votes
How did "Ore's Conjecture" become a conjecture?
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 …
2
votes
The different Branches of Arithmetic
"Has anybody quoted that passage in this meaning later?" Does this qualify?
Jennifer Geldard - Torch songs: Ambition, distraction, uglification, and derision
59
votes
What did Ramanujan get wrong?
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 …
21
votes
The half-life of a theorem, or Arnold's principle at work
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 …
17
votes
The half-life of a theorem, or Arnold's principle at work
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 …
23
votes
Extremely messy proofs
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 …
10
votes
Extremely messy proofs
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.