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History and philosophy of mathematics, biographies of mathematicians, mathematics education, recreational mathematics, communication of mathematics.
43
votes
Mathematical "urban legends"
Here's something that keeps me up at night:
During the Russian revolution, there is a story of a mathematician (I've heard Igor Tamm may be the one) who was mistaken by rebels to be a communist spy. …
6
votes
Which mathematical ideas have done most to change history?
My vote goes for calculus and in particular the Fundamental Theorem of Calculus (FTC) and Stirling's approximation for the factorial. Can you imagine doing basic mathematics in any scientific field wi …
4
votes
A gamma function identity
This is not yet an answer, but in terms of $B$ (beta) functions, one has
$B(a,1-a-b)+B(b,1-a-b)+B(a,b)=\displaystyle\frac{B\left(\frac{b}{2},\frac{1}{2}\right)}{B\left(\frac{1-a}{2},\frac{a+b}{2}\rig …
57
votes
What would you want to see at the Museum of Mathematics?
1) A high quality 3D movie (with glasses!) of sphere eversion, like this one
2) A Let's Make a Deal game show room, where people can play the game to death on a computer until they believe that they …
4
votes
What are some famous rejections of correct mathematics?
Riemann's work with curved spaces, particularly their applications to physics was at least 40 years ahead of it's time. He pushed forward ideas that space is perhaps curved and that forces such as gra …
9
votes
(Preferably rare) Audio/Video recordings of famous mathematicians?
Here is a long video about Richard Courant. Apparently he was one of the first people to own a video camera so there is some really old footage of some of the fathers of modern mathematics. If you scr …