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History and philosophy of mathematics, biographies of mathematicians, mathematics education, recreational mathematics, communication of mathematics.
22
votes
Has philosophy ever clarified mathematics?
Turing has already been mentioned in previous excellent answers as someone whose ideas sit at the boundary of philosophy and mathematics, conventionally understood. I want to mention Ludwig Wittgenst …
6
votes
What would you want to see at the Museum of Mathematics?
I come across "mind reading" games based on elementary number theory from time to time; e.g. http://www.digicc.com/fido/. It bugs me a bit when people are wowed by such tricks, but not enough to sit …
6
votes
What would you want to see at the Museum of Mathematics?
I think holographs are a compelling technology that seems like magic except in the light of some pretty cool mathematics. If some kind of learning module could get these ideas across, it'd be neat.
3
votes
Online math history lectures
I just came across these BBC podcasts the other day. These are almost certainly more populist than you had in mind, but given the title of your question I thought I would throw it up here anyway. Th …