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History and philosophy of mathematics, biographies of mathematicians, mathematics education, recreational mathematics, communication of mathematics.
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 …
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.
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 …
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 …