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ThomasR comments on Learning the foundations of math - Less Wrong

4 Post author: jsalvatier 24 October 2010 07:29PM

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Comment author: ThomasR 27 October 2010 07:39:52AM *  2 points [-]

A very excellent recent book, with fascinating new ideas and superior readable intros into many themes, is the new edition of Manin's "course in mathematical logic". So I'd recommend that. But: Why "foundations"? Like "foundational themes" in th. physics, "foundations" are not an appropriate place to start, they are a bundle of very advanced research areas whose intuitions and ideas come from core fields of research. "Foundations" in the sense of "what is it, really?" can be exprerienced probably much better by studying a good piece of core math, like number theory. Cox' "Primes of the form x^2 +n*y^2" or Khinchin's "Three Pearls of Number Theory" is what I would suggest. If your mind prefers geometry, I'd suggest to browse a good library for some of the great projective geometry textbooks from the early 20th century.