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Cover of Proofs and Refutations Proofs and Refutations
Imre Lakatos (posthumously)
ed. John Worrall & Elie Zahar
Cambridge University Press, 1976

If you will be teaching, studying, or just doing mathematics, you should read this book.

Cover of Mathematical Apocrypha Mathematical Apocrypha
Steven G. Krantz
The Mathematical Association of America, 2002

A fun, light read that consists of many, very short, amusing anecdotes, nearly all of which involve contemporary mathematicans. I quite enjoyed it.