I agree with everyone who recommends the stellar "On Proof and Progress in Mathematics". It a gem that could only have been written by a lovely man. http://arx

I agree with everyone who recommends the stellar "On Proof and Progress in Mathematics". It a gem that could only have been written by a lovely man. http://arxiv.org/pdf/math/9404236v1.pdf http://arxiv.org/pdf/math/9404236v1.pdf The parts about how communication works inside mathematical specialties and about the difference between math and computer programming are worth their weight in gold. Really, everyone, just do yourself a favor and read it – all the way to its astonishing final section and beautiful ending. It doesn't require you to remember any math.