Book: The Mathematical Experience / Philip J. Davis, Reuben Hersh

The Mathematical Experience BookI’ve lived under the illusion that Mathematics is a body of “proven” knowlege, all of which can be completely and consistently derived logically from a set of “self-evident” axioms. This misconception is referred to, in one aspect at least, as the “Euclid Myth”. Although I was vaguely aware of the existence of some pesky paradoxes and had heard of Gödel’s Incompleteness Theorem, I had never given any thought to these problems myself until recently. I started reading The Road To Reality by Roger Penrose, which begins not with math or physics, but some bold philosophical statements. I found I couldn’t continue without exploring my own questions further. What is logic and mathematical knowlege really based on? This book was an excellent guide through this jungle – a jungle that has pulled the rug out from under centuries of human mathematical thought, without necessarily invalidating it at all.

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