Visions in Mathematics

Part of the series Modern Birkhäuser Classics pp 118-161

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  • Misha GromovAffiliated withThe Courant Institute Mathematical Sciences, NYU

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Our Euclidean intuition, probably inherited from ancient primates, might have grown out of the first seeds of geometry in the motor control systems of early animals who were brought up to sea and then to land by the Cambrian explosion half a billion years ago. The primates' brain had been idling for 30–40 million years. Suddenly, in a flash of one million years, it exploded into growth under the relentless pressure of sexual-social competition and sprouted a massive neocortex (70% neurons in humans) with an inexplicable capability for language, sequential reasoning and generation of mathematical ideas. Then Man came and laid down space on papyrus in a string of axioms, lemmas and theorems around 300 B.C. in Alexandria.