Professor Sir Timothy Gowers' 2012 lecture: Hilbert's Dream

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The talk starts with David Hilbert's notion of mechanising mathematics. After briefly reviewing why this is a lost cause, Tim turns to a much weaker notion of "mechanisation". Can we write computer programs that have "flashes" of genius? Tim gives some nice examples of minor flashes of genius that might actually be discoverable by systematic methods. And he spills the beans on how mathematicians hide their tracks to make their talents appear more mysterious than they really are.