December 2011
Beginner
240 pages
6h 45m
English
Content preview from The Universal Computer
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Hilbert to the Rescue
into a contradiction using their usual methods, and I’ve proved it using
methods of which even you approve.” Or as von Neumann actually put it,
“Proof theory should construct, so to speak, classical mathematics on an
intuitionistic basis and in this way reduce intuitionism ad absurdum.”
24
Among the mathematical “treasures” his methods would rescue, Hilbert
emphatically included Cantor’s transfinite numbers, of which he said, “This
appears to me to be the most admirable flower of the mathematical intellect
and in general one of the highest achievements of purely rational human
activity.”
25
Dismissing the criticisms of Brouwer and Weyl, he proclaimed,
“No one shall be able to drive us from the paradise that Cantor created for
us.”
26 ...
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I'm always learning. So when I got on to O'Reilly, I was like a kid in a candy store. There are playlists. There are answers. There's on-demand training. It's worth its weight in gold, in terms of what it allows me to do.