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Alex Kontorovich on the Absolute Truth of Pure Math

The Joy of x

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How to Prove Parallel Postulate From Other Geometries?

Euclid is a very tight lipped writer. He doesn't show you his emotions at all. And the fact that he uses these 25 or whatever propositions before he even deploys the use of the fifth the parallel shows you that he's kind of squeamish about that one. This will not enlighten anything in the real world, in so far as anyone can tell, in asking this question. Aha, yes. The act of asking this question forces you to discover spherical and hyperbolic geometry. If some one just asked this question of me, maybe my younger self, i would say, i don't know, who really cares? Like, cannot be proved. Can

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