

Surprises in Mathematics and Theory - amichail
http://rjlipton.wordpress.com/2009/09/27/surprises-in-mathematics-and-theory/

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10ren
When I work on a proof, I worry about whether I've _really_ proven it. How can
I prove the proof? Yes, there are automatic theorem verifiers/provers (things
like COQ), that guarantee correctness... provided you haven't introduced any
other errors in the transcription, and the theorem verifier itself is
perfectly bug-free...

It makes me think that an obsession with absolute truth is a misplaced
priority, and perhaps a better view is that mathematics does not provide
absolute proofs, but just a measure of certainty - like any other field, just
much higher. And the real point of mathematics is something that you can sense
is true, that is beautiful, and works correctly whenever you try it out.

I would be interested to know how any professional mathematicians here see it.

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parse_tree
I think the 'Incompleteness Theorem'

[http://en.wikipedia.org/wiki/G%C3%B6del%27s_incompleteness_t...](http://en.wikipedia.org/wiki/G%C3%B6del%27s_incompleteness_theorems)

might address what you're describing.

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bdr
No, 10ren is merely talking about correctness within the given system.

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larryfreeman
Great post from a mathematician on the surprises in mathematics.

