Mark Gritter (markgritter) wrote,
Mark Gritter

True but Unproven

Somebody finally corrected all the flawed answers to this Quora question (Is there anything in mathematics that holds true but can't be proven?), by pointing out that Godelization doesn't say anything about our ultimate ability to prove something. We can always adopt a new axiom schema that permits us to prove the statement of interest, or adopt informal but "convincing" methods.

But I think Alon Amit's excellent answer still suffers from viewing proofs as mathematical constructs. If we view them as computational processes then it is trivial to demonstrate that there are true statements which we cannot prove--- because no compact representation of the theorem can exist in our universe, which has less than 2^(10^100) bits to work with.
Tags: mathematics
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