[donh]

I think you don't understand what mathematics is, let alone pure mathematics. Mathematics is proof. If there's no proof, than it's something other than mathematics.

See Russell's theory of types for various failures of closure of discrete formal systems, Then see Godel's proof in response to Russell, for starters. See also the proof of the four-color theorem that was wrong, but held up for several hundred years. See the developments of Aristotalian syllogistic forms that were wrong, but were accepted for 1000 years. See also the proof in Principia Mathematica that was wrong, but wasn't noticed for 60 years. Then you can explain whether or not a proof generated by a computer, which no human has been able to verify, is a proof, or not.

Your statement is vastly incorrect. There is way more math, pure or otherwise, than there is proof. And a proof exists that this discrepency cannot be cured.

[AmishDude]

Uh, anybody can get a proof wrong. The trail for Fermat's LT is littered with them, including holes by Wiles himself. To my knowledge, Appel and Haken's proof of 4-color was not wrong, just unverifiable. Robertson and Seymour, et al. nailed it down finally.

Tell ya what, submit a paper to a math journal with no proofs. Claim that there is "way more math, pure or otherwise, than there is proof" and try not to be offended by what they send back.