Provable is a rigorous concept (from a given set of axioms). Proven is not. How do you know that the rules of proof have been followed? How do you know that the people or computer program telling you have didn't commit some error. Etc. —Dan
On May 27, 2016, at 7:57 PM, Allan Wechsler <acwacw@gmail.com> wrote:
I agree with Rich here; I'm not sure I see the problem. Suppose somebody conjectures that some predicate P is true of all positive integers, and manages to prove P(n) for n > 6 x 10^54. Then somebody betters the bound to n > 2 x 10^41. Then a third person throws half the Amazon Cloud at the problem for six months and announces that they have checked P(n) for all n up to that bound. Is the conjecture not proven yet? What would it take?