Gödel proved that there are true sentences that cannot be proved.

Suppose I told you that the Goldbach conjecture is one of those. (The Goldbach conjecture supposes that every even integer number can be expressed as the sum of two odd primes.)

Is that logically possible? (And, no, I haven't proved it!)

If you could prove that the GC (Goldbach Conjecture) is true but not provable, it would mean that no matter how much/long I looked for a counterexample, I wouldn't be able to find one, and this itself would be a proof of the GC.(?)

Can this be right?

Posted by Oskar on 2004-08-22 11:40:41