An odd perfect numberAs a joke I once proclaimed: There is an odd perfect number but the universe is too small to contain a description of it.It was a joke,but it had a serious point. There are (for suitable interpretations of "are") truths that are inexpressible; conversely there are expressible truths with inexpressible proofs. It goes down like this: The world being finite, there are limits to the number of mathematical statements that will ever be created and likewise to the number of mathematical proofs. They are not synchronized; that is, there are statements that are provably true in principle that aren't provable in practice (and will never be proved) because the proof would not fit in the universe. Mathematics only nibbles at the edge of infinity, and the borders are irregular. This page was last updated July 1, 2004. |