Gödel's Proof

Gödel's Proof is short 118 page essay that explains and introduces in as near layman's terms as possible, Godel's Incompeteness Theorem. The short of it is that Gödel's therem shows that there is a fundamental limit to any formal axiomatic system; like those that try to formalize mathematics.

This is a profound statement in philosophy, logic, and mathematics since it means that no absolute proof of consistency for a deductive system (like mathematics) is possible by that system. Thus there is an endless number of true statements that cannot be formally deduced from any given set of axioms by a closed set of rules of inference. It does not mean however that there cannot be a possible finitistic proof outside of the system, but even today, no one appears to have an idea of what that proof would be like.

The description of Gödel numbering which is the mapping of all meta-mathematical statements within the calculus of mathematics is very elegantly and clearly explained. And I will never forget that 243,000,000 in Gödel numbering is 0=0.