note
bunnyman
<i>As for what I know that I know: I'd limit that to mathematics of a particular formal sort, that I've proved myself, along the lines of "given these axioms, and these rules of logic, this conclusion follows". I'd like to see a project to prove all known maths in this way, using declared rules of logic and steps small enough to permit computer verification - it boils down to nothing but symbolic manipulation. (I even registered "axiomattic.org" for a while, hoping to start the project myself.)</i>
<p>What you describe sounds like <a href="http://en.wikipedia.org/wiki/Hilbert%27s_program">Hilbert's Program</a>. Unfortunately, <a href="http://en.wikipedia.org/wiki/G%F6del%27s_incompleteness_theorem">Godel's Incompleteness Theorem</a> states that we can never find an all encompassing axiomatic system which is able to prove all mathematical truths, but no falsehoods.
379224
379267