"In 1931, the Czech-born mathematician Kurt Gödel demonstrated that within any given branch of mathematics, there would always be some propositions that couldn't be proven either true or false using the rules and axioms ... of that mathematical branch itself. You might be able to prove every conceivable statement about numbers within a system by going outside the system in order to come up with new rules and axioms, but by doing so you'll only create a larger system with its own unprovable statements. The implication is that all logical system of any complexity are, by definition, incomplete; each of them contains, at any given time, more true statements than it can possibly prove according to its own defining set of rules."
one possible interpretation of that in simple english is this...even the most basic math is inconsistent. that in itself does not bode well for higher math or for any other form of learning that has a mathematical basis.
for someone to have discovered something so paradoxical, it was devastating that he died of the very paradox himself. how he reconciled being one of the greatest unknown mathematician to have ever lived with the fact that what he had done all his life was inherently flawed, is well beyond me. i figure it would be the same if the pope himself discovered a proof for the non existence of god. godel stopped eating because he thought that someone was plotting to kill him by poisoning his food so he stopped eating altogether.
one of my favorite stories is a very well written piece about kurt godel by josh potter.
Pindeldyboz: An Incompleteness Theorem by Josh Potter
it is fairly short and a highly recommended read.
closing remarks - never say "logic is stupid" not because there might be a giant math nerd trolling the forums
but because that very statement might be recursively paradoxical in the nth degree!
enjoy the evening
