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So Turing and Godel realized there could never be a mathematical "theory of everything," Levin said.

This was a blow to people who wanted to believe mathematics held only pure and absolute "truth," Levin said.

Turing also had a tortured life, for different reasons.

He was a homosexual who lived in a society where that wasn't tolerated. He was arrested when the police learned of his relationship with another man and forced to accept injections of estrogen. Two years later, he committed suicide by eating an apple laced with cyanide.

But before he died, Turing also thought about artificial intelligence. He came up with the "Turing test" which is used today to measure the intelligence of computer "bots," or programs that converse with people.

That's cool stuff. I did my undergrad thesis on Goedel's theorem. It sums up to: any logical system that is sufficiently powerful to express the basic mathematical functions of subtraction, division, multiplication and addition is inherently self-contradictory because you can create a statement that says that it cannot be proven.

The implications are mind-boggling for classic mathematics and physics. There's another cool book out by Emmanual Goldberg called "Goedel Escher and Bach" that ties the theorem to Bach's music and Escher's drawings. The book you linked looks interesting, thanks LiT.

Dennis