(This post was originally published on the NKS Forum.)
Last Friday (April 28, 2006) would have been Kurt Gödel’s 100th birthday. I agreed to try to write something about it for publication in a newspaper … which had the dual misfeatures that (a) I had to compress what I was saying and (b) that it didn’t actually get done…
Still, I thought people on the Forum might find my draft interesting … so here it is. Please recognize that this wasn’t polished for final publication…
When Kurt Gödel was born—one hundred years ago today—the field of mathematics seemed almost complete. Two millennia of development had just been codified into a few axioms, from which it seemed one should be able almost mechanically to prove or disprove anything in mathematics—and, perhaps with some extension, in physics too.
Twenty-five years later things were proceeding apace, when at the end of a small academic conference, a quiet but ambitious fresh PhD involved with the Vienna Circle ventured that he had proved a theorem that this whole program must ultimately fail.
In the seventy-five years since then, what became known as Gödel’s theorem has been ascribed almost mystical significance, sowed the seeds for the computer revolution, and meanwhile been practically ignored by working mathematicians—and viewed as irrelevant for broader science.
The ideas behind Gödel’s theorem have, however, yet to run their course. And in fact I believe that today we are poised for a dramatic shift in science and technology for which its principles will be remarkably central.
Gödel’s original work was quite abstruse. He took the axioms of logic and arithmetic, and asked a seemingly paradoxical question: can one prove the statement “this statement is unprovable”? Continue reading