Gödel's theorem, for most working mathematicians, is like a sign warning us away from logical terrain we'd never visit anyway.I loved his "curse of the slogan" (emphasis mine). So true! Not sure what Gödel's famous Incompleteness theorem actually says? Read the whole piece. It's very readable, and Ellenberg does a great job of explaining it.
What is it about Gödel's theorem that so captures the imagination? Probably that its oversimplified plain-English form—"There are true things which cannot be proved"—is naturally appealing to anyone with a remotely romantic sensibility. Call it "the curse of the slogan": Any scientific result that can be approximated by an aphorism is ripe for misappropriation. The precise mathematical formulation that is Gödel's theorem doesn't really say "there are true things which cannot be proved" any more than Einstein's theory means "everything is relative, dude, it just depends on your point of view." And it certainly doesn't say anything directly about the world outside mathematics, though the physicist Roger Penrose does use the incompleteness theorem in making his controversial case for the role of quantum mechanics in human consciousness. Yet, Gödel is routinely deployed by people with antirationalist agendas as a stick to whack any offending piece of science that happens by. A typical recent article, "Why Evolutionary Theories Are Unbelievable," claims, "Basically, Gödel's theorems prove the Doctrine of Original Sin, the need for the sacrament of penance, and that there is a future eternity." If Gödel's theorems could prove that, he'd be even more important than Einstein and Heisenberg!
Ellenberg is a math professor at the UW-Madison and author of a novel, The Grasshopper King. His blog Quomodocumque touches on math, language, baseball, refrigerator death and assorted Madisoniana. The blog also has a link to his Slate columns. Did he catch my eye with kind words like this about Letter from Here? You bet! Blogrolling works -- you can find him on mine.