The incomplete Gödel

Is Kurt Gödel's famous incompleteness theorem completely useless?
March 10, 2005
There’s a wonderful picture (alas not this one) of Albert Einstein , smoking his pipe, bundled against the cold, smiling at a much-more-serious Kurt Gödel, the strange and transcendental mathematician, as they walked home from the Institute for Advanced Study. Einstein once said he joined the faculty of the Institute, in part so he could walk home with Gödel. The folks in Princeton could look out their windows of an afternoon and see two of the greatest brains that ever existed walking down the street. In Slate, Princeton mathematician Jordan Ellenberg explains that while Gödel’s work, especially his incompleteness theorem, is the kind of stuff that romantics in mathematics and scientists adore (“Given any system of axioms that produces no paradoxes, there exist statements about numbers which are true, but which cannot be proved using the given axioms”), it doesn’t mean much in the real world. Ellenberg is writing because a sometime-neighbor, philosopher and novelist Rebecca Goldstein, has a new book out, Incompleteness, and he disagrees with her on just how important the theorem is. (Goldstein is best known for two novels, including the simply amazing Mind-Body Problem and Mazel, the latter having nothing to do with science but has one of the great endings in recent literary fiction). People have even used the theorem to demonstrate the validity of faith or disprove evolution. Goldstein elevates the Incompleteness Theorem to relativity and quantum mechanics, but Ellenberg says it ain’t so, it bears no relevance to the real world. You can be a full-blown professional mathematician or theoretical physicist and not mess with Gödel at all. You can be a journalist and have the same privilege. But Einstein found Gödel a wonder—as did Doug Hofstadter—despite the fact the two men seemed to come from different planets. You can get a headache from all of this.