Paul Cohen, who proved that one can imagine infinite sets larger than the set of integers but smaller than the set of real numbers without leading to contradiction, and who won (to date) the only Fields Medal ever awarded for work in logic, died yesterday. He was 72. You can read more about his achievements here or in Lecture 3.
I only saw Cohen once, when he participated in a panel discussion at Berkeley about Hilbert’s problems from 1900. He came across as funny and likable — which was good since, to my mind, it might as well have been Euclid or Aristotle sitting there trading quips with the other panelists. (As Rebecca Goldstein wrote about Gödel, the man whose work paved the way for Cohen’s: “I once found the philosopher Richard Rorty standing in a bit of a daze in Davidson’s food market. He told me in hushed tones that he’d just seen Gödel in the frozen food aisle.”)
Like Cantor himself, Cohen started out not as a logician but as an analyst. The famous story is that Cohen was once teasing a logician friend about how there were no meaty, nontrivial open problems in logic — certainly nothing that an analyst couldn’t swoop in and solve. “Oh yeah?” the friend shot back. “I’d like to see you prove the independence of the Continuum Hypothesis!” So that’s what he did. I’d love to know whether the story has any grain of truth to it.