When I arrived at Princeton, the first thing I did when I got to Princeton was — there used to be these things called telephone books in the old days, and there was a Princeton Community phonebook in orange and black, and I thought — and the first thing I did was I thought “Oh, I wonder if Godel is in there,” and there it was Godel, K. Godel, and he was on Linden Lane and I just hopped on my bike and rode over to Godel’s house, and there I got one of the biggest surprises of my life, because there were those two plastic flamingo, those little kitschy things and there they were stuck, so this is like the greatest logician since Aristotle, and there were these two flamingos on the lawn, which I blamed immediately on Mrs. Godel and I’m sure it was Mrs. Godel.1 So, I mean I was already arrived as a graduate student pretty obsessed with Godel and just smitten, smitten with the proof, and with what it was — and it is. It’s unique in the history of mathematics. I guess Turing’s work, which follows Godel’s is a little — it’s in the same vein, but Godel was interested in what makes mathematics true, that’s the basic question philosophies ask. And he wanted to somehow get a mathematical proof that would imply what math is about, which is so audacious.2 It’s just so good.
And he was an undergraduate at the University of Vienna when he hatched this incredibly audacious plan, and then he sort of did it, he did something or other. He certainly proved the incompleteness theorems, but what it means in terms of what mathematics is, there’s still tremendous controversy about that, but he sure did something amazing.