Von Neumann was a famous mathematician.

This was before he was famous. But he badly wanted to be famous. The reason he made the comment was to show everybody that he’d understood the paper.

But the comment was…What was it? Incorrect?

He probably wasnt the only one there who thought that mathematics itself had been brought into question. Sometimes it takes a while to sort things out. Mathematics is constantly being questioned. That’s what it’s for. Some good mathematicians have left the discipline. Exceeding even the number who have wound up in the madhouse.

Why is that?

I thought that’s why we were here.

You no longer do math.

No. Well, maybe on the problem of problems. Which wont go away.

Which is?

The foundational problem. What to do about Frege. The Grundlagen. The beginning and the end. What are we doing and how do we know. An insight. Does something know? Is that possible? And if it does what must we become in order for it to tell us? The Langlands project. Things that are not ever going to tell me what I want to know.

I see.

I dont think so. Mathematics is ultimately a faith-based initiative. And faith is an uncertain business.

I’m not sure I understand. Mathematics as what? A sort of spiritual undertaking?

It’s just that I dont have something else to call it. I’ve thought for a long time that the basic truths of mathematics must transcend number. It is after all a rather ramshackle affair. For all its considerable beauty. The laws of mathematics supposedly derive from the rules of logic. But there is no argument for the rules of logic that does not presuppose them. I suppose one thing that might evoke the analogy with the spiritual is the understanding that the greatest spiritual insights seem to derive from the testimonies of those who stand teetering in the dark.

I dont see how mathematical truths could transcend number.

I know.

But you’re nevertheless a fan of Gödel.

Yes. Huge fan. I agree with Oppenheimer’s view.

Are most of your heroes mathematicians?

Yes. Or heroines.

Who else do you admire?

It’s a long list.

Okay.

Cantor, Gauss, Riemann, Euler. Hilbert. Poincaré. Noether. Hypatia. Klein, Minkowski, Turing, von Neumann. Hardly even a partial list. Cauchy, Lie, Dedekind, Brouwer. Boole. Peano. Church is still alive. Hamilton, Laplace, Lagrange. The ancients of course. You look at these names and the work they represent and you realize that the annals of latterday literature and philosophy by comparison are barren beyond description.

Those names are not familiar to me.

I know.

Are any of them women?

Emmy Noether. She was a great mathematician. One of the greatest. One of the founders of mathematical physics. There are others. Women. No Fields Medals yet of course.

That’s the highest honor in mathematics.

Yes.

I’m surprised that your friend Grothendieck is not on your list. Did you forget him?

I dont forget Grothendieck. All the ones I named are dead.

Is that a requirement for greatness?