Does Spengler know any math?

I dont know. He never mentions anyone. It’s all just notional. I dont know how you can write about the meaning of numbers with no mention of Frege. Even in 1917 or ’19. But even Frege doesnt get completely down to nuts and bolts. Adding and subtracting are not really mathematics. A sack of pebbles will do. But multiplication and division are a different matter. If you were to multiply two tomatoes by two tomatoes you wouldnt get four tomatoes. You would get four tomatoes squared. So what is the two? Well. It’s an independent abstract mathematical operator. Oh? And what is that? We dont know. We made it up. Do you remember any of this from Math 101?

I’m not sure I see the point.

I know. The actual issue is that someone a hundred thousand years ago sat up in his robes and said Holy Shit. Sort of. He didnt have a language yet. But what he had just understood is that one thing can be another thing. Not look like it or act upon it. Be it. Stand for it. Pebbles can be goats. Sounds can be things. The name for water is water. What seems inconsequential to us by reason of usage is in fact the founding notion of civilization. Language, art, mathematics, everything. Ultimately the world itself and all in it.

And the greatest of these I take it is mathematics.

Well. I’m a mathematician.

So is God a mathematician?

God cant add two and two. Zero and one are all he’s got to work with. The rest is us. Kronecker notwithstanding. Maybe we should shelve this for a while.

Okay. When you left school and went to Arizona did you leave the doctoral program?

No. I still hear from them occasionally.

They want to know how things are going.

They want to know how things are going.

I take it that you have a faculty advisor.

I do. I dont ever hear from her.

Did you have a falling-out?

No. But I dont really trust her.

Why is that?

I would find her agreeing with things that I knew she didnt understand. And I made her nervous.

A common theme in your life?

I suppose.

In your mathematical life?

Not so much. Mathematicians tend to be pretty straightforward. I think a lot of them dont really even understand the idea of dissimulation. They’re an odd lot, more oddly taken. Chaitin said that he was asked once if he had any connection to real life. They wanted to know if he read the newspapers.

How did your work go? In Tucson.

It took pretty much the same path as any doomed enterprise. It would move along on a gradual downward slope and then drop precipitously.

I take it this was somewhat discouraging.

Not really. I knew that what I was after was there. Doing math is a bit like selling door to door. You have to learn to handle rejection. I went through Hilbert’s problems. Not to solve them but to try to find out what if anything they had in common. Mathematics was spreading out and as it was spreading out it was thinning out. Sometime in the early twentieth century it finally became impossible for anyone to understand all of it. Cantor supposedly was the last universal mathematician. Then Poincaré. Then no one. Anyway, there were times when I considered that my career might be over. And at the same time I never questioned my ability. I was the best mathematician I knew.