I’m surprised to hear you say that understanding mathematics was beyond you. Is this something that concerns most mathematicians? Or do they just go about the business of computation?

I think for most it’s a passing concern. At best.

You said that mathematics was mostly hard work. But I’m still not sure how you go about it.

Yes. The first thing you do is take off your shoes and socks. To have a parallel access to the base ten.

How do you know I wont believe you?

How do you know you shouldnt? The core question is not how you do math but how does the unconscious do it. How is it that it’s demonstrably better at it than you are? You work on a problem and then you put it away for a while. But it doesnt go away. It reappears at lunch. Or while you’re taking a shower. It says: Take a look at this. What do you think? Then you wonder why the shower is cold. Or the soup. Is this doing math? I’m afraid it is. How is it doing it? We dont know. I’ve posed the question to some pretty good mathematicians. How does the unconscious do math? Some who’d thought about it and some who hadnt. For the most part they seemed to think it unlikely that the unconscious went about it the same way we did. What was surprising to me was the insouciance with which they greeted this news. As if the very nature of mathematics had not just been hauled into the dock. A few thought that if it had a better way of doing mathematics it ought to tell us about it. Well, maybe. Or maybe it thinks we’re not smart enough to understand it.

I’m not sure I see how that would work.

Neither does anybody else. Sometimes you get a clear sense that doing math is largely just feeding data into the substation and waiting to see what comes out. I’m not even sure that it’s all that wise to commit things to memory. What you log in becomes fixed. In a way that the machinations of the unconscious would appear not to. I dont really like to write things down. Is that good? I dont know. Grothendieck writes everything down. Witten nothing. But I think for most people to leave things unrecorded is to leave them free to look around for fresh analogies. They go about their business and come back from time to time and report to you. A written statement—or an equation—is a sort of signpost. A waystation. It tells you where you are and gives you a new place to start from. Dirac draws pictures. I dont think he believes there exist graphic representations of entities too small to subtend a particle of light, but he has an engineering background and it’s stuck with him. Odd things come in handy. People who are good with an abacus can calculate pretty well with an imaginary one.