It’s a requirement for not waking up tomorrow morning and saying something extraordinarily stupid. You asked why Grothendieck left mathematics. The notion that this implies lunacy, appealing as that may be, is probably not altogether correct. It would certainly appear to be the case that rewriting most of the mathematics of the past half century has done little to allay his skepticism. Wittgenstein was fond of saying that nothing can be its own explanation. I’m not sure how far that is from saying that things ultimately contain no information concerning themselves. But it may be true that you have to be on the outside looking in. You can ask what is even meant by a description. Is there a better description of a cube than that of its construction? I dont know. What can you say of any attribute other than that it resembles some things and not others? Color. Form. Weight. When you’re faced with a class of one you see the problem. It doesnt have to be something grand like time or space. It can be something pretty everyday. The component parts of music. Are there musical objects? Music is composed of notes? Is that right? The complexity of mathematics has shifted it from a description of things and events to the power of abstract operators. At what point are the origins of systems no longer relevant to their description, their operation? No one, however inclined to platonism, actually believes that numbers are requisite to the operation of the universe. They’re only good to talk about it. Is that right?

I dont know.

The reason mathematics works—some would argue—is that you’re at the end of your tether. You cant mathematicize mathematics. You look dubious.

Sorry.

Even fairly simple animals can count. They understand that three is more than two. They dont know what that means? Neither do I. You asked me about Grothendieck. The topos theory he came up with is a witches’ brew of topology and algebra and mathematical logic. It doesnt even have a clear identity. The power of the theory is still speculative. But it’s there. You have a sense that it is waiting quietly with answers to questions that nobody has asked yet.

That sounds a bit platonic.

Dont it though? With the refreshingly new and unhappy prospect of our species having created a thing we have yet to discover. The Kid thought Dirac’s name was Pamela.

Pamela?

He used to sometimes sign his name PAM Dirac. For Paul Adrien Maurice. Anyway, these are my people. I dont have anyone else.

You look sad. Saying that.

I am sad saying that.

It has to do with intelligence.

Yes. And again, when you’re talking about intelligence you’re talking about number. A claim that the mathless are quick to frown upon. It’s about calculation and the nature of calculation. Verbal intelligence will only take you so far. There is a wall there, and if you dont understand numbers you wont even see the wall. People from the other side will seem odd to you. And you will never understand the latitude which they extend to you. They will be cordial—or not—depending on their nature. Of course one might also add that intelligence is a basic component of evil. The more stupid you are the less capable you are of doing harm. Except perhaps in a clumsy and inadvertent manner. The word cretin comes from the French chrétien. Supposedly if you could think of nothing good to say about a dullard you would say that he was a good Christian. Diabolical on the other hand is all but synonymous with ingenious. What Satan had for sale in the garden was knowledge.