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Page One Endogenous Issue III

Endogenous

The Art in Hartmann

Three mathematicians cannot agree whether what they do is an art or a science. One of them is outvoted by his own surname.

Three of them took the corner booth at the diner on a Tuesday, the way they always do, and by the time the coffee came the question was already on the table, where it has been for a hundred years and will be for a hundred more.

Is mathematics an art, or is it a science.

Hartmann answered first, because Hartmann always answers first. "We all believe that mathematics is an art," he said, and he said it the way you'd say water is wet — not as a position but as a thing already settled, by better men, long ago. He went on about structural beauty. He said the whole job of a lecturer is to carry that beauty across the room to people who can't yet see it. He turned his cup a quarter turn so the handle faced the window. The light was, he felt, better that way.

Nason did not look up from his eggs. "You think it's art," he said, "because the word is sitting inside your name. Take the name away and ask him again."

Hartmann opened his mouth.

"Nothing is painted," Nason said. "An equilibrium is not painted. You fold the space or you don't. It holds or it buckles. That's not taste. That's a load test. It's a science, and it's a science whether or not anybody finds it pretty, and the ones who need it to be pretty are telling you something about themselves and nothing about the mathematics."

Langley had not said anything yet. Langley rarely says anything until both of the other two have committed, and then he says the thing that makes the question look like it was badly posed to begin with.

"It's neither," he said. "You're both answering a question I'd throw out. It's a correspondence. You have two things that look nothing alike — a thing over here that counts, a thing over there that flows — and the whole of my life has been one long demonstration that they are the same thing said in two languages. I didn't decide that. I didn't compose it. I found the dictionary and I spent fifty years copying it out. That's not art. It's also not a load test. It's translation. You learn the languages." He had, in fact, learned several, which he did not mention, which was itself a kind of mention.

The check came. None of the three could agree on how to split it.

Nason said divide by three. Hartmann said he'd had the smaller coffee and the arrangement should reflect that, elegantly. Langley observed that splitting a check is also a correspondence — each man over here, each dollar over there, and the only hard part is the map between them.

The waitress, who has a degree in this and is three years into paying for it, took the slip back without being asked.

"It's a science," she said. "You divide."