An Elegant Solution(67)

It was very patient and generous of her to ask, and irresistible for me. “I have no start to a solution. There is nothing that this problem can be compared to. But I’ve been reading about other infinite series and infinite sums.” And then, as she listened with her full attention, I described how each method I knew, and each method known at all, was full short of the problem. “But, I think the more difficult the problem is, the more elegant the solution must be.”

“Elegant?” she said. “What is elegant in Mathematics?”

“Everything! But there is a special quality to some Mathematics that is specially known as elegant. The elegant solution to a problem is the solution that is clean, even pure, that cuts through obstacles like an arrow through paper. It solves the one problem but also a dozen others that hadn’t even been proposed. It associates one world of Mathematics with another that had always been thought completely separate. It’s the one invisible beneath the many visible.”

“Leonhard,” she said, “when you speak of your invisible things, they seem real.”





9

THE TRIPLE SEVEN LEAVES





On Tuesday at noon I went to Gottlieb’s house to hear a lecture on Logic. I had been his student before and sat through his full course. I felt that now, as his one-time clerk, and wearing the tricorne he’d given me, I could claim a privilege of gentlemanly association and sit as guest.

He wasn’t a poor lecturer, whatever Daniel had claimed. It was more that he was dry as dust. His lectures kicked up the dust to infiltrate and irritate his listeners’ eyes and ears. What was this dust? Words and words and words. He would speak on Aristotle, and the air would be filled with the dust of ancient Athens. He would describe Pythagorus, and the dust would float in triangles. He would confess Euclid, and the dust would fill all the space in the room. He would attempt Descartes and Pascal and Newton and Leibniz and the dust would grows wings and claws and teeth and threaten the life and spirit of everyone in its cloud. Covered in dust, the students would stumble blinded and choking from the lecture room. Somehow, though, the dust would cling, and for months after the listeners would be surprised by logical thoughts sprouting in their brains like rare mushrooms in a dank forest, and paradigms sprinkling their conversations like momentary summer showers.

And Gottlieb’s lectures were always absolutely straight, starting from the beginning and proceeding to the end in unbent linearity. When he was finished, there was no doubt of the truth of his original premise. Yet no one had doubted it at the beginning: the importance was in the proving. We, in black and white, heard it laid out in black and white. Truth was truth. False was false. It was, whether we knew it or accepted it, or did not. Deny that fish swim, but they still did; and fishing for a trout in a dry meadow would leave a man hungry. I liked logic. It showed that we must accommodate truth, and not the reverse. And in a way, that because proof exists, it was proof that God exists.

I thought also about the unproof of Gottlieb’s Election, how it was only a chance motion that had made him, and not Daniel, Chair. I wondered whether Gottlieb, the beneficiary of the chance, had the same thoughts about it.

He didn’t acknowledge my presence until the end of the lecture. Then he did, politely, befitting a gentleman scholar, and one who’d already attended his lectures, and was therefore an expert himself.

“I’ve been reading the Ars Conjectandi,” I said, when the other students had left. “May I ask you about it?”

“Ask what?” he answered. It was appropriate for a student to ask questions of a Master, but Gottlieb showed no eagerness.

“Are there truly chances and randomness? Or is everything in fact ruled by laws of nature? Or does God own all actions?”

He had no interest in answering great questions, standing in his front hall. “Why are you asking such questions?” He scowled. “You, especially, who have already thought through those questions and answers more, you think, than anyone else?”

“I meant, when you were writing the book, did Master Jacob’s notes show that he’d considered those questions about chance when he was writing about chance?”

This was only somewhat less onerous to him. “He had many notes, and on many subjects. Someday you may have the opportunity to read some of them.” He didn’t sound as if he hoped I would.

“I hope to very much. Where are they?”

He scowled. “You know well where they were, and that I’d like to know where they are now.”

“Yes, sir,” I said. I’d only wanted to be sure. “I stopped at the Watch barracks yesterday and the trunk was gone. Simeon didn’t know who’d taken it, or where.”