He sat back. “Indeed.”
I proceeded. I described the steps, from one statement to the next. I was building a castle, or a palace, or a mountain. It seemed like each of them. Every part was just a breath of air and a few sounds that touched the room, then were gone. The castle was the thinnest unsubstantial thing ever built, yet it was as hard as obsidian and adamant. Nothing in creation could break it. And when I reached the end it was irrefutable and impervious.
“There are errors,” Master Johann refuted. He began stating them.
The errors he claimed were complex, where the foundations of the walls rested on untested rocks, and I’d known just where he’d mount his attack. But they weren’t errors. They were proofs yet to be found, but they were truths and I knew the proofs would eventually yield.
“An infinite product,” he said, “and you claim to still know the individual finite terms. That is unproven.”
“But they must be,” I said. “It can be proven that they’re nothing else. There would be no other part to them.”
He circled, he probed, he thrust and I parried. He challenged every line. But he was hesitating and pausing, and then he began answering his own attacks. Then finally he shook his head.
“This will take more study,” he said. “It is intriguing, Leonhard.”
“Yes, sir.”
“But it is far from convincing.”
But I was convinced.
“Have you shown this to anyone else?” he asked.
“No, Master. It only came to me yesterday.”
“Do not discuss it with anyone. I will continue to study it.”
It was very unusual for him to not give me work for the coming week. But it was plain that nothing so mundane would be taken up in the rest of our session. Indeed, the session was over. I heard the bell in the Munster tower.
“Yes, go on, Leonhard,” he said as I stood. “It will take a great deal of study.”
“Thank you, sir.”
But instead of dismissing me, he paused. I waited. He had some other subject that had come to him. “Leonhard.”
“Yes, Master?”
“You’ll be finishing your studies soon?”
“I hope to present my dissertation by next year.”
“Yes. I have expectations for it. Leonhard.”
“Yes, Master?”
“You said that this proof came to you.”
“Just last night.”
“Not that you solved it, but that it came to you.”
“It did, sir. I don’t believe I could have solved it myself.”
“I see. Then who would you say did solve it?”
“I . . . don’t know. Do you understand what I mean, Master?”
“Yes. Very much.” And he looked into me in a deep, searching way, seeing something in me he recognized. “Yes, I understand.” And he seemed to see something else in me. “If the proof is true,” he said, “it will be an elegant solution.”
“Thank you, sir.”
“To many things. But only if.”
“What does it mean,” my grandmother asked, “that you’ve proven your answer but Master Johann doesn’t believe your proof?”
“There are things that I believe are true, and he doesn’t.”
“Are they true, then? You’ve said that in Mathematics a thing is true or not, whether it is believed or not.”
“There are some parts of Mathematics that aren’t understood well enough to be sure what is true.”
“As with God,” she said.
“The two are very close. Sometimes I think Mathematics is the thing God made that is most like him.”
“What will become of your proof?”
“I want to write to Paris.”
“You? Is it acceptable for you to send letters to this Academy?”
“I think not, Grandmother. I’ll need to ask Master Johann to send a recommendation.”
After that afternoon I felt as if my thoughts had been swept clean. Everything had ebbed away that had occupied my brain and it was like a hunting dog asleep and twitching on its rug. I was exhausted but nervous and edgy. I needed something to fill my empty head again and so I thought of dust, and I went to see Lithicus.
His yard was mostly as before, but somehow dustier. The stonecutter was mostly as before, as well. “And it’s you?” he greeted me. “Here to question me?”
“You told me to come. And to ask for my Master if there’s progress for him.”
“Progress, there’s progress. Does he think I’m idle?”
There’d been little rain or wind in the last few days, though I thought that yard would always be filled with dust. Of dust was man made and to dust man returned. Here the carving of epitaphs and memorials left dust which was surely a part of a man’s return.