An Elegant Solution(102)

There was, though, a fifth proof published in that same edition, superior actually to all the others. Mr. Newton in England, it was said, had solved the problem in a few moments the very night he received the journal, after a tiring day of work. Though the attribution was anonymous, the notations made it obvious that they’d all been bested by the Englishman.

As Master Johann said when he read it, “I recognize the lion by his paw.” The saying had persisted in his family. The feelings between them had also persisted.



After Leibniz, I read Newton. The Principia was a book that would stand forever: it bested all his peers, just as his proof had bested them. Whether Mr. Newton or Herr Leibniz first understood the Calculus, I did not know. I did know that Mr. Newton’s work reached farther, and his principal that Mathematics ruled, and also explained, the motions of both planets and pebbles, of both raindrops and rainbows, was a new beginning of history. He would be famous forever. Whenever he died, and he was now very old, his fame would only keep growing.

My Master Johann would also hold a place in history. Again whether Mr. Newton or Herr Leibniz first discovered the Calculus, it was without doubt that everyone who now knew the subject learned it through Master Johann’s explanation. His books were not on the same pinnacle as the Principia, but they would always be known. He had the renown that Master Faust sought.

Daniel and Nicolaus and Gottlieb would also be remembered. In Mathematics, their family had been a constellation. Daniel wanted to outshine his father and would have paid a dear price to do it, and Nicolaus had more ambitions than he showed. And, in some obscure journal, an author might even be remembered for the first proof of the Reciprocal Squares.



It seemed to be the warmest day yet of the spring, and the sky was cloudless. All sound was deadened.

When I was admitted into Master Johann’s house, there was a thickness to the silence. I could hardly hear my own footsteps in the stairs, and Mistress Dorothea’s knock on the inner door was like a leaf fall. The call from within sounded as from a grave.

“What have you been reading this week?” he asked, and he seemed much older and worn.

I was able truthfully to give an answer pleasing to him. “Herr Leibniz.”

Though less, he was still omniscient and omnipotent in his dark room. He’d known. “I have been, also,” he said. “Even now.”

“The Nova Methodus?” I didn’t see a book on the table, only some papers. But these were what he set his hand on as he answered.

“Our correspondence.”

“From himself?” I asked, awed. I knew, of course, that there had been many letters between them, but these were those letters themselves.

“I was younger then. Leonhard, why do you pursue Mathematics?”

“I can’t not.”

“How does Mr. Newton describe the study of Mathematics?”

This was disturbing. It may have been the first time I’d ever heard that name from my Master’s lips. It was dangerous, as well. To deny my respect would be foolish, as he certainly remembered my thesis of three years before. But to show too much admiration would also be unwise. “The Principia states that Mathematics explains the revolving of earth and the motion of water and the colors of light,” I said.

“How can Mathematics do this?”

“I believe there are deep laws that govern motion and substance.”

“So is that Mathematics?” he asked, and I sensed his dissatisfaction with my answer. “It is just a principal of natural philosophy?”

“No. It is more.”

“Then what?”

“I think that natural philosophy, and Physics, and all of such things are built on Mathematics like a castle is built on a mountain. There is more to the mountain than just the portion that holds the castle.”

“There is more of Mathematics,” he said, and now he was satisfied, “than is used in the earth and heavens.”

“I believe so. Master, what do you understand that Mathematics is?”

“It is an invisible world,” he answered. “Greater and deeper than anything we see.”

“I do see invisible things,” I admitted. “Sometimes.”

“Then you see that world,” he said, “also.”

“Where did it come from?”

“Where?” He hadn’t thought that question before. “It would always have been. The world we see is created on it.”

“But could it have always been? Even the invisible world must have been created, also.”

“The created world is as it was chosen to be,” he said. “Mountains and rivers are where they are, but they could have been otherwise. Mathematics can only be as it is. There is no other possibility. So, was it created?”