An Elegant Solution(118)

“He did.”

“Was Black Death his illness?”

For every question I’d asked, he’d only paused a moment to answer. Again, with his dark eyes intent on me, he answered immediately. “His family has held that as secret.”

“It was Black Death,” I said. “I know it was. And he died before Master Johann arrived? By hours? By minutes?”

Gustavas didn’t answer. He was just still and intent on me, as if he was measuring.

“Why did you come here, Master?” he asked me.

“Master Johann took the Chair of Mathematics after Jacob died,” I said.

“He did.”

“Daniel wants the Chair of Physics.”

“He does.” It was unusual for an innkeeper to admit to knowledge of University affairs or a gentleman’s desires.

“Master Johann stayed four weeks in Strasbourg on his travel to Basel. Did he send any messages while he was stopped there?”

“He sent messages.”

“Did Magistrate Caiaphas send any messages?”

“Why did you come here, Master?” he asked me again.

“Master Gottlieb was also in Strasbourg with Master Johann, though he didn’t stay as long. He came back a week earlier. And Master Desiderius came here from Strasbourg.”

“There has been coming and going between the cities for many years. The coach has been well used.”

“I’d like to speak with Magistrate Caiaphas,” I said. “I’ll come back tonight.”

“And you are welcome to come any time, Master.”

“Please tell him it will be the same conversation he had with those other gentlemen.”

“I will tell him you wish to speak with him.”

The light was still clean and innocent, and, it seemed, pure, though that was always hard to tell.



“Leonhard,” Grandmother said, even as I came in the door. “Where have you been?”

“Just walking,” I said. “It’s very dry. There hasn’t been rain.”

“You’re dressed fine.”

“It seemed proper for the early morning. The morning light was very clear.”

“Stay in it,” she said. “Stay out of the shadow.”

“But I’ll change now for my chores.”



I did my chores, though perhaps not well. Then I had a hard time reading, like pouring water into an overfull barrel. It seemed that three o’clock would never come.



Mistress Dorothea’s speech was so continuous that her silence was inscrutable. In its shadow I followed up her stairs. I saw her looking at me with eyes very narrow.

“Why did he do it?” I said, and it was like thunderbolts thrown.

“Just ask him, Leonhard.”

That was all I could muster and that was the only answer she could have made, and the worst. She knocked on his door. The “Enter” following was deeper and from deeper. The room was larger and darker and the candle on the table was far, far away and the journey to it was eternal.

Before I’d even sat, he began our lesson, and it was as if nothing had happened in all the last weeks. “Consider a simple quadratic,” Master Johann said. “But one having no intersection with the horizontal axis.”

“Yes, Master.”

“Does it have roots?”

We have discussed this before. “I believe that it does.”

“Even with no intersection?”

“They aren’t seen.” Then I knew that perhaps he was answering.

“An unseen number? Describe it to me.”

“The principle,” I said, “is that negative numbers might have square roots. If a positive number is multiplied by itself, the result is positive. If a negative number is multiplied by itself, the result is also positive. So, the root of a negative is neither positive or negative. It is something else. So it is unseen. I’ve read about these numbers since we talked about them before.”

“What did Monsieur Descartes say about such numbers?”

“He derided them and called them imaginary. He considered them foolish. But he did concede they might exist.”

“Why foolish?”

“Real numbers can be seen and counted with real objects. He said that imaginary numbers can’t be counted. There was no use for them.”

“Does that make something foolish, if it can’t be seen?”

“No, Master,” I said. “There are many things that can’t be seen, and they are more real than what can be seen. Numbers don’t need usefulness to exist. They exist on their own whether anything seen ever reaches their count or not.”



We talked longer, not about theorems or proofs, not solving problems. We didn’t write, we only talked. He questioned me, and I him, on meanings and reasons.