An Elegant Solution

by Paul Robertson

  “You won’t see it now,” I said to Little Johann.

  “Leonhard, I have.”

  “When I looked in it before, I found something,” I answered him. “A crumb of dough. Good bread dough. So I thought you’d seen it.”

  All he said was, “I won’t tell you.”

  “I don’t know what you’d tell me,” I answered. “Did you know that Knipper came to your kitchen?”

  “I only saw the trunk. It was dusty.”

  We walked slowly back to the Munster Square. “What was in the trunk?” I asked

  “Not Knipper.”

  “No, he wasn’t. He was still on the road from Bern. What was in it? Was it papers?”

  “Notebooks of papers. It wasn’t near full.”

  “Were they Jacob’s?”

  “They were. I don’t like Latin and I didn’t read them. But I knew they were. They were wrapped in bundles, in linen. I looked in one and saw them.”

  “Gottlieb wrote the Ars Conjectandi from them. He knew what they were. I heard what Gottlieb said to Huldrych and I saw the empty trunk. It had Jacob’s spiral in it.”

  “Why was it in our kitchen?”

  “I think it had been in your house for a few years. I don’t know how it got there from Huldrych’s. It had been in an attic, I think, or somewhere, and brought to the kitchen.”

  “Because Daniel was coming home,” Little Johann said. “Poppa wanted it away so he wouldn’t find it.”

  “Do you think?” I asked.

  “I know Poppa would.”

  “Then he hired Knipper to take it somewhere away.”

  “There was a envelope in it, too.”

  “A letter?”

  “From Poppa. It had his seal, but no name on it.”

  I walked with Little Johann. We turned into the alley, and through the gate I’d just mended into the back yard, and he held the door for me into the kitchen as if it was expected. So I went in with him.

  It was about noon, as the clocks of Basel defined it. Lunch was past and the room was empty. Little Johann stopped in the middle of the floor, just before the spot the trunk had been. I stood with him.

  “What pots are there?” I asked. “Any with a dent in them?”

  He shrugged. “Heavy pots wouldn’t take a dent.”

  “Did you look?” He nodded. “When did you realize that Knipper was here?” I said.

  “When I heard how he came back.”

  “I know, and you know, and Nicolaus knows. Perhaps Gottlieb knows. Perhaps everyone in the family knows. And one person certainly knows.”

  “I don’t care,” Little Johann said. “Whoever hit him, I don’t care.” Which meant that he did, and was frightened.

  I asked, “What came of the papers in the trunk?”

  “I don’t care.” Which also meant he did.

  “There was enough space in the trunk for Knipper and the papers?”

  “I don’t know.” Which meant there was.

  “Then it might be that the papers weren’t taken out. They may still be here, or they may be somewhere else in Basel, or they went to Strasbourg.”

  I sat with my grandmother that night. I was always wanting to go to my books and papers. Sometimes, though, I reminded myself that she’d have companionship with me. So I’d sit in the kitchen, after we’d cleaned everything. Then we would talk and say slower and longer things.

  “You say that Lithicus the stonemason seems anxious at every mention of Master Johann’s name,” she said after we’d talked about what I’d seen and heard that day.

  “Always when I ask about the spiral on Master Jacob’s epitaph. And when I said that Master Johann would pay for Huldrych’s epitaph, he was very upset at that, also.”

  “What became of Master Jacob’s papers?”

  “They might still be in Master Johann’s house. They might have been in the trunk when it was taken from the house to the inn. Maybe it was Knipper and Willi who carried the trunk back, and Knipper was killed after he was at the inn. Willi will be back on the coach tomorrow, if he’s allowed out of Strasbourg. I’d care to know what he found in Mistress Dorothea’s kitchen. And I’d care to see those papers. All of Master Jacob’s papers, Grandmother.”

  “Would there be great things in them?”

  “I don’t know. Cousin Gottlieb used some of them for the Ars Conjectandi, and I’ve heard Master Johann’s teaching for all these years, too, and he’d have known what was in them. They were at his house for him to read. There must be letters Master Jacob received. But most of his letters have been published. I don’t know what else would be in his papers.” Something from the day put another thought in my mind. “Or they might even be burned. Lithicus said a man’s house should be swept clean when he dies. He said that of Master Huldrych. If only he’d seen Master Huldrych’s house! That would take a great deal of sweeping.”

  “Or maybe he did see it,” Grandmother said. “If that was what he said of Huldrych.”

  “There would be no reason for him ever to have,” I said. Unless he’d had reason. I remembered the gray dust mingled in Huldrych’s golden dust.

  “Tell me about Master Johann’s room filled with papers,” she said.

  “It looks like mine,” I said. “And it felt like mine. I think I could sit at his desk and know where every paper and book was. But it was much grander, fit for a Chair.”

  “Did he have Master Jacob’s book?”

  “No. Nor Daniel’s. Nor Mr. Newton’s, nor Monsieur L’Hopital’s. But many others. Some that I didn’t know. And ten times as many papers as I have.” But that seemed an exaggeration. “No, I don’t even have a tenth,” I admitted.

  “More papers than you?”

  “He’s a great Mathematician. Very great.”

  “Is that what you aspire to, Leonhard?”

  “Is it right to aspire? It seems prideful.”

  “It can be done humbly.”

  “Humbly, I do, Grandmother. Someday I want to be a great Mathematician.”

  “For the pride of it?”

  “No. I think I’d rather not be known at all. It would be for the Mathematics. I want to discover new Mathematics. Master Johann has already discovered so much, and all the other great men before him. I only hope there’ll be some left! I know there would be, though it might be beyond me to understand it. But I want to sit in my study and read and think and write.”

  “And a wife, and children?”

  “Yes,” I blushed. “Of course, that. And students, too.”

  “You’re eighteen now. When will you finish your school?”

  “I think next year.”

  “What does a young man do who is a Mathematician?”

  “Mathematics,” I said. She shook her head.

  “What are you thinking and writing now?”

  I was embarrassed to say it. “I’ve tried to solve the Reciprocal Squares.”

  “Then tell me what you have discovered about the Reciprocal Squares.”

  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 i
nvisible 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.”

  “There’s no need for him to know. Nor you. Now, I’m in a hurry.”

  But into the already scalding pot, I poured another cup of boiling water. “One other thing. It’s a small thing. It was one week ago that I was serving as your scribe, and you were very kind to allow me the use of this hat.” I took it off my head and we both looked at it. “But I realized I should return it and retrieve my own.”

  “What? The hat? Keep it. I have no use for it.” He seemed more surprised than angry.

  “Thank you,” I said, and very sincerely. That was very generous. It was a bit old, but it would have cost more than a few florins. “Thank you. I’ve been very proud to wear it but I was concerned as it was only borrowed.”

  “No, keep it.” He was off guard and done with the discussion but I had one other small part.

  “I hope it isn’t poor of me to ask, though, for my old hat?”

  “Why would you ask me?” Now he was suspicious and back on guard.

  “I think you may still have it,” I said. “When you put this on my head, you took the other that I’d had.”

  “Did I?” It seemed odd that he wouldn’t remember. Gottlieb was very detailed and particular. But it was also a very inconsequential detail.

  “Yes, sir.”

  “Then it’s not here now. I’d know if it was. And I’m in a hurry. I have an appointment.”

  “Do you know where the hat might be? I’m sorry to annoy you with it.”

  “My appointment is to discuss the punishment of an annoying student.”

  “He is being punished for being annoying?”

  “The student has shown disrespect to a Chair. I won’t discuss it with you, Leonhard.”

  “Anyway, the hat,” I said. “It was a hat given me by my father. I should have come sooner or spoken before.”

  “Your father. No, it’s not here and I don’t know where it is.” And that was a very final statement and the end of all sympathy. “Good day.”

  His door closed. Above it, set in the timber, was a stone square with his family’s emblem, the triple seven leaves. It might be odd that he had it made and set there, considering the many hostilities he and the other members of the family had with each other. Yet there were other bonds that held them together, nearly invisible, but which I sometimes could see.

  As I had a week before, I crossed the bridge to Small Basel out the Blaise Gate. It was like the other gates: a tall, thin tower directly over the opening in the Wall. It held a portcullis and also the gears and ropes to draw the bridge up from the moat. But as always, it was no impediment to me as I left the city.

  To the left, just across a field, was the Rhine. The river was broad, strong, and usually peaceful. As a child I had walked often beside the Rhine, beside my father. When I would now stand beside the water, on a sunny grass or in knoll shade, I might still feel small, and his hand on my shoulder. And he still walked a path on its bank many days, though it’s a distance from Riehen.

  I went out from Small Basel at the Saint Blaise Gate as I’d done a week earlier, and I ran for a while along the road with its narrow field between me and the bank. Then I crossed the field to the water’s edge and slowed because rivers were walked beside, not run past. But I didn’t saunter. I kept a brisk pace.

  It wasn’t only that the riverside path was an old friend that I chose it over the main road. The main road had gawkers and I wanted to meet the coach before the rest of the city did. It took a mile to be the first and farthest. Then I went back onto the road, and after another mile to the edge of Basel Canton, where the tariff crossing to the Landgrave of Roteln and Saussenberg marked the end of Switzerland and the beginning of the Empire, and I waited there.

  It was uncertain who might be driving the coach. But when the coach was still just dust in the far distance, I knew it was Willi. There was a uniqueness to a driver who was coming home, and that driver was.

  I saw him sure when he was closer. He was alone in his box, shoulders hunched forward. A lout was always a mess but this one looked to have been in prison for a week and all in the same clothes. He came to the customs booth and stopped to pay his toll and argue his way through. Knipper had been a match for any customs guard, but Willi was new to the job, unfamiliar to the official, and weary.

  “No crossings,” the guard said. “There’s plague.”

  “I’m not wanting out!” Willi
shouted. “I want in!”

  “I’m from Basel,” I said to the guard. “I’m come to see that the driver doesn’t make trouble for you.”

  “You?” He looked at me closer. “I’ve seen you before?”

  “Yes, sir. My father and I used to walk the riverbank together and we’d see you fishing.”

  “Your father? The pastor of Riehen?”

  “Yes, sir.”

  He considered me, now much taller than in those years. “And you’re here for the driver?”

  “He’s with the Inn in Basel. He’s replaced the usual driver.”

  “Then let him pass! It’s not for me whether they all want to die of plague. Just don’t bring it back here.”

  That was enough. Willi moved the horses forward across the line. “Wait,” I said. “Can I ride with you?” I asked, and he didn’t stop me from climbing up beside him. Closer, he looked worn in his being with gaunt face and red sores on his wrists. “You’ll be welcome in Basel,” I said. “Strasbourg’s hated for holding you.”

  “I’ll hate the place, always,” he said.

  “What was it like?”

  “Poor formed and evil.” He spat. “And high ugly.”

  “Magistrate Caiaphas was a poor ambassador for it, too.”

  Willi jerked the reins, not to stop the horses but from surprise at what I said. But the horses halted anyway and the coach nearly toppled.

  “You know his name?” Willi near shouted. “What’s he to you?”

  “He was here.”

  “What are you doing stopped?” he said to his horses. “Hi, get.” He snapped the reins and the horses heaved and the coach started. “He’s been here? To haunt Basel, too? When? I never saw him here. I’d never have gone to Strasbourg if I knew he was there, never.”

  “This last week.”

  “Liar! He wasn’t! Why do you say he was?”

  “Well, he was,” I said. “What happened to you in Strasbourg?”

  “I drove into that foul stinking city, and found that ash heap inn, The Broken Shield, and the keeper Dundrach, and told him Knipper was lost and I wanted a bed and food, and went to find them myself. And I had a bowl from the kitchen, and I had Knipper’s bed and was asleep in it, and then the Guard was on me like on a thief! And dragged through streets! And to a filthy cell and thrown food like swill. The jailer’s an ox, but the magistrate’s a sheer fiend. He threatened me with red pokers and racks if I didn’t answer his questions.”