"Are you all right? You must be tired," I said. I stood up and held out my hand to him, but he brushed me aside and walked away without a look.

  I called after him, but it was as if he hadn't heard me. He shuffled out of the office slippers, pushed on his shoes, and walked out the door. I paid the bill as quickly as I could and chased after him down the street.

  He was reaching a busy intersection when I finally caught up with him. He seemed to know the way home, but he had charged out into the street, oblivious to the traffic and the signals. I was surprised to see how quickly he could walk.

  "Wait!" I called out to slow him down, but this only succeeded in drawing wary looks from the people nearby. The heat and glare of the summer sun were dizzying.

  I was starting to get angry. He had no reason to be so rude to me. It was hardly my fault that it had been so painful; and it would have been far worse had we ignored it. Even Root was braver than this at the dentist.... Of course! That was it! I should have brought Root along. The Professor would have felt compelled to behave more like an adult with a child present. To treat me like this, after I'd kept my promise and waited for him the whole time....

  I knew it was cruel, but I had half a mind to let him go off on his own. I slowed my pace and he charged ahead, apparently determined to get home as soon as possible, ignoring the oncoming traffic. His hair was wild, and his suit was rumpled. He looked smaller than usual as his tiny, receding figure disappeared in the evening shadows. The notes on his jacket, catching a glint of sunlight, helped to keep him in sight. They blinked like coded messages, signaling the Professor's whereabouts.

  Suddenly, my hand tightened around the handle of my parasol and I checked my watch. I calculated the time from the moment the Professor left the waiting room until he returned. Ten minutes, twenty, thirty ... I ticked off the intervals. Something was wrong.

  I ran after him, shuffling to keep my sandals on my feet, my eyes fixed on the bright scraps of paper clipped to his suit as they disappeared around the corner into the shadows of the city.

  While the Professor was taking a bath, I tried to straighten up his issues of the Journal of Mathematics. He seemed to live for the puzzle problems it published, but he didn't pay much attention to the rest of magazine and left the barely opened copies strewn around his study. I gathered up all the issues and arranged them in chronological order; then I checked the tables of contents and pulled out the ones in which the Professor was mentioned for having won a prize. That still left quite a few issues. The names of prizewinners were printed in bold type and boxed in a fancy border, so they were easy to spot. The Professor's name seemed especially grand to me, printed there in magazine after magazine; and the proofs themselves, though they lost the familiarity they had in the Professor's own handwriting, seemed all the more impressive in print, the force of their incomprehensible arguments all the more powerful, even to me.

  The study was hotter than the rest of the house, perhaps because it had been closed up and silent for so long. As I packed away the issues of the journal that did not mention the Professor, I thought about the dentist's office and I calculated the time again. With the Professor, you always had to keep in mind his eighty-minute memory. Still, no matter how many times I added it up, we'd been apart less than an hour.

  I told myself that the Professor was only human, and even though he was a brilliant mathematician, there was no reason why the eighty-minute cycle should be entirely reliable. Circumstances change from day to day, and the people who are subject to them change as well. The Professor had been in pain, and strangers were poking around in his mouth; perhaps this had thrown off his inner clock.

  The stack of magazines containing the Professor's work was as high as my waist. How precious they were to me, these proofs he had devised, studded like jewels in an otherwise featureless journal. I straightened the pile. Here was the embodiment of the Professor's labors, and the concrete proof that his abilities had not been lost in that terrible accident.

  "What are you doing?" He had finished his bath and was back in the study. His lips were still slack from the Novocain, but his jaw was less swollen. He seemed more cheerful, too, as if the pain had eased. I glanced quickly at the clock on the wall; he had been in the bath for less than thirty minutes.

  "I'm straightening up the magazines," I said.

  "Well, thank you, I appreciate it. But I don't think I really need to keep them. It's a lot to ask, but would you mind throwing them out?"

  "I'm afraid I can't do that."

  "Why not?"

  "Because they're full of your work," I said, "the wonderful things you've accomplished."

  He gave me a hesitant look but said nothing. The water dripping from his hair made blotches on his notes.

  The cicadas that had been crying all morning suddenly fell silent. The garden baked under the blinding glare of the summer sun. If you looked carefully, you could see a line of thin clouds beyond the mountains at the horizon, clouds that seemed to announce the coming of autumn. They were just at the spot where the evening star would rise.

  Not long after Root started school again, a letter arrived from the Journal of Mathematics. The Professor's proof, which he had worked on all summer, had won first prize.

  The Professor, of course, showed no sign of pleasure. He barely looked at the letter before tossing it on the table without a word or a smile.

  "It's the largest prize in the history of the Janaruobu," I pointed out. Afraid I would mangle the pronunciation of the long foreign title, I had taken to calling it simply the Janaruobu.

  The Professor gave a bored sigh.

  "Do you know how hard you worked on that proof? You barely ate or slept for weeks. You literally sweated out the answer—and there are salt rings on your suit to prove it." Knowing he had forgotten all this, I wanted at least to remind him of his efforts. "Well, I remember how hard you worked," I said. "And how heavy the proof was when you gave it to me to mail, and how proud I was when I got to the window at the post office."

  "Is that so?"

  No matter what I said, he barely responded.

  Perhaps all mathematicians underestimated the importance of their accomplishments. Or perhaps this was just the Professor's nature. Surely there must be ambitious mathematicians who wanted to be known for the advancements they made in their field. But none of that seemed to matter to the Professor. He was completely indifferent to a problem as soon as he had solved it. Once the object of his attention had yielded, showing its true form, the Professor lost interest. He simply walked away in search of the next challenge.

  Nor was he like this only with numbers. When he had carried the injured Root to the hospital, or when he had protected him from the foul ball, it had been difficult for him to accept our gratitude—he was not being stubborn or perverse, he simply couldn't understand what he had done to deserve our thanks.

  He discounted the value of his own efforts, and seemed to feel that anyone would have done the same.

  "We'll have to celebrate," I said.

  "I don't think there's anything to celebrate."

  "When someone has worked hard and won first prize, his friends want to celebrate with him."

  "Why make a fuss? I simply peeked in God's notebook and copied down a bit of what I saw...."

  "No, we're going to celebrate. Root and I want to, even if you don't." As usual, I played the Root card. "And now that you mention it, we could combine this with Root's birthday party. He was born on the eleventh. He'll be delighted to share the celebration with you."

  "And how old will he be?" My stratagem had worked. He was finally beginning to show some enthusiasm.

  "Eleven," I said.

  "Eleven." He sat up and blinked, then ran his hand through his hair.

  "That's right. Eleven."

  "An exquisite number. An especially beautiful prime among primes. And it was Murayama's number. Truly wonderful, don't you think?" What I thought was that everyone has a birthday once a year, and that
was far less interesting than a mathematical proof that had won a major prize; but of course I held my tongue and nodded. "Good! Then we should have a party. Children need to celebrate. Nothing makes them happier than some cake, some candles, and a little applause. That's simple enough, isn't it?"

  "Yes, of course," I said. I took a marker and drew a big circle around the eleventh on the calendar, big enough to catch the attention of someone as distracted as the Professor. For his part, he made a new note—"Friday, September 11, Root's eleventh birthday party"—and found a spot for it just below his most important note.

  "There," he said, nodding in satisfaction as he studied the new addition. "That should do."

  Root and I talked it over and decided that we would give the Professor an Enatsu baseball card at the party. So, while he was napping in the kitchen, we crept into the study and I showed Root the cookie tin. He was immediately fascinated and seemed to forget we were keeping a secret from the Professor. Sitting on the floor, he began to examine each card, reverently admiring their every detail.

  "Be careful with them," I fussed nervously. "They're important to the Professor." But Root hardly seemed to hear me.

  It was the first time he had really had a chance to look at baseball cards. He knew that people collected them—his friends had shown him theirs—but it was as if he had avoided developing an interest in them. He was not the sort of boy who would ask his mother for something frivolous.

  But once he had seen the Professor's collection, there was no going back. Another part of the world of baseball had opened up before him, and it held a very different appeal from that of the real game. Each card was a talisman of an imaginary game that was separate from the one he saw played out on the field or heard on the radio. A photograph capturing a crucial moment, an inspiring story, and the historical record inscribed on the back—all captured on a rectangular card in a clean plastic case you could hold in the palm of your hand. Everything about the cards fascinated Root, and this particular collection was all the more delightful because it belonged to the Professor.

  "Look at this Enatsu! You can even see the sweat flying off him." "And this one of Bacque—look how long his arms are." "And this one's unbelievable! When you hold it up to the light, you get a 3-D picture of Enatsu!" He stopped to show me every new discovery.

  "I know," I said at last. "Now put them back." I'd heard a creak from the easy chair in the next room. The Professor would be getting up soon. "You can ask him to show them to you sometime soon. But be sure you put them back in the right order; he's got a very special system."

  Whether from excitement or because the cards were heavier than he'd thought, Root dropped the tin. There was a loud crash, but the cards were so tightly packed together that the damage was minimal—only a few of the second basemen had scattered across the floor.

  We retrieved them quickly, and fortunately there were no bent corners or cracked cases. The only difference was that we'd spoiled the Professor's incredibly precise order.

  I was worried that the Professor could wake up at any moment. I knew he would have been happy to show Root his collection had we simply asked, so I wasn't sure why I was sneaking around like this, or why I was hesitant to raise the subject of the cookie tin. For some reason, I had convinced myself that the Professor would not want other people to see the cards.

  "This is Shirasaka, so 'shi' should go right after Kamata Minoru."

  "How do you read this one?"

  "It's written next to the characters in the syllabary—Hondo Yasuji. So it goes back here."

  "Do you know who he is?"

  "No, but he must have been important to have a card. We can't worry about that now, we've got to hurry."

  As we concentrated on putting the cards back in order, I suddenly noticed something: the tin had a second layer underneath the one holding the cards. I was about to file a Motoyashiki Kingo when I realized that the tin was slightly deeper than the height of the card.

  "Hang on a second." Stopping Root for a moment, I wiggled my finger into the space where the second basemen had fallen out. There was no doubt about it: the tin had a false bottom.

  "What?" said Root, looking puzzled.

  "Nothing," I said. "Just hold on a minute." I had Root fetch a ruler from the desk and I very carefully slipped it under the row of cards. "Look, there's something down there. If I hold them up like this, can you pull it out?"

  "Yep, I see it. I think I can get it." Root's small hand slipped into the narrow opening, and in a few seconds he extracted the contents of the hidden compartment.

  It was a thesis of some sort. It had been typed in English and was bound with a cover page bearing what looked to be a university seal—a hundred-odd-page mathematical proof. The Professor's name was printed in Gothic letters and the work was dated 1957.

  "Is it a problem the Professor solved?"

  "It seems to be."

  "But why would he hide it here?" Root said, sounding thoroughly mystified. I did a quick mental calculation: 1992–1957—the Professor had been twenty-nine. Since the noises from the next room had stopped, I began to flip through the thesis, the Motoyashiki card still in my hand.

  This paper had been handled with as much care as the baseball cards. The paper stock and the type were showing signs of age, but there was no trace of dirt or damage from human hands, no folds or wrinkles or spots—mint condition. The high-quality paper was still soft to the touch and the typist had made no mistakes. The binding, too, was perfect, with the pages neatly gathered at the corners. An edict left by a noble king could hardly have been more carefully produced or preserved.

  Taking my cue from those who had handled it so gingerly in the past, and remembering Root's recent mishap, I held it with the greatest care. The paper smelled faintly of cookies, but it still looked impressive, in spite of being pressed down at the bottom of a tin for years under rows of baseball cards.

  As for the content, the only thing I could decipher on the first page was the title: Chapter 1. But as I flipped through the pages that followed, I came across the name Artin, and remembered the Artin conjecture that the Professor had explained with a stick in the dirt on the way home from the barber—and the formula he had added when I'd brought up the perfect number 28, and how the cherry blossoms had fluttered to the ground.

  Just then, a black-and-white photograph fell from the pages. Root picked it up. It showed the Professor seated on a clover-covered riverbank. He was young and handsome, and he looked completely relaxed with his legs stretched out in front of him. He was squinting slightly in the bright sun. His suit was much like the one he still wore, but, needless to say, there were no notes on his jacket and he seemed to radiate intelligence.

  A woman was seated next to the Professor. She leaned timidly toward him, the toes of her shoes poking out from under her flared skirt. Their bodies did not touch, but it was clear that they shared a bond. And in spite of the years that had passed since the picture was taken, I had no doubt that the woman was the Professor's sister-in-law.

  There was one more thing I could read. At the top of the cover page, a single line in Japanese:

  "For N, with my eternal love. Never forget."

  An Enatsu card, we soon realized, was not an easy thing to find. The main problem was that the Professor already owned all of the Enatsu cards from his playing days with the Tigers—that is, before 1975. The later cards all mentioned that he'd been traded, and we had no intention of giving the Professor a card with his hero in a Nankai or Hiroshima uniform.

  We started our research by combing through a baseball card magazine (the mere existence of which was news to me), and reading about the types of cards out there, the price range, and the places you could find them. We also learned what we could about the history of baseball cards, the culture of the collectors, and how to protect them. Then, over the weekend, we made a tour of all the nearby shops listed in the back of the magazine

  The card shops tended to be in aging office blocks, next
to pawnshops, private detective agencies, or fortune-tellers. The dingy elevators were enough to depress me but once we got in the shops, Root was in heaven. The world inside the Professor's tin opened up before him.

  At first, his head was turned by each new discovery; but once he had calmed down, we focused on looking for a Yutaka Enatsu card. This section, as we might have guessed, was always among the largest. The shops organized their cards much as the Professor had his cookie tin, with a special place reserved for Enatsu next to other stars such as Sadaharu Oh and Shigeo Nagashima, separated out from the rest of the players who were filed by team or era or position.

  I started at the beginning and Root at the end, and we checked every Enatsu card in each shop. It required stamina, like hunting in a dark forest without a compass. But we refused to be discouraged, and we gradually found ourselves perfecting our technique, so that we were able to get through the trays of cards more and more quickly. Lifting a card between thumb and forefinger, we would check the front. If it was obviously one the Professor already owned, we would drop it back. If it was one we hadn't seen, we would check to see whether it met our requirements. We soon found that every card was either already in his collection, or showed Enatsu wearing the wrong uniform. It became clear that the black-and-white cards from the early years that the Professor had collected were extremely rare and quite expensive. Finding a card worthy of his cookie tin was not going to be easy. We flipped through hundreds of Enatsus in several shops. Our fingers would meet in the middle of a bin of cards and we'd realize that we'd come up empty once again.

  The shopkeepers never made us feel uncomfortable, even though we spent hours looking without buying anything. When we showed up in search of Enatsu cards, they happily brought out everything they had; and when we were disappointed, they encouraged us to keep looking and not give up hope. At the very last shop on our list, the owner listened to our story and then told us he thought we should try looking for cards that had been used as prizes by a certain candy company back in 1985. The company had always included baseball cards with its candy, but in 1985 it had been celebrating its fiftieth anniversary and had commissioned a run of premium cards. That was the year the Tigers had won the championship, so their players were especially well represented.