The Gift of Numbers aka The Housekeeper and the Professor

9

One day toward the end of summer vacation, I noticed that the Professor's jaw was badly swollen. It was just as the Tigers were returning from a successful road trip on which they'd managed to go 10 and 6, vaulting into second place just two and a half games behind the division-leading Yakult.

The Professor had apparently been hiding his problem from me and had not said a word about the pain. If he had given himself one-tenth of the attention that he paid to Root, this sort of thing would never have happened; but by the time I noticed, the left side of his face was so swollen that he could barely open his mouth.

Getting him to the dentist proved easier than our trips to the barber or the baseball game. The pain had taken the fight out of him, and his stiff jaw prevented him from making the usual objections. He changed his shirt, put on his shoes, and followed me out the door. I held a parasol to protect him from the sun, and he huddled underneath, as though hiding from the pain.

"You have to wait for me, you know," he mumbled as we sat down in the waiting room. Then, unsure as to whether I'd understood or whether he could trust me, he repeated himself every few minutes while we waited.

"You can't go out for a walk while I'm in there. You have to sit right here and wait for me. Do you understand?"

"Of course. I'm not about to leave you."

I rubbed his back, hoping to ease the pain a little. The other patients stared at the floor, as embarrassed as I was. But I knew from experience what to do in this situation. You simply had to be resolute, like the Pythagorean theorem or Euler's formula, and to keep the Professor happy.

"Really?" said the Professor.

"Of course. Don't worry. I'll be right here waiting for you, no matter how long it takes."

I knew it was impossible to reassure him, but I repeated myself anyway. As the door to the examination room closed behind him, he turned around as if checking that I'd keep my promise.

The treatment took longer than expected. A number of people who had been called in after the Professor had already settled their bills and gone home, and still he had not reappeared. He rarely brushed his teeth and did little to care for his dentures, and I doubted he was a particularly cooperative patient, so the dentist probably had his hands full. I got up from time to time to try to peer through the receptionist's window, but I could only see the back of the Professor's head.

When he finally emerged from the examination room, his mood was even worse than before. He looked exhausted, and his face was bathed in sweat. His mouth, still numb from the anesthesia, was pinched into an annoyed pout, and he sniffled constantly.

"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.

"What are 'premium' cards?" Root asked.

"They made all kinds-some had real signatures by the players on them, others had holograms, and some had actual slivers from game bats embedded in them. Since Enatsu was already retired, they did a reissue of the glove card. I used to have one, but it sold right away. They're incredibly popular."

"What's a 'glove card'?" Root wanted to know.

"They cut up a glove and attach scraps of the leather to the card."

"A glove Enatsu actually used?"

"Sure. The Japan Sports Card Federation certified them, so they're genuine. They didn't produce many, and they can be tough to find, but don't give up; there's bound to be one floating around somewhere. If I get one in, I'll give you a call. I have to admit, I'm something of an Enatsu fan myself." He tipped back the brim of Root's Tigers cap and rubbed him on the head-just like the Professor.

The day of the party was approaching. I saw nothing wrong with looking for an alternative present, but Root wouldn't hear of it. He was determined to find a card.

"We can't give up now!" he insisted.

I have no doubt that his primary concern was to make the Professor happy, but it was also true that he had taken a fancy to the whole idea of card collecting, and he had begun to think of himself as a hunter in search of that one elusive card somewhere out there in the great wide world.

The Professor also seemed to be planning for the party in his own way. He had taken to checking the calendar whenever he was in the kitchen. Occasionally, he would go over and trace the circle I'd drawn to mark the eleventh, fingering the note on his chest the whole time. He was remembering the party, but he had no doubt long ago forgotten about the little matter of the Janaruobu.

The Professor never found out that we had looked in his cookie tin. I had been momentarily mesmerized by the inscription on the thesis-For N, with my eternal love. Never forget. The handwriting definitely belonged to the Professor, for whom "eternal" meant something more than it did to the rest of us, eternal in the way a mathematical theorem was eternal…

It was Root who brought me back from my daydream.

"Mama, slide the ruler under so I can put it back in." He took the thesis out of my hand and returned it to the bottom of the tin, careful not to disturb or dishonor the Professor's secret.

A moment later, all the cards were back in place, and there was no sign that the collection had ever been touched. The tin itself was undamaged, and the edges of the cards were neatly aligned. Still, something was different. Now that I knew about the thesis and its dedication, the tin was no longer a simple container for baseball cards. It had become a tomb for the Professor's memories. I set it carefully back on the bookshelf.

I hadn't really thought anything would come of the last shopkeeper's suggestion, but somehow I was disappointed when he failed to call. Root made some final efforts, sending off a postcard to the readers' exchange in the magazine and asking around among his friends and their older brothers. Not wanting to be caught without a present, I had quietly arranged a backup. It hadn't been easy to figure out what to buy. I'd thought of pencils and notebooks, clips and note cards, even a new shirt. There were very few things the Professor really needed. The fact that I couldn't discuss the choice with Root made it all the more difficult.

I decided on shoes. He needed a new pair, ones that he could wear anytime, anywhere-mold-free. I bought them and hid them away in the back of the closet, just as I had with Root's presents when he was little. If we did find the card in time, I would slip them into the Professor's shoe cupboard without saying anything.

In the end, a ray of hope came from an unexpected place. I had gone to pick up my paycheck at the Akebono Housekeeping Agency and was talking with some of the other housekeepers. As the Director was listening, I had avoided mentioning the Professor, and just said that my son had been wanting baseball cards and I'd had no luck finding good ones. Then, out of the blue, one of them mentioned that her mother used to run a little store, and she remembered seeing some leftover cards that had been included with candy in a shed where her mother stored old stock.

The first thing that caught my attention was the fact that her mother had retired and closed up the shop in 1985. She had ordered some candy to take on a trip her seniors group was planning, and the chocolates with the cards had been included in the shipment. Thinking the old folks would have no use for them, her mother had peeled off the little black prize envelopes stuck to the back of each box. She'd been planning to give them to a children's club, but had gone into the hospital later in the year and then closed the shop for good. This was how nearly a hundred mint-condition baseball cards had been stored in a shed all this time.

We went straight from the agency to her house, and I headed home with a dusty cardboard box. I told her I wanted to pay her for them, but she flatly refused. In the end, I took them gratefully, not daring to tell her that these discarded prizes were worth far more than the chocolate they had come with.

As soon as I got home, we set to work. I cut the envelopes open while Root removed the cards and checked them. It was a simple process, and we fell into a rhythm. We were now rather experienced with baseball cards, and Root could distinguish between the various types just by touch.

Oshita; Hiramatsu; Nakanishi; Kinugasa; Boomer; Oishi; Kakefu; Harimoto; Nagaike; Horiuchi; Arito; Bass; Akiyama; Kadota; Inao; Kobayashi; Fukumoto… The players appeared one after the other; just as the man at the shop had said, some of the cards had embossed pictures, some had original autographs, and some were actually gilded. Root no longer allowed himself the editorial comments on each card. He seemed to feel that we would achieve our goal more quickly if he concentrated harder. A drift of little black envelopes had begun to collect around me, while the stack of cards Root had collected toppled and scattered between us.

Each time I reached into the box my hand stirred up a moldy odor, mixed with the smell of the chocolate. But by the time we had worked our way through half the box, I had begun to lose hope.

There were too many baseball players. Which was hardly surprising as every team fielded nine players at a time, and there were so many teams that they were divided into Central and Pacific leagues, and the history of the game in Japan spanned more than fifty years. I knew that Enatsu had been a great star, but there were others-Sawamura, Kaneda, Egawa-each of whom had his own fans. So, even with this big stack in front of us, it was unlikely we'd find the one card we wanted. I found myself lowering my expectations, hoping that the effort would at least satisfy Root. After all, I had a perfectly good present hidden in the back of the closet. They weren't particularly fancy shoes, but they were well designed and comfortable-looking, and they had cost considerably more than a baseball card. I was sure the Professor would be pleased with them.

"Ah… " Root let out a very grown-up sound, the kind you might make if you'd just discovered the solution to a complex word problem. The little cry was so quiet and restrained that it took me a minute to realize that the card he was holding in his hand was the one we had been looking for. He sat staring at the card, keeping Enatsu to himself for a moment. Neither of us spoke as he showed me the 1985 limited-edition card containing a fragment of Enatsu's own glove.