The Gift of Numbers (12 page)

"But I haven't seen her since the interview," I said, shaking my
head. "And I don't remember having done anything to offend
her. She made me promise not to bother her with the Professor's
problems, and I haven't. I realize she pays my salary, but she
doesn't know a thing about what goes on in the Professor's house.
How can she fire me?"

"She knows you stayed overnight with him."

"She was spying on us?"

"She has every right to keep an eye on you while you're at
work."

I remembered having seen someone by the gate in the hedge
that night.

"The Professor is sick, and he needs special care. If I don't go
to him today, he'll be in a bad way. He's probably getting up right
now, all alone, reading his notes...."

"There are plenty of other housekeepers who can look after
him," said the Director, cutting me off. He opened the drawer in
his desk and filed away the card. "This is not negotiable," he said.
"We're done here."

And that was how I came to leave my job at the Professor's
house.

My new employers were a couple who ran a tax consulting service.
It took more than an hour by train and bus to reach their home,
and my duties often lasted until nine o'clock at night. They tended
to blur the line between tasks I would normally do in the house
and things they asked me to do for their business, and the woman
had a cruel streak. But worst of all, Root was once more a latchkey
kid. It was the Director's way of punishing me.

In my line of work, you get used to saying good-bye to employers,
and all the more so when you work for an agency like the Akebono.
The clients' needs change constantly, and you almost never
find a truly ideal fit between housekeeper and household. What's
more, the longer you stay in the same job, the greater the potential
for conflict.

A few of my previous employers had been kind enough to give
me a going-away party when I left, and I'd been quite tearful once
or twice when a child had brought me a good-bye present. But
just as frequently a job would end without so much as a parting
word, and sometimes I would even receive a bill for damage I had
allegedly done to dishes, furniture, or clothing.

However a job ends, I had always tried to take it in my stride.
There was nothing personal about it, no cause to feel sad or
wounded. To them, I was just one more housekeeper in a long line,
not someone to be remembered after I was gone. I usually forgot
them, too, as soon as I was out the door. And by the next day, I was
too busy learning the rules and expectations for my new job to
have time to feel sentimental.

With the Professor, however, things were different. And to be
honest, what bothered me most was knowing that he would have
no memory that we had ever been there. He could never ask his
sister-in-law why I had quit or what had become of Root; and he
would never remember us as he sat watching the evening star from
his easy chair, or when he paused in the middle of a math problem.
It was painful to think about. I was sad, but also angry with
myself for having broken something that could never be fixed.

My new job was mindless but physically demanding (washing
five fancy imported cars, mopping all the staircases in a four-story
building, making dinner for ten), but I still found it difficult to
concentrate, since one corner of my brain was always occupied
with thoughts of the Professor. And I invariably pictured him as
I'd seen him during his illness, sitting on the edge of the bed, bent
almost double. Preoccupied as I was with this thought, I made a
number of minor mistakes at work, and I was constantly in trouble
with the lady of the house.

I didn't know who had taken my place at the Professor's. I
hoped it was someone who looked enough like me to match the
portrait on the Professor's suit. Was he asking her telephone number
or shoe size and then expounding on the mysteries hidden in
them? I have to admit that I didn't like to imagine him sharing his
secrets with my successor. When I thought about it, the pleasures
of our shared mathematical discoveries seemed to fade—though I
knew from the Professor that the numbers themselves went on
just as they always had, regardless of changes in the world.

Sometimes I imagined that the new housekeeper would be
completely overwhelmed by the challenge of working for the Professor,
and that the Director would realize I was the only one for
the job. But I forced myself to give up such daydreams. It was vain
to assume that he couldn't get along without me; the Director had
been right, there were plenty of other housekeepers for the job.

Root would often ask why we weren't going to the Professor's
anymore.

"The situation changed," I told him.

"What situation?"

"It's complicated." He shrugged, but I could sense his disapproval.

A week after I left the Professor's, the Tigers' Yufune pitched a
no-hitter against the Hiroshima Carp. Root and I skipped our
baths and listened to the game on the radio after dinner. Mayumi
had three RBIs and Shinjo hit a homer. It was 6-0 in the bottom of
the eighth—same score as the Nakagomi game. When the Carp
went down in order, the noise in the ballpark and the announcer's
tone seemed to ratchet up a notch, but Root and I grew quiet. The
first Hiroshima batter in the ninth grounded out to second. Root
sighed. Each of us knew what the other was thinking, the memories
that this stirred up. No need to say anything.

Then Shoda, the last batter, made contact, he popped it up into
the outfield, the roar of the crowd drowned out the announcer,
and when he finally broke through again, he was still yelling "Out!
Out! Out!" over and over again.

"He did it." Root's tone was subdued. I nodded.

"This is the fifty-eighth no-hitter ... in major league history."
The announcer was coming through fitfully. "And the first for the
Tigers ... in nineteen years, since Enatsu in 1973."

We weren't sure whether we were happy or not about Yufune's
achievement. The Tigers had won, and it was a great feat to pitch
a no-hitter. But somehow the achievement had left us depressed.
The excitement pouring from the radio had brought back the
game on June 2, and along with it the realization that the Professor,
who had sat so happily in seat 714, was far away from us now.
And I couldn't help feeling that the foul ball off the bat of that
nameless pinch hitter in the ninth, the ball that had nearly hit
Root, had been an ill omen.

"Okay, time for bed. You have school in the morning," I said.
Root grunted and turned off the radio.

The foul ball foretold the end of Nakagomi's no-hitter. But more
bad luck had followed close behind with the Professor's fever and
then my dismissal. Of course, there was no way to know if it was
all due to the curse of the foul, but to me it certainly felt that
way—at that moment, everything had turned for the worse.

One day, at the bus stop on my way to work, a strange woman
tricked me out of some money. She wasn't a pickpocket or a
purse-snatcher. I willingly gave her the money, so I couldn't go to
the police; if she was practicing some new sort of swindle, then it
certainly was an effective one. She marched straight up to me,
held out her hand, and without any preamble said just one word:
"Money." She was a large, pale woman in her late thirties, and
other than the fact that she was wearing a spring coat in summer,
there was nothing odd about her appearance. She was too neatly
dressed to be a vagrant, nor did she seem to be deranged. Her
manner was as calm as if she were simply asking directions—in
fact she behaved as though I had asked for directions
from her
.

"Money," she said again.

I took out a bill and laid it on her palm. I have no idea why I
did it. Why would someone as poor as I am give money to a
stranger, short of being threatened at gunpoint? But I did, and
having slipped the bill into her pocket, she walked off as grandly
as she'd come, just as the bus pulled up to the stop.

All the way to the tax consultants' house, I tried to imagine
what my money would mean to this woman. Would it feed her
hungry children? Or buy medicine for her ailing parents? Or was
it just enough to keep her from going crazy, committing suicide
and taking her whole family with her? But no matter how much I
tried to convince myself that she really needed it, I couldn't get
over my anger at what had happened. It wasn't the loss of the
money that upset me; it was the miserable feeling that somehow I
was the one who had received some sort of handout, not the other
way around.

A few days later, Root and I went to tend my mother's grave on
the anniversary of her death. In the thicket behind the gravestone,
we discovered a dead fawn. The body was quite decayed, but
strips of spotted fur clung to its back. Its legs were splayed out under
it, as if it had struggled to stand up right to the end. The organs
had liquefied, the eyes were black holes, its jaw was slightly
parted, revealing little teeth.

Root found it. He gave a stifled cry, but then stood there frozen,
no more able to open his mouth and call me than to look away.

It had probably come running down the mountain and crashed
into the stone, dying on the spot. When we looked closer, we
could see traces of blood and skin on the grave.

"What should we do?" Root asked.

"It's okay," I told him. "We should just leave it."

We prayed longer that day for the fawn than we did for my
mother's soul. We prayed that the tiny life could go with her on
her journey.

The next day, I found a picture of Root's father in the local paper.
It seemed he had won a research prize given by some foundation.
It was just a short article with a blurry picture of a man ten
years older than when I had known him, but there was no doubt it
was him.

I closed the paper, crumpled it into a ball, and threw it in the
garbage. Then, thinking better of it, I fished it out, smoothed the
wrinkles, and cut out the article. It looked like a little piece of
trash.

"What's the big deal?" I asked myself. "No big deal at all," I
replied. "Root's father won a prize. Happy day. That's it."

I folded the article and put it away in the box that held the
stump of Root's umbilical cord.

I thought of the Professor whenever I saw a prime number—which,
as it turned out, was almost everywhere I looked: price tags
at the supermarket, house numbers above doors, on bus schedules
or the expiration date on a package of ham, Root's score on a
test. On the face of it, these numbers faithfully played their official
roles, but in secret they were primes and I knew that was what
gave them their true meaning.

Of course, I couldn't always tell immediately whether a number
was prime. Thanks to the Professor, I knew the prime numbers up
to 100 just by their feel; but when I encountered a larger number
that I suspected might be prime, I had to divide it to be sure.
There were plenty of cases where a number that looked to be
composite turned out to be prime, and just as many others where
I discovered divisors for a number that I was certain was prime.

Taking my cue from the Professor, I started carrying a pencil
and a notepad around in the pocket of my apron. That way, I
could do my calculations whenever the mood struck. One day
while I was cleaning in the kitchen in the tax consultants' house, I
found a serial number engraved on the back of the refrigerator
door: 2311. It looked intriguing, so I took out my notepad, moved
aside the detergent and the rags, and set to work. I tried 3, then 7,
and then 11. All to no avail. They all left a remainder of 1. Next I
tried 13, and 17, and 19, but none of them was a divisor. There
was no way to break up 2,311; but, more than that, its indivisibility
was positively devious. Every time I thought I had spotted a
divisor, the number seemed to slip away, leaving me oddly exhausted
yet all the more eager for the hunt—which was always the
way with primes.

Once I'd proved that 2,311 was prime, I put the notepad back
in my pocket and went back to my cleaning, though now with a
new affection for this refrigerator, which had a prime serial number.
It suddenly seemed so noble, divisible by only one and itself.

I encountered 341 while I was scrubbing the floor in their office.
A blue tax document, Form 341, had fallen under the desk.

My mop stopped in midstroke. It had to be prime. The form
was covered with dust from sitting under the desk for so long, but
341 called out to me; it had all the qualities that would have made
it a favorite of the Professor.

My employers had gone home and so I set about checking the
number in the darkened office. I hadn't really developed a system
for finding divisors, and I ended up relying mostly on intuition.
The Professor had shown me a method invented by someone
named Eratosthenes, who had been the librarian at Alexandria in
ancient Egypt, but it was complicated and I'd forgotten how to do
it. Since the Professor had such great respect for intuition when it
came to numbers, I suspected he would have been tolerant of my
method.

In the end, 341 was not a prime: 341 ÷ 11 = 31. A wonderful
equation, nonetheless.

Of course, it felt good when a number turned out to be prime.
But I wasn't disappointed if it did not. Even when my suspicions
proved unfounded, there were still things to be learned. The fact
that multiplying two primes such as 11 and 31 yielded a pseudo-prime
such as 341, led me in an unexpected direction: I now
found myself wondering whether there might be a systematic way
to find these pseudo-primes, which so closely resembled true prime
numbers.

But despite my curiosity, I set the form on the desk and rinsed
my mop in the murky bucket. Nothing would have changed if I'd
found a prime number, nor if I'd proven that one wasn't prime. I
was still facing a mountain of work. The refrigerator went on
keeping things cold, regardless of its serial number, and the person
who had filled out Form 341 was still struggling with his tax
problems. The numbers didn't make things better; perhaps they
even made them worse. Perhaps the ice cream was melting in that
refrigerator, I certainly wasn't making any progress mopping the
floor, and I suspected my employers would be unhappy with my
work. But for all that, there was no denying that 2,311 was prime,
and 341 was not.

I remembered something the Professor had said: "The mathematical
order is beautiful precisely
because
it has no effect on the
real world. Life isn't going to be easier, nor is anyone going to
make a fortune, just because they know something about prime
numbers. Of course, lots of mathematical discoveries have practical
applications, no matter how esoteric they may seem. Research
on ellipses made it possible to determine the orbits of the planets,
and Einstein used non-Euclidean geometry to describe the form
of the universe. Even prime numbers were used during the war
to create codes—to cite a regrettable example. But those things
aren't the goal of mathematics. The only goal is to discover the
truth." The Professor always said the word
truth
in the same tone
as the word
mathematics
.

"Try making a straight line right here," he'd said to me one evening
at the dinner table. Using a chopstick for a ruler, I traced a
line on the back of an advertising leaflet—our usual source of
scrap paper. "That's right. You know the definition of a straight
line. But think about it for a minute: the line you drew has a beginning
and an end. So it's actually a line 'segment'—the shortest
distance connecting two points. A true line has no ends; it extends
infinitely in either direction. But of course, a sheet of paper has
limits, as do your time and energy, so we use this segment provisionally
to represent the real thing. Now furthermore, no matter
how carefully you sharpen your pencil, the lead will always have a
thickness, so the line you draw with it will have a certain width, it
will have a surface area, and that means it will have
two
dimensions.
A real line has only
one
dimension, and that means it is impossible
to draw it on a piece of real paper."

I studied the point of the pencil.

"So you might wonder where you would ever find a real line—and
the answer would be, only in here." Again, he pointed at his
chest, just as he had when he had taught us about imaginary numbers.
"Eternal truths are ultimately invisible, and you won't find
them in material things or natural phenomena, or even in human
emotions. Mathematics, however, can illuminate them, can give
them expression—in fact, nothing can prevent it from doing so."

As I mopped the office floor, my mind churning with worries
about Root, I realized how much I needed this eternal truth that
the Professor had described. I needed the sense that this invisible
world was somehow propping up the visible one, that this one,
true line extended infinitely, without width or area, confidently
piercing through the shadows. Somehow, this line would help me
find peace.

I had just got back from shopping and was about to start dinner
for the tax consultants when a call came from the secretary at the
Akebono Housekeeping Agency.

"Get right over to that mathematician's house. It seems your
son has done something to upset them. I don't know what happened,
but get over there now. That's an order from the Director."

She hung up before I'd had time to find out more.

I remembered immediately the curse of the foul ball. At first,
I'd mistaken it for good luck when the ball missed Root, but it
seemed to have come back to haunt us, to fall right on his head.
The Professor had been right: "You should never leave a child
alone."

Maybe he had choked on the donut I'd given him as a snack.
Or he'd gotten a shock trying to plug in the radio. Frightening images
ran through my head. I didn't know what to tell my employer
as I ran off to the Professor's, her glare following me out the door.

It had been less than a month since we'd left the cottage. The
broken doorbell, the dilapidated furniture, and the overgrown
garden were the same, but the minute I stepped inside I had a bad
feeling.

It was clear that Root had not been hurt, which came as a relief.
He hadn't suffocated or been electrocuted but was sitting next to
the Professor at the table, his school backpack at his feet.

The bad feeling was coming from the Professor's sister-in-law,
who was sitting across from them. Next to her was a middle-aged
woman I had never seen before—my replacement, I assumed.
There was something indescribably unpleasant about seeing these
intruders in a space occupied, in my memory, by just the three of
us, the Professor, Root, and me.

As my feeling of relief faded, I began to realize how odd it was
for Root to be here. The widow sat at the table, in the same sort of
elegant dress she had worn during my interview. She held her
cane firmly in her left hand. Root seemed completely cowed and
refused to even look up at me. The Professor had assumed his
"thinking" pose, staring intently off into the distance, acknowledging
no one.

"I'm sorry to call you away from work," said the widow.
"Please, have a seat." She pointed to a chair. I was so out of breath
after running from the station that I forgot to give a proper answer.
"Please, sit down," she said again. "And you, get our guest some
tea, please." The other woman—I had no idea whether or not
she was an Akebono employee—got up and went to the stove. The
widow's tone was polite, but I could see that she was upset by the
way her tongue darted over her lips, and the way her fingers
drummed on the table. Unable to think of something to say, I did
as I was told and sat down. We were silent for a moment.

"You people ... ," she began at last, tapping a fingernail on
the table again. "What is it you want?" I took a breath before answering.

"Has my son done something wrong?"

Root was staring down at his lap, where he held his Tigers cap,
nervously crumpling it in his hands.

"I'll ask the questions, if you don't mind. The first thing I'd like
to know is why your boy needs to come to my brother-in-law's
house." The polish on her perfect nails was flaking off as she tapped
on the table.

"I didn't mean to—" Root started, still not looking up.

"The child of a housekeeper who has left our employ," the
widow interrupted him. Though she had said "child" more than
once, she made no attempt to look at Root—or at the Professor—as
though neither of them was in the room.

"I don't think it's a question of 'need,' " I said, still unsure what
she was getting at. "I think he just wanted to pay the Professor a
visit."

"I borrowed
The Lou Gehrig Story
from the library, and I
wanted to read it with him," Root said, looking up at last.

"Why would a ten-year-old child pay a visit to a sixty-year-old
man?" She ignored Root's explanation.

"I'm sorry my son came here without my permission, and I am
very sorry if he bothered you. I apologize for failing to supervise
him properly."

"That's not the point. I want to know why a housekeeper who
has been let go would send her son to see my brother-in-law. What
is it you want from him?"

"Want? I'm afraid there's some misunderstanding. He's just a
little boy who wanted to visit a friend. He found an interesting
book and he wanted to read it with the Professor. Isn't that enough
of a reason?"

"I'm sure it is. I'm not implying that the boy had any ulterior
motive. I'm asking what you wanted in sending him here."

"I don't want anything, except for my son to be happy."

"Then why do you involve my brother-in-law? You took him
out at night, you stayed later than was called for. I don't remember
asking you to do any of that."

The housekeeper brought over the tea. She set it in front of us
without a word or so much as a clink of the cups and went straight
back to the bedroom. It was obvious she would not be taking my
side on this.

"I realize that I was out of line, but I can assure you I had no ulterior
motive. It was all very innocent."

"Is it about money?"

"Money?!" The word was so unexpected that I nearly shouted
it back at her. "How can you say such a thing?"

"I can think of no other reason why you'd indulge my brother-in-
law like this."

"Don't be ridiculous!"

"You were fired. You have no business being here!"

"Excuse me," the new housekeeper interrupted, standing in
the kitchen doorway. She had removed her apron and was holding
her purse. "I'll be going now." She left as quietly as she'd come.
We watched as she slipped out the door.

The Professor seemed lost in thought; Root's cap was crushed
almost beyond recognition. I took a deep breath.

"It's because we're friends," I said. "Is it a crime to visit a
friend?"

"And who is friends with whom exactly?"

"My son and I, with the Professor."

"I'm afraid you've been deceiving yourself," the widow said,
shaking her head. "My brother-in-law has no property. He squandered
everything on his studies, and he has nothing to show for it."

"And what does that have to do with me?"

"He has no friends, you understand? No one has ever come to
visit him."

"Then Root and I are his
first
friends," I said.

At that moment, the Professor stood up.

"Leave the boy alone!"

He took a scrap of paper from his pocket and jotted something
down. Setting it on the table, he walked out of the room. His manner
had been utterly resolute, as if he'd decided from the beginning
that this was the only course of action. There had been no
anger or hesitation, he was calmly determined.

We stared at the note. No one moved. On the paper he had
written a single line, one simple formula:

e
^πi
+1 0

No one spoke. The widow's fingernails had ceased their tapping.
Her eyes, so full of suspicion and disdain a moment earlier,
now looked at me with a calm, understanding gaze, and I could
tell then that she knew the beauty of math.