The Gift of Numbers (7 page)

"Average," I whispered in his ear.

"Right, the average. We haven't learned averages yet, so Momma
helped me with that part. If you add up 1 through 9 and divide by
9 you get 5 ... so 5 × 9 = 45, that's the sum of the numbers 1 to 9.
And now it's time to bring back the 10."

5 × 9 + 10 = 55

Root took the pen and wrote the equation on the pad.

The Professor sat studying what he had written, and I was sure
then that my moment of inspiration must look laughably crude to
him. I'd known from the start that I would never be able to extract
something sublime and true from my poor brain cells, no chance of
imagining something that would please a real mathematician.

But then the Professor stood up and began to applaud as
warmly and enthusiastically as if we had just solved Fermat's theorem.
He clapped for a long time, filling the little house with his approval.

"Wonderful! It's magnificent, Root." He folded Root in his
arms, half crushing him.

"Okay, okay. I can't breathe," Root mumbled, his words nearly
lost in the Professor's embrace.

He was determined to make this skinny boy with the flat head
understand how beautiful his discovery was, but as I stood watching
Root's triumph, I secretly felt proud of my own contribution. I
looked at the line of figures Root had written. 5 × 9 + 10 = 55. And
even though I'd never really studied mathematics, I knew that the
formula became more impressive if you restated it in abstract form:

It was a splendid discovery, and the clarity and purity of the solution
was even more extraordinary in light of the confusion it had
emerged from, as if I'd unearthed a shard of crystal from the floor
of a dark cave. I laughed quietly, realizing that I'd praised myself
adequately, even if the Professor's compliments had been directed
elsewhere.

Root was finally released, and we bowed again like two scholars
who had just finished their presentation at an academic conference.

That day, the Tigers lost 2–3 to the Dragons. They had taken a
two-run lead on a triple by Wada, but the Dragons responded
with back-to-back home runs and won the game.

The Professor loved prime numbers more than anything in the
world. I'd been vaguely aware of their existence, but it never occurred
to me that they could be the object of someone's deepest
affection. He was tender and attentive and respectful; by turns he
would caress them or prostrate himself before them; he never
strayed far from his prime numbers. Whether at his desk or at the
dinner table, when he talked about numbers, primes were most
likely to make an appearance. At first, it was hard to see their appeal.
They seemed so stubborn, resisting division by any number
but one and themselves. Still, as we were swept up in the Professor's
enthusiasm, we gradually came to understand his devotion,
and the primes began to seem more real, as though we could reach
out and touch them. I'm sure they meant something different to
each of us, but as soon as the Professor would mention prime
numbers, we would look at each other with conspiratorial smiles.
Just as the thought of a caramel can cause your mouth to water,
the mere mention of prime numbers made us anxious to know
more about their secrets.

Evening was a precious time for the three of us. The vague tension
around my morning arrival—which for the Professor was always
our first encounter—had dissipated, and Root livened up
our quiet days. I suppose that's why I'll always remember the Professor's
face in the evening, in profile, lit by the setting sun.

Inevitably, the Professor repeated himself when he talked
about prime numbers. But Root and I had promised each other
that we would never tell him, even if we had heard the same thing
several times before—a promise we took as seriously as our agreement
to hide the truth about Enatsu. No matter how weary we
were of hearing a story, we always made an effort to listen attentively.
We felt we owed that to the Professor, who had put so much
effort into treating the two of us as real mathematicians. But our
main concern was to avoid confusing him. Any kind of uncertainty
caused him pain, so we were determined to hide the time
that had passed and the memories he'd lost. Biting our tongues
was the least we could do.

But the truth was, we were almost never bored when he spoke
of mathematics. Though he often returned to the topic of prime
numbers—the proof that there were an infinite number of them,
or a code that had been devised based on primes, or the most
enormous known examples, or twin primes, or the Mersenne
primes—the slightest change in the shape of his argument could
make you see something you had never understood before. Even a
difference in the weather or in his tone of voice seemed to cast
these numbers in a different light.

To me, the appeal of prime numbers had something to do with
the fact that you could never predict when one would appear. They
seemed to be scattered along the number line at any place that took
their fancy. The farther you get from zero, the harder they are to
find, and no theory or rule could predict where they will turn up
next. It was this tantalizing puzzle that held the Professor captive.

"Let's try finding the prime numbers up to 100," the Professor
said one day when Root had finished his homework. He took his
pencil and began making a list: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31,
37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.

It always amazed me how easily numbers seemed to flow from
the Professor, at any time, under any circumstances. How could
these trembling hands, which could barely turn on the microwave,
make such precise numbers of all shapes and sizes?

I also liked the way he wrote his numbers with his little stub of
a pencil. The 4 was so round it looked like a knot of ribbon, and
the 5 was leaning so far forward it seemed about to tip over. They
weren't lined up very neatly, but they all had a certain personality.
The Professor's lifelong affection for numbers could be seen in
every figure he wrote.

"So, what do you see?" He tended to begin with this sort of
general question.

"They're scattered all over the place." Root usually answered
first. "And 2 is the only one that's even." For some reason, he always
noticed the odd man out.

"You're right. Two is the only even prime. It's the leadoff batter
for the infinite team of prime numbers after it."

"That must be awfully lonely," said Root.

"Don't worry," said the Professor. "If it gets lonely, it has lots of
company with the other even numbers."

"But some of them come in pairs, like 17 and 19, and 41 and
43," I said, not wanting to be shown up by Root.

"A very astute observation," said the Professor. "Those are
known as 'twin primes.' "

I wondered why ordinary words seemed so exotic when they
were used in relation to numbers.
Amicable numbers
or
twin primes
had a precise quality about them, and yet they sounded as though
they'd been taken straight out of a poem. In my mind, the twins
had matching outfits and stood holding hands as they waited in
the number line.

"As the numbers get bigger, the distance between primes increases
as well, and it becomes more difficult to find twins. So we
don't know yet whether twin primes are infinite the way prime
numbers themselves are." As he spoke, the Professor circled the
consecutive pairs.

Among the many things that made the Professor an excellent
teacher was the fact that he wasn't afraid to say "we don't know."
For the Professor, there was no shame in admitting you didn't
have the answer, it was a necessary step toward the truth. It was as
important to teach us about the unknown or the unknowable as it
was to teach us what had already been safely proven.

"If numbers never end, then there should always be more
twins, right?"

"That makes sense, Root. But when you get to much bigger
numbers—a million or ten million—you're venturing into a wasteland
where the primes are terribly far apart."

"A wasteland?"

"That's right, a desert. No matter how far you go, you don't
find any. Just sand as far as the eye can see. The sun shines down
mercilessly, your throat is parched, your eyes glaze over. Then you
think you see one, a prime number at last, and you go running
toward it—only to find that it's just a mirage, nothing but hot
wind. Still, you refuse to give up, staggering on step by step,
determined to continue the search ... until you see it at last, the
oasis of another prime number, a place of rest and cool, clear
water...."

The rays of the setting sun stretched far into the room. Root
traced the circles around the twin primes as the steam from the
rice cooker floated in from the kitchen. The Professor stared
through the window as if he were looking out at the desert,
though all he could really see was his tiny, neglected garden.

The thing the Professor hated most in the whole world was a
crowd, which is why he was so reluctant to leave the house. Stations,
trains, department stores, movie theaters, shopping malls—any
place people gathered in large numbers was unbearable for
him. There was something fundamentally incompatible between
crushing, random crowds and pure mathematical beauty.

The Professor wanted peace, though that didn't necessarily
mean complete silence. Apparently, he was not disturbed by Root
when he ran down the hall or turned up the volume on the radio.
What he needed was internal calm uninterrupted by the outside
world.

When he had solved a contest problem from one of his journals
and was making a clean copy to put in the mail, you could often
hear him murmur, "How peaceful ..." He seemed to be perfectly
calm in these moments, as though everything were in its rightful
place, with nothing left to add or subtract. "Peaceful" was, to him,
the highest compliment.

When he was in a good mood, he would sit at the kitchen table
and watch me making dinner; and if I were making dumplings,
he would look on with something approaching wonder. I would
take a dumpling skin in the palm of my hand, spoon on a bit of
filling, and then pinch up the edges before setting it on the platter.
A simple process, but he was completely absorbed by it, watching
me until the last dumpling had been stuffed. I have to admit
that the scene struck me as so funny that I hardly could keep from
laughing.

When I was done at last and the dumplings were neatly arranged
on the plate, he would fold his hands on the table and nod
solemnly. "How peaceful ..."

On the sixth of May, at the end of the spring holidays, Root cut
himself with a kitchen knife. The Professor did not take it well.

After the four-day break, I arrived at the Professor's house only
to discover that the sink had been leaking and a puddle had
spread into the hall. By the time I'd called to have the water shut
off and hired a plumber to come in, I was probably a bit out of
sorts. To make matters worse, the Professor had seemed more
remote than ever, and no matter how often I pointed out my picture
among the tags on his coat, he seemed confused or oblivious. By
evening he had still not come out of his shell. While my irritation
might have contributed to Root's accident, the Professor was in no
way to blame.

Shortly after Root arrived from school, I realized that I'd run
out of cooking oil. I was uneasy leaving the Professor and Root
alone, so I talked to Root before I left.

"Do you think it's okay?"

"Is what okay?" he replied, almost curtly. It is hard to say
exactly what worried me, I had no premonition, I was simply
anxious about leaving the Professor in charge.

"I've never left you alone with the Professor and I was just wondering
if that's okay—"

"Don't worry!" Root said, running off to the study to have his
homework checked.

I was gone no more than twenty minutes, but when I opened
the door, I knew immediately that something was wrong. I discovered
the Professor, sobbing and moaning, crouched on the kitchen
floor, holding Root in his arms.

"Root ... Root ... his hand!"

He could barely speak, and the more he tried to explain what
had happened, the more incoherent he became. His teeth chattered
and sweat poured down his face. I pried Root loose from his
arms.

Root wasn't crying. He may have been trying to keep the Professor
calm, or he may have been afraid I would be angry with
him, but whatever the reason, he had been lying quietly in the
Professor's arms, waiting for me to return. Their clothes were
smeared with blood and the cut on Root's hand was still bleeding,
but I could see right away that the Professor's panic was out of all
proportion to Root's injury. The bleeding had nearly stopped, and
Root didn't appear to be in any pain. After I'd washed out the
wound at the kitchen sink, I brought him a towel and told him to
hold it on the cut. In the meantime, the Professor sat motionless
on the floor, his arms frozen as if he were still holding Root. It
seemed almost more urgent to look after him than it was to treat
Root.

"Don't worry," I said, patting him gently on the back.

"How could this have happened? Such a sweet, good boy ..."

"It's just a little cut. Boys hurt themselves all the time."

"But it's all my fault. He didn't do anything wrong. He didn't
want to bother me, so he didn't say anything ... he just sat there
bleeding...."

"It's no one's fault," I said.

"No, it's my fault. I tried to stop the bleeding, but I
couldn't.... And then he got so pale, and I was afraid he'd stop
breathing...." He hid his face in his hands, covering the sweat
and tears.

"Don't worry," I said again. "He'll be fine." As I rubbed his
back, I realized that it was surprisingly broad and sturdy.

Neither Root nor the Professor were making much sense, but I
finally managed to piece together what had happened: Root had
finished his homework and was trying to peel an apple for a snack
when he had cut himself between his thumb and index finger. The
Professor insisted that Root had asked him for help with the apple,
while Root maintained that he'd done the whole thing by himself.
In any event, Root had tried to take care of the cut but he couldn't
stop the bleeding, and the Professor had found him just as he'd
begun to panic.

Unfortunately, the clinics in the neighborhood had already
closed for the day. The only doctor answering the phone was a
pediatrician at a clinic behind the train station, who said he
could see him right away. I helped the Professor up and dried his
face, and at that point an astonishing change came over him. He
hoisted Root onto his back, and though I tried to remind him
that the child hadn't hurt his legs, he ran off to the doctor's
carrying Root piggyback. To be honest, the ride seemed so
rough that I was worried the wound would open up again. It
could hardly have been easy for the Professor to carry a sixty-pound
child on his back, but he was stronger than I'd thought.
He charged along in his moldy shoes, gasping a bit from time to
time, but holding Root's legs firmly under his arms. Root pulled
his Tigers cap down over his eyes and buried his face in the Professor's
back, less from pain than from the embarrassment of being
seen. When we got to the clinic, the Professor pounded on
the locked door, as though he were carrying a dying child on his
back.

It took only two stitches to close the cut, but the Professor and
I had to wait in the darkened corridor until they had finished
the examination. They wanted to be sure Root hadn't severed a
tendon.

The clinic was old and depressing. The ceiling was discolored,
and the grimy slippers stuck to your feet. Yellowed posters on the
walls gave instructions for weaning and inoculations. The only
light in the hall was the dim bulb outside the X-ray room.

They'd said the test was just a precaution, but Root had been in
the examination room for some time.