The Gift of Numbers by Yōko Ogawa Read Free Book Online

and
some tennis courts. When the wind blew, the petals from the
cherry trees floated around us and the dappled sunlight danced on
the Professor's face. The notes on his jacket fluttered restlessly,
and he stared down into the can as if he'd been given some mysterious
potion.
    "I was right—you look handsome, and more manly."
    "That's quite enough of that," said the Professor. For once he
smelled of shaving cream rather than of paper.
    "What kind of mathematics did you study at the university?" I
asked. I had little confidence that I would understand his answer;
maybe I brought up the subject of numbers as a way of thanking
him for coming out with me.
    "It's sometimes called the 'Queen of Mathematics,' " he said,
after taking a sip of his coffee. "Noble and beautiful, like a queen,
but cruel as a demon. In other words, I studied the whole numbers
we all know, 1, 2, 3, 4, 5, 6, 7 ... and the relationships
between them."
    His choice of the word queen surprised me—as if he were
telling a fairy tale. We could hear the sound of a tennis ball bouncing
in the distance. The joggers and bikers and mothers pushing
strollers glanced at the Professor as they passed but then quickly
looked away.
    "You look for the relationships between them?"
    "Yes, that's right. I uncovered propositions that existed out
there long before we were born. It's like copying truths from
God's notebook, though we aren't always sure where to find this
notebook or when it will be open." As he said the words "out
there," he gestured toward the distant point at which he stared
when he was doing his "thinking."
    "For example, when I was studying at Cambridge I worked on
Artin's conjecture about cubic forms with whole-number coefficients.
I used the 'circle method' and employed algebraic geometry,
whole number theory, and the Diophantine equation. I was
looking for a cubic form that didn't conform to the Artin conjecture.
... In the end, I found a proof that worked for a certain type
of form under a specific set of conditions."
    The Professor picked up a branch and began to scratch something
in the dirt. There were numbers, and letters, and some
mysterious symbols, all arranged in neat lines. I couldn't understand
a word he had said, but there seemed to be great clarity in
his reasoning, as if he were pushing through to a profound truth.
The nervous old man I'd watched at the barbershop had disappeared,
and his manner now was dignified. The withered stick
gracefully carved the Professor's thoughts into the dry earth, and
before long the lacy pattern of the formula was spread out at our
feet.
    "May I tell you about something I discovered?" I could hardly
believe the words had come out of my mouth, but the Professor's
hand fell still. Overcome by the beauty of his delicate patterns,
perhaps I'd wanted to take part; and I was absolutely sure he
would show great respect, even for the humblest discovery.
    "The sum of the divisors of 28 is 28."
    "Indeed ... ," he said. And there, next to his outline of the Artin
conjecture, he wrote: 28 = 1 + 2 + 4 + 7 + 14. "A perfect number."
    "Perfect number?" I murmured, savoring the sound of the
words.
    "The smallest perfect number is 6: 6 = 1 + 2 + 3."
    "Oh! Then they're not so special after all."
    "On the contrary, a number with this kind of perfection is rare
indeed. After 28, the next one is 496: 496 = 1 + 2 + 4 + 8 + 16 + 31
+ 62 + 124 + 248. After that, you have 8,128; and the next one after
that is 33,550,336. Then 8,589,869,056. The farther you go, the
more difficult they are to find"—though he had easily followed
the trail into the billions!
    "Naturally, the sums of the divisors of numbers other than
perfect numbers are either greater or less than the numbers themselves.
When the sum is greater, it's called an 'abundant number,'
and when it's less, it's a 'deficient number.' Marvelous names, don't
you think? The divisors of 18— + 2 + 3 + 6 + 9—equal 21, so it's an
abundant number. But 14 is deficient: 1 + 2 + 7 +