Yôko Ogawa - The Gift of Numbers aka The Housekeeper and the Professor

The Professor folded his arms and listened intently, as if hanging on to Root's every word.

"So we decided to think about 1 to 9 first, and forget about 10 for right now. The number 5 is in the middle, so it's the… uh…"

"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.