The housekeeper and the professor - By Yoko Ogawa Page 0,15

number?" The room fell silent.

Though he could see me in the mirror, he craned around from time to time, checking to see that I'd kept my promise to stay with him. When the Professor moved his head, the barber was forced to stop cutting, but he would wait patiently and then go back to work. I smiled and gave a little wave to reassure the Professor that I was still there.

The white clippings of hair fell in clumps on the cape and then scattered to the floor. As he cut and combed away, did the barber suspect that the brain inside this snowy head could list all the prime numbers up to a hundred million? And did the customers on the sofa, waiting impatiently for the strange old man to depart, have any notion of the special bond between my birthday and the Professor's wristwatch? For some reason, I felt a secret pride in knowing these things, and I smiled at the Professor just a bit more brightly in the mirror.

After the barbershop, we sat on a bench in the park and drank a can of coffee. There was a sandbox nearby, and a fountain 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