The housekeeper and the professor - By Yoko Ogawa Page 0,16

+ 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 + 10."

I tried picturing 18 and 14, but now that I'd heard the Professor's explanation, they were no longer simply numbers. Eighteen secretly carried a heavy burden, while 14 fell mute in the face of its terrible lack.

"There are lots of deficient numbers that are just one larger than the sum of their divisors, but there are no abundant numbers that are just one smaller than the sum of theirs. Or rather, no one has ever found one."

"Why is that?"

"The answer is written in God's notebook," said the Professor.

Everything around us was glowing in the sunlight; even the dried shells of the insects floating in the fountain seemed to glitter. The most important of the Professor's notes—the one that read "My memory lasts only eighty minutes"—had come loose, and I reached over to adjust the clip.

"I'll show you one more thing about perfect numbers," he said, swinging the branch and drawing his legs under the bench to make more room on the ground. "You can express them as the sum of consecutive natural numbers."

6 = 1 + 2 + 3

28 = 1 + 2 + 3 + 4 + 5 + 6 + 7

496 = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12 + 13 + 14 + 15 + 16 + 17 + 18 + 19 + 20 + 21 + 22 + 23 + 24 + 25 + 26 + 27 + 28 + 29 + 30 + 31

The Professor reached out to complete the long equation. The numbers unfolded in a simple, straight line, polished and clean. The subtle formula for the Artin conjecture and the plain line of factors for the number 28 blended seamlessly, surrounding us where we sat on the bench. The figures became stitches in the elaborate pattern woven in the dirt. I sat utterly still, afraid I might accidentally erase part of the design. It seemed as though the secret of the universe had miraculously appeared right here at our feet, as though God's notebook had opened under our bench.

"Well then," the Professor said at last. "We should probably be getting home."

"Yes, we should," I said, nodding. "Root will be there soon."

"Root?"

"My son. He's ten years old. The top of his head is flat, so we call him Root."

"Is that so? You have a son? We can't dawdle then. You should be there when he gets home from school." With that, he stood to go.

Just then, there was a cry from the sandbox. A little girl stood sobbing, a toy shovel clutched in her hand. Instantly, the Professor was at her side, bending over to comfort her. He tenderly brushed the sand from her dress.

Suddenly, the child's mother appeared and pushed the Professor away, picking the girl up and practically running off with her. The Professor was left standing in the sandbox. I watched him from behind, unsure how to help. The cherry blossoms fluttered down, mingling with the numbers in the dirt.

"I did the problem and I got it right. So now you have to keep your promise and fix the radio." These were the first words out of Root's mouth as he came through the door. "Here, look," he said, holding out his math notebook.

1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 55

The Professor studied Root's work as though it were a sophisticated proof. Unable to recall why he had assigned this problem or what connection it had to