“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. 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 — 1+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.
If I’d had any math teacher in my life who had lectured on any of the numerical marvels I read about in Yoko Ogawa’s The Housekeeper and the Professor (including amicable numbers and Euler’s Formula, the most beautiful equation, I think), maybe I wouldn’t regard numbers as, at best, something I must coexist with.
