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 repairing the radio, he was perhaps
looking for an answer in the sum itself.
The Professor carefully avoided asking us questions about
things that had happened more than eighty minutes ago. We
would have happily explained the meaning of the homework and
the radio if he had asked, but he preferred to examine the facts
before him and draw his own conclusions. Because he had been—and
in many ways still was—such a brilliant man, he no doubt understood
the nature of his memory problem. It wasn't pride that
prevented him from asking for help but a deep aversion to causing
more trouble than necessary for those of us who lived in the normal
world. When I realized why he was so reluctant to bring up
the subject of his memory, I decided I would say as little as possible
about it, too.
"You've added up the numbers from 1 to 10," he said at last.
"I got it right, didn't