The Gift of Numbers Read Free Page B

was spring, but still chilly once the sun set, so
the oil heater was burning in the corner.
    "Do you send a lot of articles to magazines?" I asked.
    "I wouldn't call them 'articles.' They're just puzzles for amateur
mathematicians. Sometimes there's even a prize. Wealthy men
who love mathematics put up the money." He looked down, checking
his suit in various places, and his gaze fell on a note clipped to
his left pocket. "Oh, I see. I sent a proof to the Journal of Mathematics today."
    It had been much more than eighty minutes since I'd made my
trip to the post office.
    "Oh, dear!" I said. "If it's a contest, I should have sent it express
mail. If it doesn't get there first, I suppose you don't get the
prize."
    "No, there was no need to send it express. Of course, it's important
to arrive at the correct answer before anyone else, but it's
just as important that the proof is elegant."
    "I had no idea a proof could be beautiful ... or ugly."
    "Of course it can," he said. Getting up from the table, he came
over to the sink where I was washing the dishes and peered at me as
he continued. "The truly correct proof is one that strikes a harmonious
balance between strength and flexibility. There are plenty of
proofs that are technically correct but are messy and inelegant or
counterintuitive. But it's not something you can put into words—explaining
why a formula is beautiful is like trying to explain why
the stars are beautiful."
    I stopped washing and nodded, not wanting to interrupt the
Professor's first real attempt at conversation.
    "Your birthday is February twentieth. Two twenty. Can I show
you something? This was a prize I won for my thesis on transcendent
number theory when I was at college." He took off his wristwatch
and held it up for me to see. It was a stylish foreign brand,
quite out of keeping with the Professor's rumpled appearance.
    "It's a wonderful prize," I said.
    "But can you see the number engraved here?" The inscription
on the back of the case read President's Prize No. 284.
    "Does that mean that it was the two hundred and eighty-fourth
prize awarded?"
    "I suppose so, but the interesting part is the number 284 itself.
Take a break from the dishes for a moment and think about these
two numbers: 220 and 284. Do they mean anything to you?"
    Pulling me by my apron strings, he sat me down at the table
and produced a pencil stub from his pocket. On the back of an
advertising insert, he wrote the two numbers, separated strangely
on the card.
    220
    284
    "Well, what do you make of them?"
    I wiped my hands on my apron, feeling awkward, as the Professor
looked at me expectantly. I wanted to respond, but had no
idea what sort of answer would please a mathematician. To me,
they were just numbers.
    "Well ... ," I stammered. "I suppose you could say they're both
three-digit numbers. And that they're fairly similar in size—for example,
if I were in the meat section at the supermarket, there'd be
very little difference between a package of sausage that weighed
220 grams and one that weighed 284 grams. They're so close that I
would just buy the one that was fresher. They seem pretty much the
same—they're both in the two hundreds, and they're both even—"
    "Good!" he almost shouted, shaking the leather strap of his
watch. I didn't know what to say. "It's important to use your intuition.
You swoop down on the numbers, like a kingfisher catching
the glint of sunlight on the fish's fin." He pulled up a chair, as if
wanting to be closer to the numbers. The musty paper smell from
the study clung to the Professor.
    "You know what a factor is, don't you?"
    "I think so. I'm sure I learned about them at some point...."
    "For 220 is divisible by 1 and by 220 itself, with nothing leftover.
So 1 and 220 are factors of 220. Natural numbers always have 1
and the number itself as factors. But what else can you divide it
by?"
    "By 2, and 10...."
    "Exactly! So let's try writing out the factors of 220 and 284, excluding
the numbers