"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.
