The Devotion of Suspect X - Keigo Higashino [31]
The long-haired student let his hand fall down to the desktop. He grinned and shrugged. “Nah. I try to avoid doing anything unnecessary. I’m in physics, you know. We just use the theorems you mathematicians come up with. I’ll leave working out the proofs to you.”
“But you do understand what it—what this—means?” Ishigami asked, gesturing at his notebook page.
“Yes, because it’s already been proven. No harm in knowing what has a proof and what doesn’t,” the student explained, steadily meeting Ishigami’s gaze. “The four-color problem? Solved. You can color any map with only four colors.”
“Not any map.”
“Oh, that’s right. There were conditions. It had to be a map on a plane or a sphere, like a map of the world.”
It was one of the most famous problems in mathematics, first put into print in a paper in 1879 by one Arthur Cayley, who had asked the question: are four colors sufficient to color the contiguous countries on any map, such that no two adjacent countries are ever colored the same? All one had to do was prove that four colors were sufficient, or present a map where such separation was impossible—a process which had taken nearly one hundred years. The final proof had come from two mathematicians at the University of Illinois, Kenneth Appel and Wolfgang Haken. They had used a computer to confirm that all maps were only variations on roughly 150 basic maps, all of which could be colored with four colors.
That was in 1976.
“I don’t consider that a very convincing proof,” Ishigami stated.
“Of course you don’t. That’s why you’re trying to solve it there with your paper and pencil.”
“The way they proved it would take too long for humans to do with their hands. That’s why they used a computer. But that makes it impossible to determine, beyond a doubt, whether their proof is correct. It’s not real mathematics if you have to use a computer to verify it.”
“Like I said, a true adherent of Erdős,” the long-haired student observed with a chuckle.
Paul Erdős was a Hungarian-born mathematician famous for traveling the world and engaging in joint research with other mathematicians wherever he went. He believed that the best theorems were those with clear, naturally elegant proofs. Though he’d acknowledged that Appel and Haken’s work on the four-color problem was probably correct, he had disparaged their proof for its lack of beauty.
Ishigami felt like this peculiar visitor had somehow peered directly into his soul.
“I went to one of my professors the other day about an examination problem concerning numbers analysis,” the other student said, changing the subject. “The issue wasn’t with the problem itself. It was that the answer wasn’t very elegant. As I suspected, he’d made a mistake typing up the problem. What surprised me was that another student had already come to him with the same issue. To tell the truth, I was a little disappointed. I thought I was the only one who had truly solved the problem.”
“Oh that? That was nothing—” Ishigami began, then closed his mouth.
“—Nothing special?” the other finished for him. “Not for a student like Ishigami—that’s what my professor said. Even when you’re at the top, there’s always something higher, eh? It was about then that I figured I wouldn’t make it as a mathematician.”
“You said you’re a physics major, right?”
“Yukawa’s the name. Pleased to meet you.” He extended a hand toward Ishigami.
Ishigami took his hand, wondering at his peculiar new acquaintance. Then, he began to feel happy. He’d always thought he was the only weird one.
* * *
He wouldn’t have called Yukawa a “friend,” but from then on, whenever they chanced to meet in the hall, they would always stop and exchange a few words. Yukawa was well read, and he knew a lot about fields outside of mathematics and physics. He could even hold his own in a conversation about literature or the arts—topics that Ishigami secretly despised. Of course, lacking any basis for comparison, Ishigami didn’t know how deep the man’s knowledge of such things went. Besides, Yukawa soon noticed Ishigami’s lack of interest in anything