He walked out of the foyer and into the hall. The rows of lockers seemed tighter, the ceiling lower. The whole school was shabby and damp. He wondered why they hadn't rented out some place nice.

Nomura saw a light on at the end of the hall, in one of the classrooms. He imagined he must have followed this same route to the classroom ten years ago, but he couldn't remember why. He remembered it only from sleep now. The school, the halls and the classroom had become stock scenery for dreams. He could meet new acquaintances here along with old ones.

As he came closer he saw a reflection through the glass partition next to the door, itself half open. A tiny human figure warped in the glass, vanishing into the distance as he came closer. Nomura put his hand to the door and pulled it open.

An old man was seated at the desk, his back arched in the chair. His pen hand rested on a piece of paper in front of him, but it dangled rather than ran. He seemed to be scribbling something, or tracing lazy circles.

"Yes? Can I help you?"

"Oh, I'm sorry." Nomura said. "I didn't mean to disturb you, I..."

"Yes?"

"I'm here for the reunion."

"I see."

"I was here ten years ago. I don't know if you were even here then, I...Takashi Nomura? Did you know?"

The old man looked up, but his features barely cracked.

"Of course, you were in Class A, you sat in that second row over there. Don't tell me you've forgotten Moriyama already."

Now memories came back to him. He remembered long mathematics classes, always in the afternoon. The row of windows opened onto the sun. Everyone was sleepy and they always cheated.

He remembered Moriyama, too. Once, the old man had kept him after class. Nomura had failed test after test, and had been forced to admit that he understood nothing about the sides of a triangle, or any relationship they shared. He was certain information of that sort had nothing to do with life.

"Mr. Moriyama, of course. I still remember that Pythagorean theorem."

"Yes. It took you a while, didn't it? But I bet you still know it."

"In a right triangle,

*c*square equals

*a*square plus

*b*square. The sum of the squares of the legs is equal to the square of the hypotenuse."

Moriyama gave a little smile of appreciation, as if Nomura had performed a dog trick.

"And has it come in handy?"

Nomura didn't know what to say. As he had expected, the Pythagorean theorem had had no bearing on the course of his life. It only rattled at the back of his mind like a tear-off tab in a tin can.

"To be honest I haven't ever used Pythagorean theorem. I still remember it, if that's what you mean."

Moriyama shuffled the papers on his desk and pushed them aside.

"I'll tell you something, Nomura." he said. "And you can make of it what you will. You see, Pythagorean theorem isn't technically...

*true*, in all respects."

Moriyama was smiling now, a true smile.

"What do you mean by that?" Nomura said.

"Come closer, I'll show you."

And the old man was already writing on the back of a notebook, tracing a set of axioms. Nomura bent over his shoulder. It had been years since he'd followed a set of equations. Many times he asked Moriyama to stop. The old man let a proud patience overtake his haste. After half an hour, they arrived at the Q.E.D. Nomura felt like he was back in Class A.

"There. There it is. The sum of the squared lengths of

*a*and

*b*is clearly far greater than the square of

*c*."

Nomura studied the proof, which had spread from the notebook's back cover to its inside pages. Everything seemed to make sense. But he felt certain that someone more qualified could rescue the theorem.

"It seems...wrong, somehow."

"Wrong? How? The proof is airtight. Pythagorean theorem is manifestly true only on an extremely reduced, local scale. The theorem itself is not valid in any real mathematical sense."

Nomura wished for a chair. He wondered why Moriyama hadn't offered him one.

"So why are you telling me this now?" Nomura said.

Moriyama's smile broke for a moment.

"Well, you took the trouble to visit me, didn't you? I didn't think I should let you go empty-handed."

"That's not what I meant." Nomura said. "I meant, if you can prove Pythagorean theorem is false, why aren't you publishing this information? Why aren't you writing some kind of...book? Paper?"

Moriyama closed the notebook.

"Well, when you get to be my age, Nomura, things like that seem a lot less important. I could write a paper and make a fuss and have my name in all kinds of journals, and when a correct theorem came out, I'd still be in this classroom teaching it. So why go to all that trouble?"

"I always thought that was the whole point of um...science..."

"Pythagorean theorem isn't hurting anyone." Moriyama said. "I wouldn't worry about these things so much. I just thought I should tell you, seeing as you worked so hard on it in my class."

Now Moriyama's smile was paternal. Nomura decided to leave.

Before he reached the door, Moriyama pushed the notebook towards him.

"Here," he said. "Maybe it'll revive your interest in mathematics."

Nomura took the notebook and slotted it into his briefcase and walked back to the foyer. He passed through a short side hall into the auditorium. The reunion was ending; his old classmates were exchanging cards and numbers. A pink slush rocked in the punch bowl every time someone bumped the table. Someone took his arm and he stared into the smile of a woman he was supposed to recognize. Nomura was afraid, here. He felt like he had amnesia. He wanted to be able to hide behind his wife Mayumi, who was at the hotel now.

"I'll use you to deflect conversation." he'd told her. "Everyone will ask questions about you, and you can ask them what I was like in high school. Maybe they remember."

"It won't work. I'm not the only thing that's happened to you in ten years." Mayumi said. "Most

*important*, but..."

A vigorous looking man punched him on the shoulder. This was not the first time Nomura had been punched tonight. The vigorous and friendly punches were one of the reasons he'd gone for his walk.

"Where'd you go, buddy?" the man said. "We missed you."

---

Back at the hotel, Mayumi had ordered pizza. There was no time for anything else because they had to be back in Osaka by five. His appointment was at eight.

Nomura decided that it wasn't right for him to eat pizza from the box while wearing his business suit, so he took it off. Mayumi was in pajamas.

"How was it?" she said. "Did you meet any of your old friends?"

"I think so." Nomura said.

"You don't know?"

Nomura felt disappointed she hadn't protected him.

"You should have come." he said.

"You know that's not my kind of thing."

Nomura stared down at the pizza.

"Do you know what Pythagorean theorem is?" he said.

"The square of the hypotenuse is equal to the sum of the squares of the other two sides?"

Now he felt a kind of contempt for Mayumi. With the notebook in his briefcase, he could destroy her understanding of triangles. But he knew Mayumi would only be amazed for a few moments. After that her eyes would dull. Did these things matter, if the world continued to function? He imagined this was how Moriyama felt every day.

Mayumi asked him more questions about the reunion, then talked about her high school class when she saw he wasn't listening. Nomura tried to respond, but his thoughts kept returning to the briefcase.

Moriyama had claimed that the truth of the theorem meant nothing. But Nomura remembered the sensation of it rattling in the back of his mind. Perhaps the memory he had retained of the theorem had only been a memory of Moriyama himself.

He thought: by unveiling the truth of the theorem, Moriyama had been trying to force him into sympathy. Anyone could claim their accomplishments in public with modesty and grace. But to be a sharer of secrets to one person was a greater happiness, a private, selfish joy-

Now he felt a great dislike for Moriyama. It was nothing he hadn't felt before, ten years earlier. Moriyama meant nothing, yet he had destroyed a tiny part of the world. It seemed to him that if he began to doubt his received impressions, there would be no end to the concepts cast on the fire. But if he trusted what people told him, believing what he read and saw, there would always be an opening for another Moriyama, another old man cramped with secrets. So why should he doubt or trust anything?

It was not that these things meant anything. It was that he did not like to be

*told*.

Nomura decided he would cut back on belief. He would believe as little as possible; would prune his mind like a tree. But with Mayumi sitting across from him, digressing, with his appointment the next day, where to begin...?