“2.316 is not an integer. That is the whole point.”她靠在枕头上,氧气管里气泡一下一下冒着。“If the critical dimension were two or three, someone would have found it a century ago. But 2.316—who would look there? It is not elegant. It does not simplify nicely. It just sits there, between two and three, like a crack in the floor that nobody notices because they are looking at the walls.”
Schmidt没有打断她,她端起杯子,没喝,又放下。“The classical theory says turbulence starts and never stops. Energy cascades from large scales to small scales, and nothing can block it. But I kept thinking—what if there is a threshold? What if, at a certain dimension, the cascade gets stuck? Not because the physics is wrong, but because the mathematics runs out of tools.”
她把氧气管往上推了推。“Fractional NS equations. Integer dimensions are special cases. Fractional dimensions are the general rule. The energy cascade in three-dimensional turbulence is essentially a projection phenomenon in fractional—dimensional space. When the dimension drops to a critical value, the cascade is suppressed. Mathematically unprovable, but physically it is there.”
Schmidt沉默了一会儿。“And you found it.”
“I did not find it. I chased it. For years. The proof always slipped away at the last step. Like trying to grab a handful of wind.”她停了一下, “But I know where it hides.”
她把杯子放在床头柜上。“The smoothness of the solution breaks at exactly that point. The equations do not fail—they just refuse to give a smooth answer. And mathematicians hate that. They want things to be either smooth or not smooth, either proven or not proven. 2.316 is neither. It is a crack in the floor.”
“Then you should write that down. Not the proof—the direction. Let someone else find the proof. You found the crack.”
苏布德靠在枕头上,看着窗外。阳光从窗帘缝隙里漏进来,落在被子上。“I did. It is in the manuscript.”
“Then it will be read.”
她沉默了一会儿。“The mathematicians in Göttingen will look at it and say, ‘She almost had it. The old woman from Beijing. She almost proved it.‘ And maybe one of them will pick up where I left off. Not because they owe me anything, but because the crack is still there. And someone has to step into it.”
Schmidt端起茶杯。“Riemann never proved his hypothesis. Hilbert never finished his program. You are in good company.”
“I know.”她靠在枕头上,嘴角微微翘着。“I would have liked to prove it, though. Just once. To see the whole thing come together. But I suppose that is not how mathematics works. You do not get to choose which problems you solve. The problems choose you, and then they keep you for life.”
“And 2.316 kept you.”
“It kept me. And now I am letting it go.” 她靠在枕头上沉默了一会儿,呼吸很轻。
片刻后,她轻声说,“I just wish I could see the proof. Just once.”
Schmidt端起茶杯,没有喝,又放下了。他看着苏布德,语气很轻。
“Ramanujan left behind over three thousand formulas. Not a single proof among them. When someone asked him why, he said the formulas came from the gods. Then he wrote: Known. Proof omitted.”
苏布德微微侧过头,眼角有笑意。
“So I will follow Ramanujan,” Schmidt said. “NS equals 2.316. Known. Proof omitted.”
苏布德轻轻笑了,氧气管里的气泡轻轻颤了一下。她端起杯子,没有喝,只是捧在手心里。
“The laziest paper I ever wrote,” she said.
“And the most honest one,” Schmidt said.
They exchanged a glance across their teacups and smiled.