119: Chapter 119 The Mathematician's Pastime

The morning light at the Institute for Advanced Study in Princeton filtered through the blinds, casting long, thin gratings of light across the dark walnut floor.

Professor Wells took a sip of his long-cold coffee and sank comfortably into his signature high-backed leather chair.

Browsing the daily new submissions on arXiv was not work for him, but a pastime tinged with a sense of condescending amusement.

It was like a connoisseur strolling through a flea market full of forgeries, occasionally discovering something hilarious.

He skillfully called up the interface of the AI screening tool, CloseAI, and swiped his fingertips across the touchscreen.

"Ha, another warrior trying to prove the Goldbach Conjecture."

He scoffed and clicked on one.

"God, did he even create his own system of mathematical axioms? What's next, inventing a perpetual motion machine?"

He shook his head and closed the page with a hint of pity.

The next one seemed more rigorous, but after scanning only a few lines, Professor Wells's brows knitted together.

"The conclusion is a castle in the air! Basic convergence conditions were ignored; CloseAI's screening algorithm needs an upgrade."

He muttered impatiently, preparing to end this inspection.

Just then, a title abruptly caught his eye:

"Proof of the Existence and Smoothness of the Navier-Stokes Equations"

Author: Chen Youhua.

"N-S? Existence and smoothness?"

Professor Wells raised an eyebrow, his tone carrying his usual mockery.

"Another warrior trying to slay the dragon? The name looks like it's from Rabbit Country; CloseAI is being a bit unreliable today."

He intended to skip it, but a sliver of curiosity drove him to click the link.

The preprint interface loaded, and there was no tidy LaTeX formatting, only hundreds of... photos?

Yes, photos of handwritten manuscript paper taken with a mobile phone!

The edges of the paper were even curled, the ink varied in darkness, and the one shot where the pages were stacked together looked particularly messy.

"Good heavens..."

Professor Wells couldn't help but groan and lean back against his chair.

"Posting photos of a manuscript on arXiv? Mr. Chen, do you disdain writing formal papers, or do you simply not understand academic standards?"

The significance of a preprint lies in rapid dissemination and establishing priority, but it at least requires a decent, readable document!

What is this? Performance art?

A sense of offended, judgmental anger rose up in him.

He decided to properly review this bizarre work and prepared to leave the sharpest, most professional critique in the comments section to warn others and save them from wasting their time.

He clicked on the first photo and zoomed in.

The handwriting was scrawled yet exceptionally powerful; the tension-filled mathematical symbols rushed at him.

He habitually scanned quickly, his gaze searching like a searchlight for obvious logical gaps or calculation errors.

One line, two lines... turning the page... his speed gradually slowed down.

The initial contempt was replaced by a hint of gravity.

This was not like those unconstrained, hole-ridden crank works.

The use of symbols was standard, and the thread of the derivation... seemed to have a traceable logic?

Although the writing was casual, the intention behind every step revealed a strange sense of rigor.

Professor Wells sat up straight, his fingers tapping unconsciously on the desktop.

He closed all other windows, leaving the screen entirely to the hundreds of manuscript photos.

He reopened the first page, no longer scanning, but reading line by line, his brain performing the derivations in sync.

Time slipped by quietly amidst the ink flowing from the pen tip and the cold light of the screen.

The coffee had gone completely cold, forgotten at the corner of the desk.

Professor Wells's gaze became increasingly focused, his brows occasionally knitting, then relaxing.

He recognized those familiar, classic mathematical tools used to storm the fortress of fluid mechanics.

The Galerkin method, energy estimates, compactness theorems... but this Chen Youhua did not stop there.

The author was like a master craftsman, boldly and ingeniously modifying and extending these tools, and even creatively introducing several brand-new tools to pry open that door which had been closed for a century.

"Here... he bypassed the bottleneck of traditional Sobolev embedding?"

Professor Wells muttered to himself, his finger tapping heavily on a spot on the screen, as if trying to poke through the paper.

"Using this kind of nonlinear iteration to construct an approximating sequence?... Interesting... Wait, the scale of this estimate..."

He was completely immersed.

The sunlight outside the window changed from the morning glow to the scorching intensity of noon, then gradually slanted westward, casting long shadows on the floor.

In the study, only the faint sound of him occasionally scrolling the mouse wheel remained, along with the increasingly rapid breathing he hadn't even noticed himself.

Sweat soaked his bangs.

When he finally finished flipping through the last photo and his gaze lingered on that stack of manuscripts, a strong sense of dizziness washed over him.

He threw himself back against the chair, taking a long, deep breath, as if he had just surfaced from the deep sea.

Shock.

Pure shock.

This manuscript was absolutely no child's play!

The writer possessed an extremely profound mathematical foundation; the grandeur of the proof's reasoning, the meticulousness of the logical chain, and the ingenuity in handling difficult nodes all demonstrated the extraordinary insight and formidable skills of a top mathematician.

The entire proof process was like a meticulously constructed epic movement, every note fitting perfectly, pointing toward that ultimate goal.

He could not immediately assert that this proof was one hundred percent correct.

The Navier-Stokes Equation is notoriously tricky; any tiny corner could hide a fatal trap, requiring the world's top experts to spend months or even years repeatedly verifying it.

But!

Professor Wells clicked on the comments section of the arXiv page.

The sharp, caustic critiques he had thought of earlier had long since vanished.

He typed on the keyboard, every word carrying a sense of caution.

Comment (Albert Wells, Princeton IAS):

Title: A Shockingly Rigorous Attempt

The author has submitted a... unique but extremely serious preprint. I must admit, when I first saw the format, I held great prejudice. However, after reading it in depth, that prejudice was completely shattered.

The structure of the proof is magnificent, the logical chain is clear and powerful...

The proof process demonstrates extraordinary mathematical depth and rigor...

Although the final establishment of the conclusion requires rigorous examination and long-term peer review by colleagues in the global mathematical community, this manuscript is by no means aimless or crudely made.

It is an extremely serious, heavily significant academic contribution that very likely contains a major breakthrough.

After typing the final period, Professor Wells felt his fingers going a bit numb.

He clicked submit comment without hesitation.

This was likely the most solemn, least mocking comment he had ever written on arXiv in his life.

After doing all this, he did not pause at all.

He immediately opened his email, his fingers typing rapidly on the keyboard; the recipient list prominently featured several names who hold the reins in the field of fluid mathematics.

Recipients: Michael Strange (Courant Institute) / Elena Popova (ENS Paris) / Rajiv Mehta (Cambridge DPMMS)...

Click send.

The email turned into an electric wave, instantly shooting toward several top mathematical temples around the globe.

He was eager to know if this paper really had solved the problem that had plagued mathematicians for centuries.

At this moment, the only thing he could do was to spread this paper, arouse the attention of the academic circle, and attract more people's focus.