A genius? I just love studying.

Chapter 250 Schultz's Epiphany
"Internal combustion engine combustion efficiency?"

In the corridor outside the teaching and research room, Chen Hui learned about the research project that Chen Ling'er was working on.

Actually, it has something to do with him.

Originally, an internal combustion engine company in Hebei sponsored a project for Chen Ling'er's laboratory to study the improvement of internal combustion engine efficiency.

However, with the advent of gallium oxide, the internal combustion engine seemed poised to disappear from the historical stage, and the company suspended payments. Naturally, the research institute also prepared to suspend the project.

However, Chen Ling'er has been in charge of this project. She has been researching it for more than a year and plans to continue. Her idea is simple: even though the internal combustion engine is about to be phased out, mathematical methods will always be valuable.

Furthermore, even with major breakthroughs in batteries today, internal combustion engines still have significant applications in some extreme environments, such as extreme low temperatures where batteries experience capacity decay or even complete deactivation. In aerospace applications, unless there is another major breakthrough in battery materials, their energy density will still be inferior to that of internal combustion engines. Therefore, internal combustion engines are unlikely to disappear completely in the short term.

Research on the combustion efficiency of internal combustion engines is valuable!

Chen Hui nodded, agreeing with Chen Ling'er's idea. In the short term, internal combustion engines cannot be completely replaced, and batteries still have a long way to go.

What problem are you having, and how can I help?

Chen Hui was particularly interested in Chen Ling'er's research on the application of the NS equation in internal combustion engines.

While both are Navier-Stokes equations, mathematical proofs and engineering applications are not the same thing. By numerically solving the Navier-Stokes equations, engineers can perform high-precision simulations of key processes such as in-cylinder turbulence, fuel spray, mixture formation, and chemical reactions, thereby guiding the design of combustion systems.

Such numerical solutions are usually approximate solutions, so the difficulty is much lower.

However, this process also faces challenges such as high computational complexity, model simplification errors, and multi-physics coupling, and it is not as simple as it seems.

Chen Ling'er's eyes lit up. "Solving the complete Navier-Stokes equations and detailed chemical reaction mechanisms requires a mesh size of at least 10^6. Single-condition simulations take several weeks, and full-cycle simulations require millions of time steps. Even with simplified mechanisms, it still requires solving for tens of millions of variables..."

She didn't know that Chen Hui had completed the proof of the Navier-Stokes equations, but she knew that with Chen Hui's current abilities, he could at least offer her some constructive suggestions.

"Ah."

Chen Hui nodded slightly. This was also a problem he would encounter when researching confined plasma, requiring the simulation of eddies using the Navier-Stokes equations.

"I need specific data."

The students in Chen Ling'er's teaching and research room were still excited when they saw their idol, Chen Shen, return. This time, they followed Chen Ling'er directly into the teaching and research room.

……

UCLA
Terence Tao walked through the campus with a smile on his face, responding kindly to the students who greeted him.

Although he grew up in the West, the Chinese virtues ingrained in his bones are clearly evident in him.

Despite his great achievements, he possesses a relaxed quality that other mathematicians lack. He doesn't race against time. While other mathematicians may be eager to seek breakthroughs and results, he simply plays freely in the garden of mathematics. If he can gain something, that is of course a great pleasure. If he doesn't gain anything, that doesn't matter either. The process of playing itself can bring him great pleasure.

"Tao, I think we're almost there!"

As soon as he entered the lab, Leonard, one of his doctoral students, flashed a bright smile.

Terence Tao didn't care. That's just how Westerners are. Sometimes they're so confident that you think they're fools, but when it comes to actually doing things, this mindset can actually bring unexpected results. He's gotten used to it.

They are currently working on a research project called the Equation Theory Project, which was proposed by Terence Tao himself. It aims to explore the logical relationships between primitive group equations in the field of algebra. He has boldly pioneered a new research paradigm of collaboration between human mathematicians and AI.

By analyzing 2202942 logical implications among 4694 primitive group equations, a complete mathematical structure map was established. If traditional methods were used, it would take at least several decades to complete this task, but through human-computer collaboration, they only took 57 days!
This achievement is currently in the paper writing stage, and Terence Tao is very happy. His success is just a small step for him personally, but a giant leap for mankind.

This success verifies the feasibility of decentralized mathematical research and provides scalable solutions to complex mathematical problems. It is foreseeable that in the future, human mathematicians, in combination with artificial intelligence, will produce a large number of amazing results.

Arriving at his workstation, turning on his computer, Terence Tao opened his email. This was his work habit; before starting any work session, he would first process the tasks in his email.

As for writing papers, that was naturally not his responsibility.

Arrange the inboxes from morning to night by time. When he saw Chen Hui's reply, Tao Zhexuan smiled. He himself often fell into this state when he was young, ignoring everything in the outside world. Naturally, he could understand why Chen Hui hadn't replied to his emails for the previous two months.

After thinking for a moment, Terence Tao briefly described his achievements over the past few days in an email and replied to Chen Hui's email.

When Terence Tao opened the last email, he discovered it was a peer review invitation.

This time, it wasn't a peer review invitation from a specific journal, but rather an invitation from the International Mathematical Union.

"A proof of the Navier-Stokes equations?"

Tao Zhexuan clicked his tongue. If the sender hadn't actually been the International Mathematical Union, he wouldn't have bothered to open the email and take a second look.

"Chen Hui?"

However, when he clicked on the attachment and saw the author of the paper, his expression immediately turned serious.

Based on Chen Hui's reply to his email earlier.

So, he's been studying the Navier-Stokes equations for the past few months?

And it even completed the proof?

Instead of rushing to review the paper, Terence Tao downloaded it, printed it out, took a deep breath, and devoted himself to it.

"Physical spacetime is embedded in a carefully constructed four-dimensional complex manifold, on which the Keller form ingeniously integrates spacetime measurement and vortex dissipation."

(R3×[0, T])X, with Kahler form K∣R3×[0, T]=dx∧dy∧dz∧dt+νdω∧dω
"Wonderful!"

"Wonderful!"

Looking at this formula, Terence Tao was full of praise.

After proving that the boundary satisfies strong quasi-convexity, the -Neumann operator, this divine sword of complex geometry, finally unleashes its unparalleled power. The key constant C is independent of the Reynolds number, which means that the regularity of the singularity neighborhood is unbreakable!
After carefully reading the proof, Terence Tao discovered that Chen Hui had cleverly introduced the formula for the monotonicity of singular entropy, which he used as the ultimate shield to suppress the divergence of nonlinear terms.

This is the result of Mr. Qiu Chengwu's work back then.

He had long known that Chen Hui was Qiu Chengwu's grand-disciple, and only with Qiu's personal guidance could this achievement be used so skillfully.

Energy Dissipation Rate≤Λ∣c1(V)∣

In this paper, Chen Hui constructed a non-exchangeable fiber bundle with vortex phase space as the base space and vortex phase space information as the fiber.

Its first class c1(V) is like the Sword of Damocles hanging high, coldly and precisely restraining the most violent and unpredictable energy dissipation during the annihilation of the vortex tube with an absolute upper limit attitude!

The "bones" of topology and the "soul" of complex geometry are ultimately unified in the numerical representation of Chern classes.

After reading the paper, Terence Tao was drenched in sweat, feeling a sense of exhilaration, like returning to an air-conditioned room after a sweltering basketball game outdoors on a hot summer day, his body soaked in sweat. However, he soon felt somewhat frustrated.

Compared to Chen Hui's achievement, his equation theory plan pales in comparison.

He was very smart throughout his life and loved to find shortcuts, which allowed him to easily achieve results that 99% of mathematicians in the world could only dream of.

For example, this application of artificial intelligence in mathematical proofs is also an exploration of shortcuts.

But now, he suddenly feels a little lost.

Was he right or wrong in doing this?

Many years ago, someone told him that he was wasting his talent, and that if he could focus on a particular problem, he would achieve amazing success with his talent.

But back then, young and impetuous, he didn't take it seriously. Over the years, he has never regretted it because he has already achieved amazing results on the path he chose. Successful people don't reflect on whether they were wrong.

I've already succeeded, and you still say I'm wrong?

But now, looking at the paper in front of him, and at Chen Hui's name, he suddenly hesitated.

Perhaps, if I had chosen a different path back then, would I be the same as Chen Hui now?
However, he quickly snapped out of his daze.

He is now over fifty years old, no longer the young man he once was, and there is no turning back.

With a wry smile, I placed my hands on the keyboard and replied to the email from the International Mathematical Union, providing my review comments.

He quickly regained his composure, picked up his phone, and as a mathematician who loves social media, he immediately posted a message on social media: "Congratulations to Hui for completing the proof of the Navier-Stokes equations. The proof process is perfect and breathtaking!"
At fifty, one knows one's destiny.

At his age, he has long since made peace with himself and will not easily fall into internal strife.

[Holy crap! The Navier-Stokes equations have been solved?! Chen Hui just casually dropped a bombshell! Terence Tao even personally certified it; the history of mathematics is about to be rewritten!]

[Having studied the Navier-Stokes equations for five years: I hope this time it doesn't end up being 'almost' like in 2014... But since Tao Shen says it's okay, I'll get a little excited! Frenziedly refreshing arXiv]

[Interesting. The Pentagon just declassified UFO documents, and then some 'unknown' person suddenly appears and solves the Navier-Stokes equations? Coincidence? What about the peer reviewers??]

[Chen's Proof → Quantum-Resistant Blockchain → Buy MathCoin Now!]

[Applied mathematician: 'This will change engineering!' Pure mathematician: 'But is it elegant enough?' Chen Hui: He throws out a 300-page PDF full of PDEs]

[I won't open my million-dollar champagne until the Clay Institute makes an official announcement. Remember that Russian who disappeared after proving the Poincaré conjecture?]

[Hey upstairs, stop waiting! Chen Shen has already received the grand prize from the Clay Research Institute.]

[Winning the Clay Research Institute's grand prize once a year—just thinking about it is exciting!]

Terence Tao's post caused a huge uproar online. Although China's internal and external networks are isolated, many netizens still surfed the internet using VPNs. After arguing with Western netizens, they promptly shared the news back in China.

While this news was still circulating domestically, it had already caused a huge uproar in Western academic circles.

Schultz had just finished his experiment and stepped out of the lab when he learned of the news from his students. Upon receiving this sudden news, his lips parted slightly, a look of disbelief flashed in his eyes, and he froze on the spot.

He has recently made great strides in high-temperature superconductivity. Following his previous breakthrough, they have discovered a superconducting material with even better performance that is suitable for industrialization. These successive breakthroughs have filled him with fighting spirit.

Chen Hui's proof of the Navier-Stokes equations was like a wake-up call, making him suddenly realize the truth after being immersed in a series of breakthroughs.

The key challenges of materials prediction models have long been solved, and subsequent breakthroughs were inevitable. They are simply reaping the benefits brought by these model breakthroughs.

The work he's been doing these past few days has been nothing more than accumulating data and adjusting models. His students could easily handle that kind of work, which explains why Chen Hui stopped paying attention to that area of ​​research after publishing his paper.

He was blinded by the breakthroughs and wasted a lot of time.

"Müller, the rest of the experiments and optimization work is now in your hands."

Schultz's eyes cleared, and he looked at his student. "Come to me if you encounter any problems you can't solve."

He's going to solve even more difficult problems!

"Oh, by the way, could you print out a copy of Professor Chen's paper for me?"

Schultz gave a quick instruction and strode towards the cafeteria; he hadn't had lunch yet.

Cambridge, Massachusetts

At the Clay Institute headquarters, Burton Clay looked at Terence Tao's tweets and exchanged glances with his wife beside him.

Just a few months ago, they helped Chen Hui win the Clay Institute Prize, and now they've proven another Millennium Problem.

Are you here to do wholesale?

"Geniuses cannot be judged by conventional standards."

Burton's wife sighed softly, "This news was released by the International Mathematical Union, so it must be true."

"Let's wait a bit longer and let the bullets fly for a while."

If it were a year ago, Burton would have spoken out immediately upon hearing this news, as the Clay Institute desperately needed a millennium certificate to boost morale.

But now, he feels it's better to let his international mathematics colleagues verify it again before making a decision.

At Princeton, Fefferman held the printed paper. He hadn't read it yet, but he already had a feeling that Chen Hui had indeed completed the proof.

When he presented the Navier-Stokes equations as the Clay Institute's prize-winning problem at the Collège de France, he never imagined he would live to see a complete proof.

That young Chinese man is the creator of a miracle!
At this rate, it's only a matter of time before that guy solves the remaining millennium problems, if he's willing.
Fefferman didn't know, but he knew that this guy was definitely a peerless genius comparable to Gauss and Euler.

A person like this should come to Princeton!

Edward Witten had already reviewed Chen Hui's evidence and could find no flaws; in fact, he was completely convinced by it.

As a researcher who switched from historian to theoretical physicist and eventually won the Fields Medal, the crown jewel of mathematics, Witten had always felt superior and looked down on everything, even at Princeton, a university teeming with Fields Medals and Nobel Prize winners. But that young Chinese guy still made him feel inferior.

Proving two millennium problems in just two years is something even Weiteng itself wouldn't have dared to dream of.

(End of this chapter)