A genius? I just love studying.

Chapter 184 Temporary Topic Change
Conference room of the Institute of Mathematics, Hungarian Academy of Sciences building.
At this moment, more than a dozen people were already sitting in the small conference room, including Faltings, Deligne and others. If someone were to throw a trinitrotoluene compound here, the mathematical community of Blue Star would lose half of its territory.

"Why did you call us here? Now you can tell us, right?"

Everyone had been here for a while, and Faltings, with his fiery temper, couldn't hold back any longer and opened fire on the organizer, Bourguignon.

Now that they had finished listening to the two meetings they were following, everyone present was preparing to leave, as their time was very valuable.

If it weren't for the fact that Schultz and Tao hadn't invited him, he wouldn't have come here at all. This meeting forced him to change his flight back, and the disruption to his itinerary was undoubtedly infuriating.

Bourguignon lifted his head from the paper in his hands, his eyes still filled with countless unresolved questions.

Schultz suggested that Chen Hui change his topic, increase the duration of the presentation from thirty minutes to sixty minutes, and gave him this paper.

Proof of the existence of the Yang-Mills equation!
Bourguignon almost thought Schultz was playing a trick on him, especially since the author of this paper was the same guy who discovered the flaw at Bryant's presentation. What a coincidence!
This was just one blunder, and now another one?
But he knew Schultz; he wasn't the kind of person who liked to play pranks.

Since it's a paper he approved, it probably won't be the same as Bryant's.

If this paper could be presented at this conference, the European Mathematical Society Annual Meeting would likely become an indelible milestone in the history of mathematics, an honor he did not want to miss.

However, he was unable to determine the authenticity of the paper in a short period of time.

If the topic is changed at the last minute, and another blunder occurs, then he, as chairman, will become a laughing stock, and he will lose face for the European Mathematical Society.

Therefore, he invited the academic leaders attending the meeting, hoping they could offer their advice.

“Take a look at this paper.”

Bourguignon had already had enough copies printed, and his staff distributed the paper to all the bigwigs, one copy for each person.

The Non-Perturbation Existence Theorem of Four-Dimensional Non-Abel-Yan-Mills Equations: A Rigorous Construction Based on Quantum Geometric Topological Weaving and Holographic Duality

It was another proof of the existence of the Yang-Mills equation. Faltings' face darkened. Wasn't this just making fun of them?

Arancone, however, looked at the paper's abstract with great interest, because he saw the author of the paper: Chen Hui!

This paper addresses the existential and regularity challenges of solutions to the four-dimensional spacetime non-Abel-Yan-Mills equations by proposing a novel mathematical framework that integrates topological quantum geometry, holographic duality, and nonlinear energy analysis, thus completely resolving the core mathematical and physical challenges of this Millennium Problem. By introducing Gaussian Topological Weaving (GTW), we encode the degrees of freedom of the infinite-dimensional gauge field into a finite-dimensional braid group algebraic structure and construct a dynamic quantum grid that satisfies local gauge invariance using fractal fiber bundle discretization techniques. Furthermore, by combining the Holographic Gaussian Dual Mirror (HGDM) method, we reduce the dimension of the four-dimensional nonlinear problem to a solvable model with a two-dimensional conformal boundary, avoiding singularity divergence through strict constraints of topological confinement operators. Finally, using the Quantum Munger-Amber Algorithm (QMAA), we prove the existence of energy-finite, globally smooth solutions within the infinite-dimensional optimal transport framework.

Group discrimination, holographic gauge dual mirror, topological confinement operator, quantum Munger-Amber algorithm...

Arancone was somewhat bewildered when he saw this collection of cutting-edge mathematical methods, as well as the new tool, the standard topology weaving technique, which was clearly created by Chen Hui.

If the author of the paper were covered, he would think it was written by an old mathematician who had been studying cutting-edge mathematics for decades.

That little guy who was participating in the IMO just a few months ago, how come his knowledge has already reached this level?
Did he solve the existence problem of the Yang-Mills equation?
He thought he had overestimated the little guy enough, but he still didn't expect that the little guy would exceed his expectations time and time again.

After a brief moment of shock, he refocused his attention on the paper. The abstract was flowery, but the content was insignificant, though not impossible.

Of course, he knew the chances were slim; otherwise, Bourguignon and Schulz wouldn't have called them over.

But given that Bryant's incident had just happened, he decided to take a closer look first.

Deligne did not rush to conclusions, but instead began to study the text carefully.

As Grothendieck's prized student, Deligne's mastery of algebraic geometry was deeply inherited from his teacher. He also made another breakthrough by standing on the shoulders of giants, completing the proof of one of the most challenging topics in algebraic geometry—the Weil conjecture. In the process of proving the conjecture, he also promoted the integration of Hodge theory with other branches of mathematics.

He became one of only three people in global history to have won all three major mathematics awards.

Another of these three remarkable figures was Jean-Pierre Serre, Alain Connie's teacher.

The reason they are not as famous as Gauss and Euler is partly due to their achievements, but also because the frontiers of mathematics they are currently researching are still too far removed from ordinary people.

Just like what Gauss and Euler studied back then, it was also very distant for ordinary people of that era.

But decades or centuries later, when what they studied becomes the foundational knowledge for middle school students, their names will be as renowned as those of Gauss and Euler.

Deline did not lose patience with the paper despite Bryant's blunder; he trusted Schultz and Tao, and the paper's abstract piqued his interest.

The more he read, the more astonished he became.

By using braid group operations and fractal fiber bundle discretization, he achieved finite-dimensional algebraic control of an infinite degree of freedom in a four-dimensional gauge field. This amazing operation was something he had never even imagined, but the final result was unexpectedly good.

Then, by utilizing the mathematical essence of AdS/CFT duality, the existence of solutions to the non-perturbative Yang-Mills equations is transformed into a unitary proof in two-dimensional conformal field theory.

A wild horse soaring through the sky, a gazelle hanging its horns on a tree!
These two steps alone demonstrate the author's deep mastery of mathematical knowledge in various sub-fields. Only by thoroughly understanding the essence of these methods can one use them with ease, place them in the most appropriate positions, and then generate wonderful chemical reactions.

Finally, using quantum optimal transport theory, he constructed the minimum energy flow of gauge field curvature, strictly eliminated singularities and ensured the global regularity of the solution, and used supercomputing to assist in the proof. This approach reminded him of Schultz.

Using computers for proofs is a very new method, even at the forefront of mathematics. Only young people can accept these new methods so easily, use them without any psychological burden, and create amazing results.

After reading this paper, Deligne was filled with amazement.

Solid, exquisite, and rigorous!
This is his most genuine feeling.

Unlike the paper by Bryant's team, after reading this paper, his mathematical intuition told him that this paper was correct, even though he had not yet seen the supercomputer verification results.

Looking up, he saw that everyone else around him was still studying the paper diligently. Even Faltings, who had been grumbling, calmed down and started studying it after everyone else had done so. He not only studied it carefully, but he also picked up a pen and started writing and drawing on the draft paper while reading, and also taking notes on the paper.

"This is the supercomputing verification result data."

Schultz handed the supercomputing results to Delineer. The supercomputing verification results perfectly matched the paper's description!
Deligne's heart finally stirred as he thought of the little fellow he had just seen in the lecture hall.

It's unbelievable that this paper was written by that little guy!
He is truly a genius!
"Can I share this paper with other people?"

"I ask politely," Deligne asked.

"of course."

Schultz nodded. "The paper has been uploaded to arXiv."

Having received an affirmative reply, Deligne asked Schulz for an electronic copy, then left the conference room and called back to have his assistant perform supercomputing verification of the paper's content.

Although his intuition told him that the paper was correct, and he couldn't find any flaws in the proof, he still decided to do the calculations out of a mathematician's rigor.

When he returned to the conference room, many people had already finished reading the papers. Arancone was whispering with Wiles, while Faltings touched his bald forehead, lost in thought...

"You know, Chen Hui has a presentation tomorrow. If it were to be changed to a proof of the existence of the Yang-Mills equation, that would probably be something everyone would like to see?"

Bourguignon looked at Deligne and asked uncertainly.

Deligne, of course, understood Bourguignon's meaning and smiled slightly, "Why should we let him report on the proof process? Wouldn't it be better to let him explain his newly created tool and standardize topological weaving?"

As he said this, he also considered canceling his plane ticket for tonight, because he absolutely could not miss the report meeting tomorrow.

Bourguignon also smiled happily. If he wanted to explain the standard topology weaving technique clearly, how could he not give examples? And if he wanted to give examples, there was only one example to give at the moment.

In this way, the proof process is explained, and it is not as sensational as proving the existence of the Yang-Mills equation. Even if there are any flaws, they will not have a significant impact, since it is just an introduction to a new tool, and it is normal to have defects.

Furthermore, gauge topological weaving provides a universal discrete framework for high-dimensional nonlinear partial differential equations, and the combination of holographic duality and quantum optimal transport opens up a new paradigm for quantum field theory and geometric analysis. Its methodology will profoundly influence the future development of string theory, topological quantum computing, and quantum gravity theory.

Solving a mathematical conjecture can lead to the creation of new mathematical tools and have a huge impact on the development of the mathematical community.

Therefore, the tools mentioned in this paper are of great value in themselves. Not to mention a one-hour report at the European Mathematical Society meeting, if this paper can gain widespread recognition in the mathematics community, even a one-hour report at the ICM (International Congress of Mathematicians) would be worthwhile.

This approach ensures that even if the questions are changed at the last minute, it won't cause too much negative impact, making it a win-win situation.

"The paper mentions encoding the degrees of freedom of an infinite-dimensional gauge field into a finite-dimensional algebraic structure through 'braid group operations'. However, braid groups are usually used to describe topological entanglement in two- or three-dimensional space, such as any substatistics. How can we rigorously prove its applicability in four-dimensional gauge fields? Are there any unconsidered additional topological constraints?"

After reading the paper, Faltings couldn't wait to ask Schultz a question, his eyes blazing with a burning desire for battle and a thirst for knowledge.

Schultz shrugged. "If you have any questions, please ask the authors of this paper at tomorrow's presentation!"

Upon receiving this answer, the fire in Faltings' eyes temporarily died down. He took the paper and walked out of the conference room, intending to go back and study it carefully several more times so that he could ask questions at the presentation the next day.

Fefferman clicked his tongue in amazement, greeted Bourguignon, and then left the conference room as well.

He also had many questions, but since Chen Hui would be presenting the paper at tomorrow's conference, he didn't need to rush. On the contrary, there was another matter that was more urgent for him.

After leaving the conference room, he dialed Weiteng's number.

"If you don't give me a satisfactory reason, believe me, I will definitely bulldoze your office!"

Witten frowned; he hated it when people called him, even if it was Fefferman.

Hearing the familiar curses, Fefferman was satisfied and said with a happy smile, "Hey, old man, there's a presentation tomorrow, I'm sure you don't want to miss it."

"Tomorrow's report meeting?"

Witten was puzzled. He had already heard about Bryant's report today and had not heard of any other report to look forward to tomorrow, so why would Fefferman say that?
"I've already sent the paper to your email. Whether you come or not is up to you."

Considering the scolding he had just received, Fefferman decided to play the riddle-maker. "By the way, the presentation starts tomorrow morning, so you'd better hurry up."

The call ended immediately after I finished speaking.

Wei Teng snorted and threw his phone onto the desk.

After thinking about it, he turned on his computer and received the email from Fefferman.

"Another proof of the Yang-Mills equation?"

A frown appeared on Wei Teng's forehead. Lately, there had been too much Yang-Mills equations. He wasn't an editor of some low-quality journal, and he didn't want to have his eyes dirtyed by trashy papers.

But he still downloaded the paper, since it was sent by Fefferman.

Soon, Wei Teng's forehead relaxed, and he subconsciously reached for the pen on the desk and began to do calculations.

Not long after, he frowned again, and the pen in his hand stopped moving.

His brow furrowed and relaxed intermittently, and the pile of draft paper around him grew larger and larger, while the sunlight by the window began to slant westward.

Three hours later, Witten scrolled to the last page, suddenly looked up, picked up the phone, and dialed his assistant. "Book me a flight to Budapest, quick!"

It was already past 4 p.m. in Princeton, and there seemed to be plenty of time, but there was a six-hour time difference between Budapest and Princeton. It was already 10 p.m. in Budapest, and he didn't have much time left.

(End of this chapter)