A genius? I just love studying.

Chapter 178 The Not-So-Obvious Conclusion
On December 26, in the multi-functional hall of the CEU Conference Center next to the Hungarian Academy of Sciences building,

The Mathematical Society meeting was not held in the Academy of Sciences building. The Academy of Sciences building does have a Mathematics Institute and conference halls, but these are small conference halls with a capacity of 30-50 people, suitable for small, in-depth discussions. Large conferences like this can only be held in the adjacent CEU Conference Center.

In the multi-functional hall, all three hundred seats were filled. The president of the European Mathematical Society, Bourguignon, sat on the stage. Looking at the grand occasion, especially glancing at the people sitting in the first row, he felt a surge of emotion. He had been the president for so many years and had been committed to the development of the European Mathematical Society. Today, he was finally seeing some results.

Such a grand occasion, if not unprecedented, is certainly unparalleled.

Of course, he also understood that these people were not there for him, because the first lecture would be held here after the opening ceremony.

"Welcome everyone to this annual meeting..."

"Next, please welcome our first speaker, Yuan Xinyi from China, who will report on his work on the Langlands Programme."

After a brief five-minute welcome speech, Bourguignon invited Yuan Xinyi to the stage to give a report, as he himself was also full of anticipation for the report.

Good afternoon! Thank you all for gathering here amidst your busy academic schedules.

Today, we embark together on a profound and magnificent mathematical journey—a journey that may lead us to the legendary Rosetta Stone, the central landmark of the Langlands Program, connecting number theory, geometry, and representation theory.

This wasn't Yuan Xinyi's first time giving a report, so he was naturally quite familiar with it. But even after preparing for so long, he couldn't help but feel a little nervous when he saw the group of bigwigs sitting in the first row.

"First, please allow me to share a historical glimpse: In 1967, Mr. Robert Langlands proposed a bold conjecture in a letter to André Weil—to closely link the Galois representation and the automorphic representation in number theory through the L function."

This conjecture is like a gravitational wave thrown into the mathematical universe, pulling the constellations of algebra, geometry, analysis, and even physics into the same orbit.

Today, we will focus on the progress in proving this program—not only is it a breakthrough in a single theorem, but it is also an ultimate question about whether humanity can establish a unified grammar amidst the complexities of mathematical languages…

As he finished speaking, the screen behind Yuan Xinyi lit up, and the presentation slides were displayed in front of everyone.

When he started talking about his strengths, Yuan Xinyi's nervousness completely disappeared, and the expressions of the audience below the stage became serious.

Forty-five minutes later, Yuan Xinyi played the last slide of the PPT, took a sip of water, and then spoke again, "Next, I would like to conclude with a quote from Mr. Langlands: 'The mission of mathematics is not to solve problems, but to make them clearer.' Thank you for listening. Now, we will have a Q&A session. Please feel free to ask any questions you may have..."

As Yuan Xinyi finished speaking,
The bigwigs sitting in the front row all showed delight on their faces. Papers can only contain so much content; the collision of ideas still requires face-to-face communication.

After listening to Yuan Xinyi's report, they finally gained a clear understanding of some of the ambiguities in the paper, and suddenly everything became clear.

They seemed to see a bright door to mathematics opening up!

Soon, someone in the third row stood up. "Professor Yuan, hello. I am Claire, a graduate student from Princeton. I would like to ask, after the geometric Langlands conjecture is turned into a theorem, how does it provide a new paradigm for the vision of a 'grand unification of mathematics' under the global Langlands program? Do its core tools, such as categorization methods and geometric representation theory, imply a deeper 'homology' between number theory and geometry?"

"Excellent question!"

Yuan Xinyi, with his seasoned experience, first offered a word of praise, while in reality he was conceiving the answer to the question in his mind: "The proof of the geometric Langlands conjecture establishes a direct bridge between automorphic representation and geometric Langlands duality by transforming the arithmetic problem of the number field into geometric objects on the Riemann surface. This paradigm has revolutionized the traditional proof path. For example, it uses the Fargues-Scholze geometrization method to extend the local Langlands correspondence to any reduced group and reveals the hidden symmetry between the L-function and geometric invariants."

"However, the generalization of the global domain, especially the case of feature p, still requires reconciling the noncommutativity of harmonic analysis with the rigid structure of arithmetic geometry. A universal 'decomposition-reconstruction' toolchain has not yet been found."

This is an interesting topic, and perhaps our team will focus on this area of ​​research in the future. If you are interested, you can contact me…”

"Okay, thank you for your reply."

The person who asked the question sat down, and soon someone else stood up.

These questions are all based on the assumption that Yuan Xinyi's proof is valid. Clearly, even though the Journal of Mathematics has not yet published Yuan Xinyi's paper, the academic community has almost reached a consensus.

The bigwigs in the front row of the room did not stand up to ask questions. Of course, they had questions, but those questions would be discussed at tonight's reception.

Fifteen minutes passed quickly, the report went very smoothly, and the atmosphere was quite good.

"Okay, I'll answer one last question. It's time to hand over this stage to younger mathematicians."

Yuan Xinyi glanced at the time and chuckled, "If you have any further questions, feel free to email me."

A burst of enthusiastic laughter erupted in the hall, and some people even started clapping.

At this moment, a well-off, balding middle-aged man sitting in the back stood up and asked, "Hello, what are your views on academic misconduct?"

Without a doubt, the one who stood up was Franklin Lee, a Chinese professor at the University of California, "especially your student Chen Hui for plagiarizing Oliver's paper from Duke University!"

The air in the room fell silent instantly.

They certainly knew what Franklin was talking about, but they weren't interested in Rashomon-like events at all. Such cases were not uncommon in academia, and in the end, they all remained unsolved mysteries.

Bringing this up in this context is practically a slap in the face to Yuan Xinyi; it's an attempt to offend him terribly!

But thinking about it, it doesn't really matter. Yuan Xinyi has been back in China for many years and no longer works in Western academic circles, so his influence on Western academic circles is limited. Franklin Lee, on the other hand, is clearly determined to work in the West, so offending Yuan Xinyi is no big deal.

Even if he can no longer stay in academia, given his current pledge of allegiance, he might actually achieve great things by turning to politics.

Sitting in the middle, Adrien looked at Bryant not far away, his eyes practically spitting fire.

Even now, even with the evidence Oliver has presented, he still doesn't believe that Oliver wrote the paper independently. He has this inexplicable confidence because he has had in-depth discussions with Chen Hui.

He originally thought that since Chen Hui wouldn't pursue the matter, he wouldn't bother with it either. He never expected that someone would cause trouble at Yuan Xinyi's report meeting.

This was something he could not tolerate. He was one of the key figures at the seminar at Yanbei University, and he had guaranteed it with his academic reputation.

Dobessie's expression was also not very good. Compared to the others, she knew more about the inside story. She was the one who least wanted to make a big fuss about this matter. Otherwise, the credibility and authority that Duke Mathematics Journal had spent decades building up would be completely destroyed.

Robert Spengler, the editor-in-chief of the Communications in Mathematical Physics, remained calmly seated in the room, looking quite interested, seemingly oblivious to the possibility that the fire might spread to him.

Everyone else looked at Bryant, and they all clearly believed that Franklin was arranged by Bryant.

Bryant's face turned somewhat green.

No, buddy?
He was so angry he felt like he was going to vomit blood. If he could go back to the night before last, he would definitely beat this guy up the moment he saw him, so he wouldn't be able to attend today's report meeting. Yuan Xinyi stood on the stage, not answering immediately; clearly, this question was indeed very tricky.

Franklin gave a disdainful sneer, looking down at the room. Everyone thought the matter was over, but for him, it was not. He wanted to restore order to academia.

At this moment, Chen Hui stood up and walked towards the main stage.

In the middle of the lecture hall, Yun Wei and Qiu Chengwu sat by the aisle.

Upon seeing Chen Hui stand up, Qiu Chengwu subconsciously looked at Tian Yang, who was sitting on the other side of the lecture hall, and Tian Yang was also looking at him.

The next moment, both of them panicked.

They both saw the answer in each other's eyes, and even though they were several meters apart, it was as if they had already completed a conversation across the distance.

"Was he told the method of proof?"

"Shouldn't you be the one to tell him?"

It was too late when the two finished the final proof yesterday. Although Tian Yang didn't say it, he decided to leave the opportunity to Qiu Chengwu. He was already Chen Hui's great-grandfather and didn't need to curry favor with him, so he didn't take the draft paper with him when he left.

Qiu Chengwu was an extremely proud man. Even though he had spent a lot of energy on this matter, once it was done, he no longer cared about it. Having already achieved success and fame, he had no need to curry favor with a little guy.

He did all this simply because he found the little guy clever and liked him.

Therefore, he naturally wouldn't try to reap the rewards of this victory.

After receiving the other party's answer, the two frowned. They hadn't expected that their plan would backfire. The proof they had spent a lot of time on was ultimately not told to Chen Hui. It was all for nothing.

However, the two of them quickly looked at Yun Wei, a glimmer of hope flashing in their eyes.

Yunwei was both amused and exasperated. "Why are you two looking at me like that?"
Since the proof was done by the two of you, why would I go and reap the rewards?
The three men's expressions darkened. They hadn't expected those people to cause trouble at Yuan Xinyi's report meeting; otherwise, three days would have been more than enough.

Unfortunately, it's too late to say anything now.

"Chen Hui, don't be impulsive!"

After taking only two steps, Yun Wei stopped Chen Hui and shook his head slightly at him.

He did remember the proof, but it was obviously too late to tell Chen Hui now. Not to mention that so many people were watching, if he really did it, it would be a case of trying to cover up the truth and admitting it without being asked.

Moreover, the proof wasn't that obvious, and even if he explained it to Chen Hui, Chen Hui might not be able to fully understand it immediately.

This is absolutely terrible!
At this point, Chen Hui's move to the stage only added fuel to the fire and did nothing to help. It would be better to let things settle down. After all, the worst outcome would be for time to calm things down and for this incident to become an unsolved mystery, left for future generations to judge.

Unfortunately, despite having found the key to turning the tide, they unexpectedly failed to use it due to unforeseen circumstances.

A game they were certain to win ended in a draw, which was something they didn't want to see.

Because if they don't produce this proof today, it won't be of any use even if they do later.

Chen Hui also shook his head slightly, brushed Yun Wei's hand away, and continued walking towards the podium.

"Today is an academic conference, so we'll only discuss academic matters. We can ask other unrelated questions later."

At this point, the president of the European Mathematical Society, Bourguignon, stood up and said that as the host, he naturally could not allow his invited guests to lose face.

call!
Bryant breathed a sigh of relief; he was genuinely worried that something might go wrong if the argument continued.

That's fine now.

"Since this is an academic report, let's talk about academics today!"

But just then, a young man suddenly appeared on the platform.

Chen Hui approached his teacher, Yuan Xinyi, stood in front of the podium, picked up the microphone, faced the audience in the lecture hall, looked at the portly, bald middle-aged man, then turned his gaze to Bryant and Oliver sitting on the left side of the third row, before turning around and going to the back of the podium to stand next to Yuan Xinyi.

"Teacher, excuse me, could I borrow your computer for a moment?"

As he spoke, Chen Hui moved the computer that Yuan Xinyi was using for his presentation, skillfully opened the webpage, went to the official website of "Mathematical Physics Communications", found Oliver's paper, downloaded it, opened it, and finished it all in one go.

Yuan Xinyi was about to say something, but seeing Chen Hui's confident look, he stopped talking and instead stood up to give his seat to Chen Hui.

Oliver, who had been looking gloomy, suddenly raised his head and looked at the podium, his panic barely concealed.

Even Bryant became a little nervous.

"Is there some kind of trap in the paper?"

"No, that's impossible. Even if there are problems with the paper, he can't prove it's plagiarism!"

Bryant steadied himself and looked toward the podium.

Franklin frowned. He didn't know what tricks this kid was up to, but he believed that the kid couldn't come up with anything too complicated.

Soon, Chen Hui had completed the operation. Two papers were displayed on the left and right sides of the projector on the stage. Chen Hui moved the mouse, and the two papers scrolled down, finally stopping on a certain page.

"Many of you have probably read these two papers. I wonder if you have noticed that both papers use the same lemma, which states that for any two-dimensional fractional Chern insulator with C_n rotational symmetry, the denominator n of its fractional Chern number must be a prime factor of the corresponding modular series N. That is, there exists a prime number p such that p | N and p = n."

"This lemma is the cornerstone of the subsequent proofs. If this lemma is not true, then the subsequent proofs are just castles in the air and are invalid."

Chen Hui looked up at Oliver and asked, "Then I'd like to ask the author of this paper, Mr. Oliver, how did you arrive at this lemma?"

(End of this chapter)