A genius? I just love studying.

Chapter 179 can't possibly be the same, right?
Oliver turned pale and panicked instantly.

While others were unaware, he was certain that he had directly taken this lemma from Chen Hui's paper; without it, he would not have been able to complete the subsequent proof.

However, time was of the essence, and he didn't have time to complete the proof himself.

I never imagined that a single wrong decision would create such a huge hidden danger for me.

No wonder he's been feeling uneasy these past few days.

"Hey Oliver, wake up!"

Bryant whispered a reminder.

Now, many eyes in the lecture hall were on them, and Oliver's reaction was undoubtedly a guilty conscience, an admission of guilt.

"Mr. Oliver, can you answer my question?"

Chen Hui asked again.

Now that the other side has drawn its sword, there is no room for compromise.

Qiu Chengwu and Tian Yang exchanged another glance, both seeing a look of satisfaction in each other's eyes.

They were wondering at the time whether Chen Hui knew how to prove this lemma, and now it seems that Chen Hui obviously does!

"Thank you to this young friend for pointing out the problem with the paper. It was our proof that was not rigorous enough. We will supplement the proof of this lemma later."

Oliver was already in a panic. Faced with Chen Hui's questioning, Bryant had no choice but to stand up and answer for Oliver. He had thought of this question long ago, otherwise he would not have been so confident in letting Oliver use the conclusions in Chen Hui's paper directly.

It's not that easy to make him admit defeat with such a small trick.

"Mr. Bryant is right. It is normal to use some seemingly obvious conclusions in a paper. Mathematicians are bound to make some small mistakes."

Chen Hui shrugged noncommittally, skipped over that page of the paper, and moved the mouse again.

"Let's look at this lemma. For any fractional Chern insulator with Cn symmetry, the Fourier coefficient mapping ap: prime → Q of its corresponding modular form f(z)∈Sk(Γ0(N)) is injective, that is, the coefficients corresponding to different prime numbers p1≠p2 satisfy a_p1≠a_p2."

"Coincidentally, both papers used this lemma at the same time, which shows that the two authors were truly in sync."

Chen Hui looked at Bryant, "You agree, Mr. Bryant?"

"There is only one path to truth, and it is normal that everyone is walking on the same path."

Bryant said without batting an eye that he had experienced this kind of scene many times before.

I don't really agree with that.

Chen Hui shook his head. "There are many paths to the truth, all roads lead to Rome, but the paths to error are varied and different."

"So I'm curious why both papers cite the same incorrect lemma. Does Mr. Bryant know why?"

Bryant's gaze sharpened as he looked at the projector on the stage, his head buzzing.

Is this lemma wrong?
Even with his skill level, he couldn't spot the obvious problem right away.

Indeed, if the error were so obvious, neither of these papers would have passed the academic editor's review.

But clearly, this lemma is flawed!
But why would this guy include a wrong lemma in his paper?
Did he know his paper would be plagiarized before it was published?
This is impossible!

Chen Hui had no idea what Bryant was thinking. He had already picked up a marker and walked to the whiteboard prepared for the presenter. “The classical modular form of weight k=12 and series N=1, Δ(z)=∑n=1∞τ(n)qn, has coefficients τ(p) that are 0 at prime numbers p=23 and p=691, which obviously violates injectivity.”

This lemma is actually wrong!

Proving the correctness of a theorem may be complicated, but proving the error of a lemma only requires a simple counterexample.

Bryant's back hunched slightly, and cold sweat began to seep from his back. Using the same lemma could still make sense, but making the same mistake again was a bit much. By now, even a fool would know what had happened.

Even if he has done many such things, being exposed in public will still ruin his reputation.

Fortunately, this was just his student's paper; at most, he was simply misjudging people.

But he still couldn't understand why this guy would put a wrong lemma in his paper.

What puzzled them even more were Dobesi, the editor-in-chief of Duke Mathematics Journal, and Spengler, the editor-in-chief of Mathematical Physics Communications; they never imagined things would develop in this direction.

Now look what's happened; they not only do nothing about the plagiarism incident, but they also ignore it completely.

This is at most due to their lack of awareness; they weren't the ones who plagiarized, so they can't be blamed.

But now, they have actually published a paper with errors, which is a huge slap in the face for them. The reputation that their journal has built up over decades has been punctured by this erroneous lemma.

They looked at Bryant in the auditorium, wishing they could tear him to pieces.

Yuan Xinyi, who was already seated in the audience, smiled. Although he had mentioned the filth of academia to Chen Hui before, he did not expect that Chen Hui would be so well-prepared for his first submission.

Of course, he was also a little embarrassed, since the paper had been reviewed by him before it was submitted, and he hadn't expected that even he hadn't noticed the error.

Tian Yang and Qiu Chengwu had already leaned back in their chairs, watching the presentation unfold with composure. The younger generation was so promising; it was so easy for the older generation to relax.

Yunwei stared blankly at the stage, his mind racing with thoughts.

He still remembered the scene when he first met Chen Hui in the conference room of Yanbei University a few months ago. He never expected that in the blink of an eye, this little guy had grown up to this extent.

He was involved in the proof of the first lemma from start to finish and knew how difficult it was. Yet, Chen Hui had prepared more than one such lemma.

This little guy, he's becoming a bit unfathomable!

Franklin, who stood up to ask the question, blushed slightly; he had never expected this outcome.

These two questionable papers do indeed contain plagiarism, but it wasn't that Chinese kid who plagiarized others; rather, it was that clean-cut guy from Duke University who plagiarized!

"You knew there were problems with the paper, yet you still submitted it, giving a wrong conclusion and luring others into your trap. Journals are places for academic exchange, not your battlefield. Do you know how much time this wrong conclusion might waste for mathematicians? This is an extremely irresponsible attitude towards academia!"

"This is disrespectful to all other mathematicians!"

Enraged, Franklin had a sudden inspiration.

Since we can't accuse Chen Hui of plagiarism, we can slander his character. This is a common and sophisticated tactic in online arguments: if we can't solve the problem, we can target the person who raised the issue by throwing mud at them.

If the other person has character flaws, then no one will believe anything they say.

This trick works every time!

"Luring others into a trap?"

Chen Hui found it somewhat amusing. "I never expected someone to copy even the wrong lemma. It's truly unbelievable, just like copying someone's name along with their homework in elementary school."

"If this is also a trap, then it is truly a pity for those who fall into such a trap."

"Whether or not you are responsible for academic work is not up to you to decide."

Chen Hui went to the whiteboard again and picked up a marker.

Seeing Chen Hui's imposing manner, Franklin suddenly felt a little uneasy for some reason.

He pointed out the mistake himself; how can he prove that the mistake was correct?

Probably not?
"The core proof of my paper only requires that the modular coefficients a_p be non-zero at a specific prime number p=n, rather than being injective, to derive the fractional Chern number C_h^pm/n=0. Even if different prime numbers correspond to the same coefficient value, as long as ap=n≠0, the physical requirements can be met."

Chen Hui quickly wrote down the proof process on the whiteboard: "In step 3 of the paper, the proof by contradiction forces n to be a prime number. At this time, we only need to focus on the coefficient a_p of a single prime number p=n. The injectivity condition is weakened to "there exists at least one prime number p such that a_p≠0", and the latter has been guaranteed by the modular nontriviality theorem."

"Therefore, this lemma is used in the paper to help explain the uniqueness of the modular formal parameters, but in the actual proof, the uniqueness is directly guaranteed by the irreducibility of the Galois representation. Even if this lemma is removed, the core argument of the paper through Langlands correspondence and stability conditions still holds!"

After writing a lengthy proof on a whiteboard, Chen Hui turned to look at Franklin. The lecture hall remained silent for several minutes, and no one stood up to speak.

Chen Hui didn't look at Bryant again; he believed the proof he had just given was clear enough.

He put down the microphone and stepped down from the stage.

The faint chirping of crickets only began to echo in the lecture hall after Chen Hui left.

"Congratulations, you've taken on a great student!"

Alancone came to Yuan Xinyi's side and said sourly.

If Yuan Xinyi hadn't beaten him to it, he believed he could have made Chen Hui his student.

"I wish I had met this little guy sooner!"

Talagran, standing beside Aranconne, sighed with regret, making no attempt to hide his remorse.

“Mathematicians are a treasure to the world, Mr. Talaglan has no reason to regret.”

Yuan Xinyi said with a smile, "Brother Xu told me about Mr. Chen's outspokenness at the IMO. Speaking of which, Chen Hui can also be considered Mr. Chen's student."

It is foreseeable that Chen Hui will soon rise to prominence in the world of mathematics. As the saying goes, the tallest tree in the forest is the first to be felled by the wind. Yuan Xinyi wanted to try to win over some allies for Chen Hui. The upright Tarragrand and the benevolent Arancone were both very good people to befriend.

Taragra shook his head repeatedly, "Now I'm so glad I stuck to my principles and didn't cancel Chen Hui's gold medal because of those Americans' coercion. Otherwise, I would be a laughing stock now!"

"It is an honor for the IMO to award him the gold medal, not for him!"

"Not many people can receive such praise, but Hui's name is definitely among them!"

Taragra gave Chen Hui a very high evaluation.

"Hmph, now I'd like to see who dares to plagiarize Hui's paper!"

Adrienne's relieved voice rang out. These past few days, because he, as a Western scholar, had sided with Chen Hui, he had been ridiculed by his peers in the field. Now that the truth was out, he naturally felt a great sense of satisfaction.

Yuan Xinyi waved his hand modestly and said, "There are two pitfalls in one paper. I would have been better off writing another paper. I'm just a kid and I don't know any better. I'm sorry for making you all laugh."

"As it turns out, he was right!"

"The mathematics community is not an isolated place; there are bound to be some bad apples. Now that one has been caught, we will naturally know who the rest are. From now on, everyone should stay far away from him. Hui has done a good thing for everyone."

Adrienne knew nothing of politeness. He looked in the direction of Bryant, Duke University, and the editor-in-chief of the Mathematical Physics Communications, Spengler, with a contemptuous expression and extremely sarcastic words.

Turning back, his face was now full of a warm smile. "But Brother Yuan is right. Hui's two proofs are enough to publish a paper. The construction of the dual group of crystal symmetry and modal form parameters is very ingenious. As expected of Brother Yuan's student, Hui's application of Langlands program theorem is already superb and is very valuable for learning!"

“That’s right, there are indeed many things to learn from this proof. We will get the complete proof process from Hui and include it in the results of this conference.”

The president of the European Mathematical Society, Bourguignon, also came over and said with a smile, "And Mr. Yuan's paper, if you don't mind, this conference can include it as a highlight."

It's no secret that Yuan Xinyi submitted his paper to the Annals of Mathematics. It hasn't been published yet, and Bourguignon certainly wouldn't be so arrogant as to think that Yuan Xinyi would abandon the Annals of Mathematics and submit it to their conference instead, but it's still possible for him to be included as a highlight.

For example, renowned journals such as Nature and Science often excerpt important findings from other journals. This is not a direct citation of the original paper, but rather a concise summary of the core conclusions in a few sentences to highlight the research breakthroughs. This does not affect the publication of Yuan Xinyi's paper.

Fefferman got up and walked out of the lecture hall, even though the next lecture would be held there soon, he had no interest in it.

He was very satisfied with Yuan Xinyi's report, and some of his previous doubts were also resolved. They could have in-depth discussions on related issues at tonight's reception, so this trip to Budapest was not in vain.

Surprisingly, the little guy was even more interesting.

To others, it might just be that Chen Hui had laid traps in his paper and looked intimidating, but he saw the rigor in this young man. Rigor is the most important thing in mathematical research!
It's a pity that old guy Wei Teng didn't come. If he heard about this, he'd probably regret it.

Just thinking about Witten's angry face made Fefferman laugh happily.

"Laughing so happily, anyone who didn't know better would think that little guy is from Princeton!"

Faltings's cold laugh rang out from behind Fefferman. Both of them were extremely arrogant people. Although they had been colleagues at Princeton for quite some time, their relationship was not good, and they often argued.

Surprisingly, Fefferman didn't retaliate this time. Instead, he smiled and said, "Hey, old buddy, you might not know this, but that old guy Witten really likes that kid and wanted to take him on as a student. Unfortunately, he declined the invitation to this meeting."

"That's definitely good news!"

Faltings also calmed down and nodded in agreement, neither confirming nor denying it.

At Princeton, there may be many arguments, whether for the sake of truth or because of differences in character, but no matter what, as long as you criticize Witten, you can be good friends for the time being.

(End of this chapter)