A genius? I just love studying.

Chapter 103 Elite Disciple
In the lounge, Yuan Xinyi finished his story, and the lounge was quiet for a moment.

Zhang Yitang, who was already 69 years old, suddenly exclaimed, "Truly, heroes emerge from among the young!"

The people present were all top mathematicians, so they naturally understood what Yuan Xinyi was doing. This young man wanted to unify the correspondence between geometry and number theory Langlands, solve the problem of analytic extension of L-functions on the critical line, and provide a completely new approach to the BSD conjecture.

If this is actually accomplished, this little guy will definitely have a place in the Fields Medal two years from now.

And from Yuan Xinyi's introduction just now, they know that Yuan Xinyi is now only one step away from that ultimate truth!

He achieved fame at a young age and had the support of a strong teacher.

Zhang Yitang was overcome with grief. Years ago, his relationship with his teacher broke down, and after graduating with his doctorate, he couldn't even get a letter of recommendation, which disqualified him from entering the academic circle. Moreover, he was researching the Riemann Hypothesis, one of the Millennium Problems, and it would be difficult to produce results in a short period of time.

Ultimately, he was forced to drift from place to place at the bottom of society, working as a dishwasher and cashier, and even had to live with friends because of the hardship of making a living.

More than twenty years!

It wasn't until more than a decade ago, when he published the twin prime conjecture, that he truly returned to academia.

But that year, he was already 58 years old!

This young man in front of me is only 36 years old!
After sighing and lamenting, Zhang Yitang also composed himself and began to think about the question raised by Yuan Xinyi. Because of his own experience, he was quite willing to help this young man.

This thought process lasted for more than ten minutes.

Zhang Yitang stood up and said, “The key contradiction is that when we raise the automorphic representation to GL(4), the corresponding L function has a non-physical singularity near Re(s)=1/2, which is like the ghost zero of the Riemann zeta function hindering the analytic extension.”

Arriving at the whiteboard, I picked up a marker and drew the abnormal fluctuation at s=1/2+23.7i on the whiteboard.

Figali suddenly stood up and wrote a series of complex formulas under the diagram drawn by Zhang Yitang. “This is essentially the collapse of the measure space! Traditional trace formulas cannot capture the probability leakage in high-dimensional representations.”

With someone taking the lead, inspiration finally collided in the minds of these great mathematicians, sparking a dazzling display.

"Perhaps we should consider egomorphisms as connections on Sasaki-Einstein manifolds and absorb anomalies using curvature integrals..."

Tian Yang already knew about Yuan Xinyi's topic and joined the discussion. However, before he could finish speaking, Sun Binyang interrupted him, "Look here! The Dynkin graph of GL(4) has a hidden Spin(8) symmetry. If we construct a pseudo-spinor representation..."

As he spoke, he wrote the isomorphism formula on the whiteboard.

Aut4Spin(8)/Z2
Lin Shan, who is skilled in applied mathematics, began to conduct numerical simulations.

“My Monte Carlo sampling shows that the anomalous singularity is suppressed when a virtual phase angle θ≈0.37π is introduced.”

Lin Shan quickly concluded, "This suggests the need for some kind of phase compensation mechanism!"

"It is precisely by compensating for the leakage of the measure that we can construct a pseudo-Haar measure."

Figali also got into the zone, snatched the marker from Sun Binyang's hand, and wrote a differential transformation expression on the blackboard.

dg=e^(iθN(g))dg(θ∈R)
“Where N(g) is the quantum number representing the companion,” Figali explained.

"This is equivalent to introducing a topological θ term into the Langlands correspondence, just like the CP violation parameter in quantum chromodynamics!"

Yuan Xinyi's heart pounded wildly. He felt the bottleneck that had been trapping him loosen slightly, and he saw the light!
"If this phase factor is interpreted as the B-field flux on the Calabi-Yau manifold... then the quantization condition of the deformation parameter automatically satisfies θ=kπ/4, k∈."

A light also shone in Tian Yang's eyes.

The other mathematicians were also excited; if this could solve the problem, the achievement would naturally belong to everyone present.

“By constructing a central extension group _4×U(1), where U(1) carries the phase degree of freedom, we can maintain the integrity of the representation theory framework.”

Sun Binyang took the marker and drew a group expansion diagram on the whiteboard.

Lin Shan has already completed the numerical simulation, "When θ = π/3, the L function of GL(4) is at 100

"They succeeded!"

Even Yuan Xinyi himself didn't expect that the problem that had troubled him for several years could be solved in less than an hour.

"Strangely, the system memory overflows when T>1e5."

Lin Shan looked at the results on the screen, his brows furrowing slightly, feeling that something seemed amiss.

"Oh, my friend, you're overthinking it!"

"The probability conservation of the new measure is expressed as fe^(2iθN(g))dg=δ(θ), which holds true in the sense of distribution!" Figali exclaimed excitedly.

"Hey friends, look what we've found!"

The optimism unique to Westerners was infectious, and everyone else also subtly revealed their smiles.

Yes, they have indeed achieved remarkable results!

"If we prove that L_new(s) is holomorphic in Re(s)≥1/2 for all cases where θ≠0, perhaps we can develop a generalized Riemann hypothesis..."

Zhang Yitang stared at the whiteboard, lost in thought.

The Langlands program is a new tool, and using it to work on the Riemann Hypothesis might actually be a good approach.

"Therefore, combining everyone's ideas, the solution is divided into three steps. First, virtual phase degrees of freedom are introduced through Spin(8) symmetry. Then, the anomalous singularities are suppressed by the modified Haar measure. Finally, geometric quantization is achieved by using the B-field flux."

Tian Yang picked up a marker and drew a triangle diagram on the whiteboard that included number theory, geometry, and physics relationships, and then summarized.

“The irreducible representations of the central extended group are classifiable, which ensures the self-consistency of the scheme—at least at the categorical level,” Sun Binyang added.

Yuan Xinyi said impatiently, "I will immediately apply for supercomputing resources to verify the zeros of the 10^6 level L function using θ=π/4! The results are expected in 72 hours!"

After he finished speaking, he looked at his teacher, his face full of excitement.

clap clap clap...

A lively and insightful discussion finally came to an end.

Only then did Sun Jianfeng and Xiao Ming dare to speak.

"congratulations!"

"A good teacher produces outstanding students!"

One sentence was enough to elevate both Tian Yang and Yuan Xinyi.

Although they couldn't understand what the mathematicians were discussing, they could see the smiles on their faces. Clearly, Yuan Xinyi's research had made a major breakthrough.

Who knows, China might actually produce a Fields Medal winner of Chinese descent.

"Congratulations to Mr. Tian!"

Zhang Yitang, Sun Binyang, and the others all spoke to Tian Yang with envy. They were not young anymore, and when they thought of their students, envy naturally arose.

"Happy together."

Tian Yang replied with a smile.

As for sharing the joy, it naturally means that today's achievements belong to everyone. In the future, the names of several people will inevitably be added to the author list of the paper, and at least a few people will be missing from the acknowledgments. It is icing on the cake for them and can be considered a happy event.

Having overcome the toughest challenges, all that remained was to await supercomputing verification. They weren't in a rush. The atmosphere in the lounge immediately relaxed; these renowned mathematicians, being human, began chatting about insider gossip.

For example, after Kunihiko Kodaira won the Fields Medal, he had a brilliant disciple, but worried that the disciple would form his own school of thought, so he insisted that the disciple marry his daughter before he would feel comfortable supporting him...

Sun Jianfeng and his companion listened with great interest. They would have been completely unaware of such gossip within academic circles if it weren't for a bigwig in the field revealing it.

It seems that there isn't much difference between academia, politics, and business; both are full of investment and exchange.

Academic luminaries invest everywhere, recruiting geniuses to their ranks, and then crediting them with their work. With one academic luminary at the core, they form a group of interests, acquiring resources and attracting talent, which naturally leads to fruitful results.

Isn't that how it's done in the business and political worlds?

"Speaking of outstanding disciples, Master Ran has taken on an exceptional one."

While chatting happily, Yuan Xinyi suddenly thought of the paper he had seen not long ago: "A high school student who is only sixteen years old is already able to write a high-level paper on group theory."

"Oh?"

Upon hearing this, the bigwigs in the lounge also showed some interest, looking at Ran Peng and anticipating what he would say next.

Although Ran Peng is also a Yangtze River Scholar, his achievements and honors in the mathematics community are far from comparable to those of the other big names. He also failed to offer any constructive suggestions in the previous discussion and has become virtually invisible. Unexpectedly, he has suddenly become the focus of everyone's attention.

"It can't be considered independent writing; it was just providing constructive suggestions for a graduate student's thesis. There's still a long way to go before I can independently write a high-level thesis."

Ran Peng dared not put on airs in front of these big shots, so he waved his hand and told the truth.

"Professor Ran, there's no need to be modest. I've read that paper. The essence is just a few suggestions. Given more time, that young man will surely become an excellent mathematician."

Yuan Xinyi praised Chen Hui, saying that he really thought highly of Chen Hui and admired the inspiration Chen Hui displayed in that paper, an inspiration unique to mathematical geniuses.

"Oh right, I remember he also participated in the finals of this year's Azerbaijan!"

Yuan Xinyi reviewed Chen Hui's preliminary round answers, so he naturally remembered them.

"Oh? What a coincidence?"

"May I ask what your name is, young friend?"

Xiao Ming immediately perked up, "Would any of you be interested in seeing how that young friend answered the questions?"

The sixteen-year-old high school student immediately thought of that person.

If it really is Chen Hui, then all he needs to do is hire some online trolls to promote him, and these big shots might just recruit him, and their plan will be halfway done.

Although it deviated somewhat from his initial expectations, one must always take things one step at a time; it's impossible to achieve everything at once.

"Yes, Xinyi, what's that child's name? Since we're already here, why not take a look?"

Tian Yang also said with a smile.

Everyone is in a good mood now, and it's nice to see the younger generation of mathematical geniuses. Mathematicians, like generals, are like beauties and famous generals throughout history, who are not allowed to grow old in this world. It is precisely for this reason that they are particularly fond of young people.

They naturally preferred a sixteen-year-old who was gifted in mathematics.

"Chen Hui!"

Yuan Xinyi said the name.

With the stone settled, Xiao Ming looked at Sun Jianfeng.

Sun Jianfeng understood and walked out of the lounge.

Ran Peng inwardly groaned. The people present were all big names in the mathematics circle, whose status and academic level were far beyond his reach. If Chen Hui caught their eye, he, a mere junior like Karami, would not be able to compete with him.

A few minutes later, Sun Jianfeng returned with a tablet and turned on the large TV in the lounge.

A few dozen seconds later, a quiz screen appeared on the TV. In the upper right corner of the screen was a one-inch portrait of the person answering the question, which was the surveillance footage of the person answering the question.

However, no one was interested in the surveillance footage; they all looked at the question displayed in the center of the screen.

This is the fifth problem in the final round, the Algebra and Number Theory track.

Clearly, this is a candidate's answer interface. Based on the previous chat content, it's not hard to guess that this candidate is Chen Hui.

Algebra and Number Theory Track!
"interesting!"

Tian Yang became increasingly interested.

Compared to other fields, those of them who do pure mathematical research always feel more at home with algebra and number theory.

Suddenly, he seemed to remember something, took out his phone and checked the time: 12:48.
It's getting late. They were having such a heated discussion that they forgot to eat lunch. Luckily, there were plenty of pastries in the lounge, and everyone had already eaten quite a bit, so they weren't too hungry and weren't in a hurry to eat.

However, less than four hours into the exam, that little guy had already gotten to the fifth question?

"Can we see his previous answer records?"

Tian Yang looked at Sun Jianfeng and asked.

This set of questions was selected by the organizing committee from the question bank, so he was certainly aware of its difficulty.

This set of questions has a total of six questions. If he was able to complete the fifth question in five hours, and if the previous questions were not too difficult, then this sixteen-year-old's mathematical ability is at least on par with that of a doctoral student.

"Of course!"

Sun Jianfeng made a few moves on the tablet, and the image on the large TV screen in the lounge began to change.

The fourth question requires a comprehensive application of knowledge from number theory, such as the circumscribed field, norms, and ideal decompositions in algebraic number theory. These concepts are relatively abstract and are difficult to understand and apply.

However, Chen Hui's answer was very clear in its approach. He defined the norm, then analyzed the values ​​of the norm. By introducing the norm, he transformed the original equation's equality relationship in the number field into an equality relationship between integers. He then used the properties of integers to deduce the contradiction. This transformation method was very ingenious.

The fact that the person was able to answer this question with such ease demonstrates a solid grasp of the fundamentals, and their ability to apply that knowledge flexibly showcases their talent.

Question 3, Question 2, Question 1...

They answered each question thoroughly. After reviewing the answer to the fourth question, everyone simply glanced at the answers to the first three questions and was able to conclude that there shouldn't be any major problems.

Everyone became even more interested in this little guy.

Although there is a big difference between mathematicians and problem solvers, many mathematicians do not actually have very good competition results.

But true geniuses will never have weak competition results. For example, Schultz and Tao are both IMO gold medalists, with Tao winning the IMO gold medal at the age of 13.

This sixteen-year-old is able to do this much, which clearly shows he has a good talent for mathematics.

Let's go back to question five.

Tian Yang nodded slightly, glanced at the other mathematicians, and then spoke to Sun Jianfeng.

When the camera returned, there was no movement on the screen; Chen Hui was still deep in thought.

"Let's take a look at the other contestants."

Zhang Yitang spoke first.
The other mathematicians nodded slightly. They certainly couldn't waste time with Chen Hui here. If Chen Hui was thinking for a whole day, were they going to wait here for the whole day too?
(End of this chapter)