International Congress of Mathematicians

"Let's assume that this point belongs to the set {where the ξ function is not an obvious zero}. According to the principle of Shen's twin matching method, then naturally the overall product of this set must be 0..."

"Since s has traversed to the two zeros of the k-th twin pair, then I and II are contradictory... Academician Lin's logic becomes inconsistent here."

"In other words, the cases where x equals βk and γ = γk, and x = 1 - βk and γ = -γk, are difficult to rewrite as a system of ordinary equations. The RT Third Expression has not been proven..."

"I haven't attained it yet... Hehe, hehehe, I understand, I've realized it, I've attained it!"

Click!

A forked bolt of lightning ripped through the night sky!

Using the blinding flash of lightning, Shen Qi wrote down a formula on the draft paper:

ζ(s)=∑(0≤n≤T*-a)(n+a)^-1/2-it+O((T*)^1/2(1+t)^-1),0≤t≤T

After writing the equation, Shen Qi opened the window and roared at the darkness and lightning, "I am Shen Qi, I have proven the RT Third Expression! Man can conquer nature, the world Sun Yat-sen University, but I am the only one..."

Click!

Click!

Chain lightning!

Shen Qi quickly closed the window and wiped the rain off his face.

The problem that had troubled Shen Qi for more than half a year was solved by him in 20 minutes on a stormy night.

Over the next few days, Shen Qi continued to refine his paper on <RT Third Expression>.

After several revisions, the report paper "<RT Third Expression>" was condensed by Shen Qi to 52 pages, of which 44 pages were the work of Ou Ye, Mary, and Jonas, which Shen Qi summarized, sorted, and integrated to form a combined manuscript.

It's only 8 pages long, and it's Shen Qi's exclusive specialty.

History is quite remarkable; the paper in which Riemann proposed the Riemann Hypothesis in 1859 was also a mere eight pages long.

Having made all the preparations, Shen Qi and his team boarded an international flight from New York to Brasilia, the capital of Brazil.

The authors listed on the homepage of <RT Third Expression> are: Shen Qi, Ou Ye, Mary -Schmidt, and Jonas Carr.

In the conclusion of the paper, the authors thanked authoritative experts such as Faltings, Lyndon Strauss, Muller, and Gong Changwei for their technical support.

The entire team of eight set out and arrived in Brasilia in late October.

This year's International Congress of Mathematicians was held in Brasilia and lasted for nine days. The first eight days were dedicated to academic presentations, and the final day saw the awarding of four Fields Medal.

In Brasilia, the Four Prodigies of Yanjing University School of Mathematics successfully met and had a brief but friendly exchange.

Shen Qi, Education: Yenching University, Princeton. Currently a lecturer at Princeton, specializing in number theory. He will give a one-hour presentation at this conference.

Gong Changwei, Education: Yenching University, Columbia University. Currently a professor at Columbia University, specializing in number theory, giving a 45-minute presentation.

Yun Wei, Education: Yenching University, Princeton. Currently a professor at Yale University, specializing in Algebraic Geometry, giving a 45-minute presentation.

Xu Yang, Education: Yenching University, Princeton. Currently a professor at Yenching University, specializing in Algebraic Geometry, giving a 45-minute presentation.

Shen Qi was very familiar with Gong Changwei, and had dealt with Xu Yang when they were in China. This time, he met Yun Wei.

Four Prodigies of Yanjing University School of Mathematics will represent China in the race for this year's Fields Medal.

The eyes of the Chinese Mathematics Community are focused on Brasilia, and the nation's expectations are pinned on four young mathematicians: Shen, Gong, Yun, and Xu.

When the Premier met with representatives from the fields of science, education, and culture at the Two Sessions, he said that China already has Nobel Prize, and only lacks a Fields Medal.

Will there be any Chinese names among the four winners of this year's Fields Medal?

On the first day of the conference, Gong Changwei, Yun Wei, and Xu Yang delivered a 45-minute academic report.

This is the second highest level of report, and Gong, Yun, and Xu have a certain probability of winning the Fields Medal.

In Professor Faltings' prediction system, the winning rate for Gong, Yun, and Xu is between 1.2% and 1.8%.

Shen Qi listened attentively at the conference, continuing into the afternoon, until the first speaker, a top-level expert, took the stage for a one-hour presentation.

Alessio Faltings, an Italy mathematician, is currently a professor in the Princeton Mathematics Department. He is Shen Qi's colleague and Zhou Yu'an's mentor.

Professor Faltings' prediction system has seven top candidates, with Faltings ranking seventh.

Even the person predicted to be seventh has a Fields Medal dream.

Faltings delivered his speech with great emotion and unwavering determination; his eyes told everyone that he longed for the Fields Medal.

"Assume that the partial differential inequality (7) has a final positive solution UH(t, x) under the boundary condition (2), (t, x)∈[T,∞)×Ω..."

"... Therefore, based on the characteristic function corresponding to the first eigenvalue of the Dirichlet problem, I obtained the area element over δΩ!"

"... Therefore, I have proved this theorem for Parabolic Partial Differential Equations, which will play an important role in the field of impulse vectors. Thank you!"

The audience erupted in applause; Faltings's one-hour report was truly brilliant.

Shen Qi was also clapping, and felt a little nervous.

Professor Faltings is going all out, he's even using his entire fortune!

Faltings, who has Differential Geometry background in Partial Differential Equations, has been focusing on partial differential equations in recent years. He is particularly skilled in elliptic and parabolic PDEs.

The Parabolic Partial Differential Equations theorem that was just reported is Faltings's latest research result.

In recent months, Princeton Mathematics Department coffee time, Faltings has been keeping quiet, listening more and saying less.

Shen Qi knew that Faltings was preparing a big move. Old Figari, I never expected you to be such a cunning guy. You've been biding your time, waiting for a comeback!

I, Shen Qi, am so naive. I announced the latest research progress on the RT Third Expression 20 days in advance. Of course, I also had a big surprise in mind, which was my 8-page fourth path... During the conference break, Shen Qi took the initiative to talk to Faltings: "Alessio, after listening to your speech, I have become your fan."

"Really? I'm very satisfied with my report too." Faltings was beaming; he was still immersed in the passionate report he had just given.

"Alessio, your ranking has risen to fourth," said Professor Faltings, the Princeton prediction guru.

Seventh to Fourth, Faltings, who had turned his fortunes around, was in high spirits. He said to Shen Qi, "Qi, your Chinese classmate, Zhou, is very promising. Recently, he has helped me solve some problems using Differential Geometry. I'm thinking that I should let him graduate with his master's degree next semester and enter the doctoral program as soon as possible."

"It's Zhou's honor to be able to follow you, Alessio." Shen Qi smiled to himself, thinking, "Zhou Yu'an, you're quite something. You kept it from me for months, and it turns out you were helping Professor Faltings with his work." Recently, Shen Qi has been flying all over the world and leading a team on a research project, so he's been too busy to pay attention to Zhou Yu'an.

In fact, Faltings is also Shen Qi's competitor. Shen Qi had not paid much attention to Faltings before, but now he has to pay attention to him again. Faltings is his Princeton colleague and Zhou Yu'an's mentor.