Great Country Academician

Soon, Cai Peng's report meeting began.

The problem of minimum differential calculation of dimensional polynomials in differential equations is not very famous in the mathematics community, but it is a 'fundamental' problem.

Its solution not only provides a new approach to the intensity concept of Einstein's system of partial differential equations in "physical fields", but also involves the development of mathematical disciplines such as geometry, algebra, and statistics.

In addition, polynomials are also an important concept that can be used to derive many concepts.

For example, the concept of symmetry can be derived from the symmetry relationship of the coefficients of polynomials, and in calculus, the concepts of integral and differential can also be derived from the form and change laws of polynomials.

On the whole, its solution will be an important progress in differential algebra and its applications, and its impact on mathematics will be considerable.

On the lecture stage, Cai Peng went from being nervous and unfamiliar at the beginning to gradually becoming fluent and then becoming more and more comfortable. The nervousness of giving a report at such an international conference for the first time also faded away.

Looking at Cai Peng, Xu Chuan nodded approvingly.

Although this student has taken many detours in mathematics, when he truly enters the field in which he is interested and talented, his potential is quite good.

On the other side, in the corner of the lecture hall, looking at Cai Peng who was sitting on the stage giving a report, Professor Zhou Hai, who had been successfully promoted to professor and director of the School of Mathematics at NTU, couldn't help but feel a little emotional.

"I didn't expect that this kid would reach this height after following him."

On the side, Rong Zhizhuan, the dean of the Institute of Mathematics, said with a smile: "Cai Peng is also a genius, but he didn't find a suitable field for himself before. Now he has entered a suitable major, and with the training of Academician Xu, he has achieved this achievement. It’s not surprising either.”

"Speaking of which, he should be graduating if he can prove the minimum differential problem of dimensional polynomials in differential equations."

"After the report is over, you can be hired as a mathematics professor in our school. This is also a very good talent. It happened that the college was reorganized into a college two years ago, and there is an urgent need for excellent professors."

Zhou Hai said with a smile: "It's not difficult to get him to take up the post. After all, Academician Xu is still here. I believe Cai Peng is also willing. Let's talk to him later."

After a pause, he seemed to have thought of something, and continued with some emotion: "I don't know if this kid has a chance to win another Fields Medal for our country and NTU."

So far, the only Fields Medal awarded by a Chinese scholar is Xu Chuan.

Thinking of Amelia, who had won the award before, he couldn't help but hope that his former student could win a Fields Medal.

After all, this is the highest honor in mathematics.

On the side, Rong Zhizhuan said with a smile: "There is a chance. If I remember correctly, he seems to be less than thirty this year. He has already made achievements in the field of differential equations and polynomials. If he can solve the remaining problems, There is still great hope for polynomial calculations with minimum differential dimensions.”

Half an hour has passed and the report will gradually come to an end.

After the last calculation report was completed, Cai Peng breathed a sigh of relief, but quickly concentrated his energy again, and he was so focused that he did not dare to relax at all.

Because the following question and answer session is the core part of the entire report meeting.

Especially for someone like him who has proven a phased result but has not yet passed peer review, there must be many colleagues who have doubts.

The first person to ask the question was Professor Terence Tao from the University of California.

In the world of mathematics, as the saying goes, mathematical problems and proofs without Tao Zhexuan's support are unqualified. This "all-round mathematician" known as the new generation stood up and spoke briefly.

"I noticed the expression in the sixth line of page 11. There is a line that is very interesting. If R and R[x] are condensed rings, then 1

"Page 11, line 6?"

Cai Peng turned over the paper and said: "Based on Lemma 1.4, the representation dimension of any ring R is not 1, and we limit FPD(R)=0 and 1

"Thanks."

After listening to Cai Peng's statement, Tao Zhexuan nodded approvingly. He is a very good young man. No, he should be called a 'mathematician'.

After all, he solved part of the minimum differential calculation problem of dimensional polynomials in differential equations, which is enough to deserve the title of a mathematician.

After Terence Tao's questions ended, the question-and-answer session continued.

Fifteen minutes is not a long time for questions and it is impossible to accommodate everyone. But for Cai Peng, as long as he solved the doubts in the minds of the big guys sitting in the front row, the report meeting would be a success.

Following Tao Zhexuan, several big names in the field of differential equations and polynomials also stepped forward and asked several questions, and finally got perfect explanations.

Overall, this report meeting went quite smoothly.

"Professor, I did it!"

After the report meeting, Cai Peng ran over quickly with excitement on his face.

Xu Chuan patted him on the shoulder and said with a smile: "It's a wonderful report, very good. I hope you can reach new heights in the future of mathematics!"

Cai Peng nodded firmly and said seriously: "I can do it, Professor!"

Xu Chuan smiled and said: "Come on."

As a professor, there is nothing more fulfilling than watching the students you teach grow and thrive step by step.

Whether it is Gu Bing and Amelia before, or Cai Peng now, or Ding Rui, Tong Yang and others who are studying with him.

Watching batches of students grow up from his hands, I really feel like an old father.

The core of the International Congress of Mathematicians is always academic exchanges. There are 20 groups and academic reports in different fields. A large number of wonderful papers and reports emerged during the conference.

During the conference, Xu Chuan also gained quite a lot. Whether it was the Gauss Medal or the Fields Medal Special Award, they were all new achievements in life.

Of course, the more important thing is the academic gains.

The theory related to space and time has already had enough ideas and is being improved. The fields of number theory and pure mathematics, which were relatively rarely touched before, also saw a number of wonderful reports and papers at this report meeting.

Time passed very quickly, and in the blink of an eye, this International Congress of Mathematicians also came to the last day.

The report on the Yang-Mills mass gap will be the most grand event in this mathematics conference.

In order to meet the needs of scholars who came to listen to the lecture, not only mathematicians, but also many physicists, the IMU committee that organized the conference specially placed the report in the very large lecture hall that hosted the opening ceremony of the conference.

It can accommodate more than 3,000 people seated at the same time, but it is still packed to the brim at this moment.

It can be said that most of the scholars who participated in this conference were present.

Not only that, but many physicists who had not been very interested in mathematics conferences also came from all over the world on this day.

Everyone was looking at the reporting table eagerly, and their eyes fell on the young figure standing on it.

If an ordinary person or an ordinary scholar were to stand here, facing the crowd of people in the audience, facing this huge pressure, he would probably be so nervous that he would not even be able to speak.

But for Xu Chuan, who was used to such large-scale lectures, this was not a scene worthy of making his heart beat faster.

It is not difficult for him, whether it is to go on stage to give a report or to answer the doubts of those who ask questions.

After all, this is not the first time that he has stood on such a stage and faced scholars from all over the world, nor is it the first time that he has solved such a difficult problem.

Responding to the gazes of the audience, Xu Chuan, who was standing on the newsstand, spoke slowly.

"As for the Yang-Mills mass gap problem, I believe you have read my paper before coming here. So I won't waste your time."

After a pause, he continued: "I will briefly explain the proof process in the paper again, and explain in detail some of the ideas I used to prove this problem."

"If you still have any questions, you can point them out in the final question and answer session, and I will leave enough time for you."

With that said, Xu Chuan clicked on the PPT he had prepared and projected it on the huge screen behind him.

"For any compact simple group G, there exists a massive quantum Yang-Mills field with G as the gauge group on R4, and there is a mass gap \u003e 0! 》

The caption on the picture is long, but it’s the best response to the question of Young-Mills’ presence and quality gap.

Looking at the screen beside him, Xu Chuan began to explain step by step.

". Let all spatial derivatives of the gauge field A = A(t, x k) vanish faster than any power of xk xk as xk Z coordinate system.) Let AdG represent the local Lie algebra of this gauge field, and G represent the corresponding infinite-dimensional local Lie group."

[tAk = Ek, tEk =jFjk[Aj, Fjk], Fjk =jAkkAj[Aj, Ak]]

“Here, invariant couplers of differentiable structures on high-dimensional manifolds are introduced, and through the characterization theorem, the S-transform is a topological linear isomorphism of (C).”

On the reporting platform, Xu Chuan explained the steps and key nodes of proving the Yang-Mills mass gap while comparing it with the PPT behind him.

Time passed little by little, and when the last mathematical formula was completed, Xu Chuan turned his head and looked at the lecture hall. After scanning the crowd, he slowly spoke.

"As for the Yang-Mills existence and the mass gap problem, I think we have obtained sufficient answers. Those predictions based on the Yang-Mills equation and the wave-particle duality of matter can describe the objective existence of elementary particles. We have been able to explain it concretely using new mathematical concepts.”

"I believe this will increase our understanding of the nature of matter and will be an important step in our long-term exploration of understanding the universe through mathematics and physics."

"That concludes my report, thank you all for listening."

The moment the words fell, applause spread from the front row to the back row like a tide, filling the entire report conference in an instant.

Sitting next to Deligne, Edward Witten applauded and said with a smile, with some emotion in his tone: "Another epic problem ended in his hands."

Looking at the young figure standing on the reporting platform, Deligne nodded and said: "Indeed, in today's mathematics world, unless someone completes the Riemann Hypothesis and achieves the unification of algebra and geometry, I'm afraid there will be no No one can surpass him."

Witten smiled and said: "Isn't he already interested in the Riemann Hypothesis? What will happen if he solves this problem again?"

Hearing this question, Deligne turned to look at his friend. After thinking for a moment, he said: "If he solves the Riemann Hypothesis and completes the unification of algebra and geometry, I am afraid that his status in the mathematical world will no longer be mine." It can be evaluated.”

After a pause, he added: "At least, he will completely surpass my mentor."

Applause came in wave after wave in the lecture hall like a tidal wave, lasting for a long time.

Looking at the audience in the audience, Xu Chuan continued: "The following will be a question and answer session. If you have questions about the proof of Yang-Mills's existence and quality gap, you can raise your hands to ask questions."

As soon as he finished speaking, everyone in the audience raised their arms. Starting from the front row, Xu Chuan selected the audience to answer questions.

He originally thought that many people would have many doubts about this proof, but in fact, except for some scholars, more scholars were wondering when strong and weak electricity would be unified. He was not interested in other millennium problems. Interested in topics beyond these reports.

As for the paper itself, maybe the scholars who asked the questions have no doubts anymore, or maybe it has conquered everyone!

After the last report on the Yang-Mills mass gap, this International Congress of Mathematicians is about to come to an end.

As usual, before the closing ceremony of Tsarist Russian opera, classical music, etc., the Secretary-General of the International Union of Mathematicians will announce the location of the next International Congress of Mathematicians.

This is the finale program of the International Congress of Mathematicians, second only to the Fields Medal award in importance. The International Mathematical Union Committee selects from a list of cities in various countries.

Unlike the Olympic Games, which were once rushed to be held but now have almost no bidders, the International Congress of Mathematicians does not theoretically require the support of the applicant country or city.

Because its funding expenditures are paid by the International Mathematical Union itself, whether it is hotel expenses or other support, they are all internal expenses.

Of course, generally speaking, no matter which city or country the International Congress of Mathematicians chooses to host, the corresponding city will provide considerable support.

For example, transportation, security, management, and even communicating with the hotel to reduce or reduce some or even all fees, etc.

After all, being able to hold such a grand event will greatly enhance and promote a country's mathematical strength, influence, academic reputation and other aspects.

However, it is not easy for your own country and city to host such a grand event.

Because everyone wants to hold such a grand event at their doorstep, which is not only convenient and respectable, but can also promote the development of the field of mathematics in the motherland.

After all, going abroad for exchange is a very difficult thing for 'poor' mathematicians, especially those new students such as postgraduate and doctoral students. In most cases, you can only rely on the professor to take you out to see the world.

But holding it in your own country is completely different. It only takes a little time and money to communicate face-to-face with many top experts.

This is extremely beneficial to promoting the development of mathematics in a country.

Standing on the reporting platform, Professor Helden Holden, Secretary General of the International Mathematical Union, faced the blazing gazes of the audience, smiled, cleared his throat, and said in a loud and clear voice:

"After discussion by the International Mathematical Union Committee, the venue for the 30th International Congress of Mathematicians is——"

"China Jinling!"