Amelia and Gu Bing's reports were completed very smoothly, and Xu Chuan was sincerely pleased for these two students who had grown up.
For him, in addition to researching those unknown fields, spreading the knowledge he has learned is also his life goal.
After all, the development of a discipline, a country, and a civilization cannot be sustained by one person. Behind the development, there is always the silent dedication of a group of people.
"Professor! We report...it's done!"
After the report meeting, Amelia and Gu Bing ran over immediately, with excitement and excitement in their voices.
Xu Chuan looked at the two of them with a smile and encouraged: "Well done!"
For the first time in my life, I stand on the world stage and give reports to scholars from all over the world, including some top experts. It not only tests the mathematical level and expression ability of the scholars who give the reports, but also a person's psychological endurance.
Quite a test.
After experiencing this transformation, both Amelia and Gu Bing have the ability to stand on their own.
Gu Bing grinned and said, "You don't know how fast my heart beats when I stand on the stage! It feels like it's about to jump out of my throat."
Xu Chuan smiled, remembering that when he interviewed Gu Bing, he felt a little emotional when he saw him so nervous that he couldn't even finish his sentence.
Several years have passed in the blink of an eye, and the former students have graduated and can even stand in front of thousands of people and give speeches and reports.
"Professor, Senior Brother Gu and Senior Sister Mi, I'm so nervous. Do you have any experience or skills in giving reports on stage? Please teach me some, I need them too!"
On the side, Cai Peng looked at the three of them with expectant eyes. He also had a forty-five-minute report at this International Congress of Mathematicians.
Although it was not as good as Gu Bing and Amelia's one hour report, his report was based on the paper "Stagewise Proof of Minimum Differential Calculation of Dimension Polynomials for Differential Equations".
This paper has not yet been peer-reviewed, which means that he needs to face questions from top experts, which is more difficult than Gu Bing and Amelia.
Xu Chuan smiled and patted his shoulder and said: "I don't have any experience or skills. I just have strength and a heart that loves academics. I can solve the minimum differential calculation problem of differential equations and dimensional polynomials. I believe you will be fine."
of."
The teachers and students chatted for a while. Amelia looked at Xu Chuan, took a deep breath, and said, "Professor, there is something I want to tell you."
"Huh?" Xu Chuan looked at Amelia and smiled: "What's wrong?"
Pursing her lips, Amelia said, "Princeton University has invited me to serve as a professor in the Department of Mathematics. I would like to ask for your opinion."
Hearing this, Xu Chuan had a look of surprise in his eyes, but it soon turned into a smile: "Princeton is a very good choice. If you go to be a professor there, I believe you can go further in mathematics."
"Do you mean to recommend me to take up the post?" Amelia asked, and then added: "But I haven't fully learned the calculation methods of mathematical physics."
Xu Chuan smiled and said: "I have given you the core of mathematical calculation methods for exploring physics. I believe you can further complete your own expansion in the future."
"And following me forever is actually not necessarily a good thing. You are greatly influenced by me. If you follow my steps all the way, it will be difficult to create something that is truly your own."
"So, go to Princeton to experience it!"
After a pause, he smiled and said: "Maybe I will still need your help after China's Large Strong Particle Collider is built."
Hearing this, Amelia nodded vigorously.
Although she hopes to continue studying with Xu Chuan, she also knows that if she continues like this, it will be difficult for her to find her own path.
Going to Princeton to be a professor is not a new learning experience. There, she may be able to stand in a higher position and be closer to the person in front of her.
...
After a report meeting ended, Amelia was surrounded by media reporters as expected.
For a long time, mathematics has been considered a male domain because there are really few women who can make outstanding achievements in this field.
And this means that the achievements made by women in the field of mathematics will have a greater impact than men.
"Professor Amelia, I am a media reporter from the BBC. You won the Fields Medal at the age of twenty-six, breaking the previous record in one fell swoop. What do you think?"
Amelia: "First of all, I want to say that I have not broken the record of my predecessors. The record of being the youngest person to win the Fields Medal was held by my mentor."
"As for my feelings, excitement? Excitement? Pleasure? It seems to be a little bit of it. I don't know how to describe the mood of this moment. But I think I should most thank my mentor, Professor Xu Chuan, who gave me this life-changing opportunity.
Chance."
BBC reporter: "I heard that you are still studying with Professor Xu. As someone who has already won the Fields Medal, are you not eligible to graduate under Professor Xu?"
Amelia shook her head and said: "No, I have already graduated in mathematics and got a diploma. I am studying with the professor to further my education."
"Further study? Can you give a brief introduction?"
"Of course." Amelia smiled and nodded, saying with some pride in her tone: "Professor, he is not only good at mathematics, physics, astronomy and other fields. He also has great contributions and achievements, especially in
Introducing the subject of mathematics into other subjects to promote development is what he is best at."
"And this is what I studied with the professor."
BBC reporter: "I see, I heard that you were interning at CERN some time ago. Will you continue to work at CERN in the future?"
The BBC reporter dug a little hole into this question. The competition between CERN and China in the field of hadron collider is well known, and whether Amelia continues to work at CERN or chooses to work in China, she will be left behind.
Some 'stories' to write.
But what he didn't expect was that Amelia's answer was completely off track.
"I have received an offer from Princeton and will probably go to Princeton as a mathematics professor during the fall semester."
The BBC reporter was stunned for a moment. He really hadn't considered this, but he quickly realized it and congratulated him with a smile.
Although I dug a small hole and didn’t catch anyone, it was pretty good to get an interview with a 26-year-old female Fields Medal winner.
...
After Amelia and Gu Bing's report meeting in the morning, there were still two hours left. Xu Chuan certainly didn't want to waste it, so he started looking for it at the conference site.
An international conference of mathematicians was divided into 20 group reports, and each group had three to eleven small report segments.
From logical groups to algebra, to number theory, algebra and complex geometry, almost every major and minor category of mathematics has a corresponding venue and reporting period.
Naturally, it is impossible for Xu Chuan to read every one of the numerous reports. Finding and selecting fields of interest and needs is also a basic skill for a scholar.
Starting from the field of algebraic geometry, Xu Chuan looked at the lecture venue and finally targeted the field of number theory.
It just so happened that the person who gave the report in the field of number theory was a mathematician who was no less than a Fields Medal winner.
James Maynard is a professor of mathematics at the University of Oxford, where the sun never sets. His research focuses on using the tools of analytic number theory, especially sifting methods, to study prime numbers.
In the original course of history, Professor Maynard would have won this year's Fields Medal. His contribution to analytic number theory, as well as his understanding of the structure of prime numbers and Diophantine approximation are very good, and his overall strength is very strong.
Overall, this mathematician is somewhat similar to Professor Zhang Wei from the golden generation of Peking University. His overall research level is relatively high, but he lacks a big mathematical conjecture as a cornerstone.
In addition, he is only thirty-five years old this year and can wait for another term, so he was squeezed out by Amelia.
In fact, speaking of it, Professor Maynard is quite interesting.
Not only is he lagging behind in the Fields Medal, but he is also lagging behind in some other mathematical achievements, awards, etc.
Speaking of prime numbers, some enthusiasts can easily name some familiar, easy-to-understand, but very difficult mathematical conjectures, such as Goldbach's conjecture, twin prime conjecture, new Mersenne prime conjecture, etc., which all belong to the prime number conjecture.
part.
One of Professor Maynard's most famous achievements is to prove that there are infinite pairs of prime numbers in the "twin prime number conjecture", and the interval is less than 600.
But unfortunately, half a year before he published this result, 55-year-old Zhang Yitang proved that there are infinite pairs of prime numbers, with intervals less than 70 million.
Although Professor Maynard's interval value is much smaller than that of Zhang Yitang, Zhang Yitang was the first scholar to prove that there are infinite pairs of prime numbers and that their intervals have a finite upper bound. Therefore, he has received honors related to the twin prime conjecture, such as the "Highest Award in Number Theory"
"The Kohl Prize and other awards were all taken away by Zhang Yitang.
There is no way, the world of mathematics is like this 'reality'. If there are many people working on the same problem, then often only the first person to solve it can get most of the credit.
And for Professor Maynard, this is not the only tragedy.
After crashing with Zhang Yitang, he also crashed with another famous mathematician, that is Terence Tao.
At almost the same time, the two of them pushed the interval between twin primes to the order of several hundred.
However, when Terence Tao later learned that Maynard had obtained the same result, he voluntarily gave up his proof.
In the end, Professor Maynard published a paper on this result alone, which can be regarded as the lucky thing among misfortunes.
Influenced by the research on space holes and the Riemann Hypothesis, Xu Chuan was very interested in knowledge in the field of number theory at this mathematics conference.
After finding Professor Maynard's lecture hall, he found a seat in the back row of the venue and listened with interest.
To put it simply, the content of Professor Maynard's report is related to prime numbers. He proposed a method for the distribution of prime numbers in the residual class, and extended the principle of his method beyond the generalized Riemann Hypothesis.
Xu Chuan still knew something about prime numbers and analytic number theory, so the content he described did not feel as difficult to understand as other scholars did.
Although this mathematician is a bit poor in luck, it must be said that he is also a "genius" player.
The residual prime number distribution calculation method he conceived has considerable potential to be tapped in the field of prime numbers.
At least in Xu Chuan's view, it is possible that this method can continue to advance the twin prime conjecture and even solve this problem.
However, for him, solving the twin prime conjecture was not his goal, so he took some notes and left quietly after listening to the main part of the lecture.
...
The days passed like this. During the day, Xu Chuan was at the report meeting looking for some reports that he was interested in or that would be helpful for his research. At night, he continued to improve calculations and papers on "space holes".
On the third day of the report meeting, which is also the fourth day of the International Congress of Mathematicians, another of his students Cai Peng will also formally take the stage to give a presentation on the paper "Stage Proof of Minimum Differential Calculation of Dimensional Polynomials for Differential Equations"
A report of my own.
Although it was only a 45-minute lecture, finding an algorithm to prove the minimum differential dimension polynomial problem in the field of differential expansion still attracted a lot of math circles and even some physicists.
Because the concept of differential dimensional polynomials is closely related to the concept of strength of the system of partial differential equations that determine the 'physical field'.
Using the language of differential algebra, the problem of finding the highest intensity of a physical field is the problem of finding the minimum differential dimension polynomial of a certain differential extension field.
Therefore, this problem is not only a problem of differential algebra in mathematics, but its solution may also lead to some new important results in theoretical physics.
As for things in this cutting-edge field, I am afraid that no theoretical physicist present will miss it.
Of course, apart from the paper itself, another reason that attracted many scholars to come to listen to the lecture was that Cai Peng was also a student of that person.
Two generations of students, the first of which has already won a Fields Medal.
The second generation also made considerable achievements and contributions in the field of mathematics, solving part of a world-class conjecture.
This has made many mathematicians curious, eager to know whether there are differences and similarities between the two generations of students, and eager to know how that person taught the students!
