"If we take into account graduate courses, these seven branches contain a total of more than 80 sub-courses, and there are 11 sub-courses under a functional analysis alone. ”

Of course, undergraduate students in the Department of Mathematics only need to learn the most basic functional analysis theories such as linear operator theory and variational method, and advanced courses such as Banach space and topological linear space are the learning tasks of graduate students. Witten said that he is an expert in functional analysis, and physical problems are inseparable from the mathematical processing methods of functional analysis.

"So, when you entered Princeton's graduate school, what branch did you initially choose to focus on?" Witten asked.

"My main major is mathematical physics, dear Professor Witten, the first advisor I applied for was you. Shen Qi told a secret.

"Charles, there is such a thing, how come I don't know?" Witten looked at Director Peverman suspiciously.

"Hey, Edward, please, don't look at me like that! You yourself said a few years ago when you were the head of the department that you won't take any graduate students with you in the future. "Director Feverman won the Philippine Award at the age of 29, he is such a smart person, he will not take the blame, and he is reasonable, timely and accurate.

"Oh yes, maybe I forgot. Witten looked at Shen Qi and expressed regret that he would never have the opportunity to become Shen Qi's mentor again in his life, because Shen Qi would participate in the doctoral graduation defense in a few months.

"Carl handles the day-to-day affairs of admissions in the mathematics department, and Edward, you were the head of the department, and you know the admissions process. Karl did exactly what you had instructed him to do, and you can't blame him. Director Peverman explained.

"I see. Witten nodded, he was on an equal footing with Peverman in the math department.

The head of the Department of Mathematics of the University is changed every three years, and the top bulls take turns to be the director, and the position of director has no additional income or subsidies, and is purely in the nature of serving the people.

Newly retired F++A superstar John Milno, who has been the head of the department, Andrew Wiles, who has returned to the UK, has been the head of the department, and Witten is the head of the department in the previous class, and this time it is the turn of Peverman.

Taking the Department of Mathematics of Princeton University as an example, the old director Witten and the current director of the Department of Mathematics are not very much in charge of daily administration, except for personnel appointments and dismissals and academic fund approvals, which involve people and money, and other miscellaneous daily trivial matters in the department are handed over to the secretary.

The secretary of the Department of Mathematics is Carl, who has served as the secretary for 18 years and has served six department heads, in a sense, Carl is the chief executive of the Department of Mathematics.

Shen Qi has seen Carl, this old man is equivalent to the general manager of the Inner Palace, and many things outside of academia are decided by Carl.

Because of the relatively independent system of politics and learning, Shen Qi did not complain that Professor Witten did not accept him as a student: "The past goes with it, and living in the present is the most important." ”

"Closer to home, Qi, your main focus is mathematical physics, but your achievements in number theory, functional analysis, and abstract algebra are even greater, and your last four papers are related to these three branches, two of which have been published in two of the four major mathematical journals. Director Peverman said.

Shen Qi said: "I am ashamed to say that after I studied at Princeton, I did not achieve any results in the main direction of attack, and the same is true in my first auxiliary major algebra geometry. Number theory is my second auxiliary major, and group theory, or abstract algebra, is my third auxiliary major. The 'Miller-Shen theorem' was an improvisation, and the non-Euclidean geometry tutorial was a teaching assistant in the department, and I had not previously included functional analysis and geometry in my formal scope of study. ”

My opinion is that after passing the doctoral defense, let Qi do one or two semesters of lecturer work, as for which course he teaches it no longer matters, anyway, it is a transition period. Witten offered his opinion.

Shen Qi agreed: "Choose one of the three for number theory, abstract algebra, and functional analysis, or choose two of the three, in fact, I would like to open a new course, which I will call "History of Number Theory" for the time being, but the biggest problem is that there is no textbook for this course, because my textbook is still being written, and the progress is ...... It's about 1% done, well, the rough outline is written. ”

"I think it's okay, the most interesting thing is a position that focuses on academic research, and maybe a new branch or even school of mathematics can be created by combining it. A professor or associate professor needs to apply again as a lecturer, and with two papers in the Annals of Mathematics and the Journal of the American Mathematical Society, Qi is eligible to apply as a professor or associate professor, of course, provided that you first get a PhD and become a full lecturer at Princeton. Peverman took a sip of coffee and looked at Shen Qi: "For extremely good young talents, Princeton sometimes relaxes the standards. ”

But no matter how much Princeton relaxes its standards, there is a bottom line.

PhDs are awarded for at least one year of Ph.D., and lecturers are allowed to apply for professors or associate professors for at least one semester, which is the bottom line for Princeton.

The two bigwigs, Peverman and Witten, seem to have helped Shen Qi plan his career path for the next few years, and Shen Qi has no objection, he has to stay in Princeton for a while, at least until the day when Ouye gets his doctorate.

As for Shen Qi's doctoral defense, in fact, it is a procedure, with two papers from the four major journals, at least he can apply for the position of associate professor of the University, and the doctoral defense is not a trivial matter.

In the casual chat over coffee, the two bigwigs decided on Shen Qi's future lecturer position, and if everything goes well, Shen Qi will officially take up his post this autumn.

Chatting and chatting, Shen Qi talked about his "Shen's Proximity Theorem": "Shen's Proximity Theorem in Barnach space, I submitted this paper to "Mathematical Inventions" on Christmas Eve, and it is currently under review, this is my latest paper, I know the rules, it doesn't matter if it passes the journal, it doesn't matter if it passes Princeton." ”

Witten asked, "What is the main conclusion of Shen's proximity theorem in Banach space?"

Shen Qi wrote on the blackboard:

H={x*∈X*：x*（x0）= x*（x0）=1}

……

Therefore, z*α(x0)=1→z*α(x0)=1→z*∈H,x*∉co^ω*(B(X*)/B(x0*))

Shen Qi explained: "From this, each ω* closed convex set of X* is an approximate tight Chebyshev set. I will tentatively name this conclusion 'Shen's Nearness Theorem', and the final name needs to be approved by the IMU. I can only write a core overview on the blackboard, and I can submit the full paper to Professor Witten and Director Feverman for review at any time. ”

"This proof of Qi is correct. At a glance, Witten, who is good at functional analysis and space theory, recognizes the "Shen's proximity theorem".

"Mathematical Inventions, that's so interesting, odd, you're going to have three Big Four journal papers, and you've done it in less than two years. Strange, what is your age this year?" asked Director Peverman.

Shen Qi: "22 years old. ”

Director Peverman nodded in appreciation: "Amazing. ”

Shen Qi and Witten drank coffee and didn't speak, they both knew that the most amazing thing was Director Peverman.

At the age of 22, Peverman had been promoted to full professor at the University of Chicago, at the age of 22 Witten was a Ph.D. student in Princeton's physics department, and at the age of 22, Shen Qi was a Ph.D. student in Princeton's mathematics department.

Peverman is a gifted child, and Witten and Shen Qi are late bloomers.

Wednesday coffee time, pretend to be B time, and the big winner in the end is Director Peverman.

Before the coffee break, Peverman asked, "By the way, strange, there will be an international academic conference and award ceremony at NASA in some time, and I don't know if you have heard of the Breakthrough Prize and New Horizons?"

"I've heard of it. "Shen Qi is a little surprised, isn't it another award?