Could Another Award Be Coming?
"If we take postgraduate courses into account, these seven major branches contain more than 80 sub-courses in total, with Functional Analysis alone having 11 sub-courses."
"Of course, undergraduate Mathematics Department students only need to learn the most basic Functional Analysis theories such as linear operator theory and variational methods. Advanced courses such as Banach space and topological linear spaces are the learning tasks for graduate students," said Witten, an expert in Functional Analysis, who said that physical problems cannot be solved without the mathematical processing methods of Functional Analysis.
"That's strange. When you entered Princeton's graduate school, which area of study did you initially choose?" Witten asked.
"My chosen field of study is Mathematical Physics. Dear Professor Witten, you were the first advisor I applied to," Shen Qi revealed a secret.
"Charles, is there such a thing? How come I didn't know?" Witten looked at Director Feierman with suspicion.
"Hey, Edward, please, don't look at me like that! You yourself said a few years ago when you were the department head that you wouldn't supervise any graduate students anymore." Professor Feierman, who won the Fields Medal at the age of 29, was too smart to take the blame, and his attempt to deflect responsibility was both reasonable and timely.
"Oh, really? Maybe I forgot." Witten looked at Shen Qi with regret. He would never have the chance to be Shen Qi's mentor again, because Shen Qi would be defending his doctoral dissertation in a few months.
"Carl handles routine matters like admissions for the Mathematics Department. Edward, you were the department head, so you know the admissions process well. Carl was just following your instructions, so you can't blame him," Director Feierman explained.
"I understand." Witten nodded; he was on par with Feierman in the Mathematics Department.
The head of the Mathematics Department at Princeton University is replaced every three years, with top experts taking turns in the position. There is no extra income or subsidy for the head of the department; it is purely a service to the people.
John Milnor, a super-elite F+W+A professor who just retired, served as department head; Andrew Wiles, who has returned to the UK, also served as department head; Witten was the previous department head; and this time it's Feierman's turn.
At Princeton, the top leaders at all levels mainly focus on academics. For example, in Princeton University Mathematics Department, former chair Witten and current chair Feierman do not manage daily administration much. Apart from major matters involving people and money, such as personnel appointments and the approval of academic funding, all other miscellaneous daily affairs within the department are handled by the chief secretary.
The chief secretary of the Mathematics Department was Karl, who served in that position for eighteen years, serving six different department heads. In a sense, Karl was the chief administrator of the Mathematics Department.
Shen Qi had met Karl before. This old man was like the chief steward; Karl made the decisions on many things outside of academics.
Because of the relatively independent system between politics and academia, Shen Qi didn't complain that Professor Witten hadn't taken him as a student, "Let bygones be bygones, living in the present is the most important thing."
"Getting back to the point, Qi, your main research area is Mathematical Physics, but you have achieved even greater success in number theory, Functional Analysis, and Abstract Algebra. Your four most recent papers are related to these three branches, with two of them published in two of the four major mathematics journals," Director Feierman said.
Shen Qi said, "To my shame, after I enrolled at Princeton, I didn't achieve any results in my major field, and the same was true for my first minor, algebraic Algebraic Geometry. Number theory was my second minor, and Group Theory, or rather Abstract Algebra, was my third minor. The 'Muller -Shen theorem' was an impromptu project, Non-Euclidean Geometry tutorial was a teaching assistant assignment arranged by the department. I hadn't included Functional Analysis and geometry in my formal research scope before."
"Qi's comprehensive yet professional academic characteristics should no longer be subject to the formulaic settings of main focus and auxiliary roles. My suggestion is that after passing the doctoral defense, Qi should work as a lecturer for one or two semesters. As for which course he teaches, it is no longer important, since it is just a transition period." Witten put forward his opinion.
Shen Qi agreed, "Choose one from number theory, Abstract Algebra, and Functional Analysis, or two. Actually, I really want to start a new course, which I'll tentatively call <History of Number Theory>, but the biggest problem is that there's no textbook for it, because my textbook is still being written. As for the progress... I've probably completed about 1%, um, the rough outline is done."
"I think there's no problem. The most suitable position for Qi would be one focused on academic research. A comprehensive understanding might even lead to the creation of a new branch or school of thought in mathematics. For a professorship or Associate Professor, Qi would need to apply again as a lecturer. With two papers published in the * Annals of Mathematics * and the * Journal of the American Mathematical Society *, Qi would be qualified for a professorship or Associate Professor. Of course, the prerequisite is that you must first obtain a PhD and become a full-time lecturer at Princeton." Feierman took a sip of coffee and looked at Shen Qi: "Princeton sometimes relaxes its standards for exceptionally talented young people."
But no matter how much Princeton relaxes its standards, there is still a bottom line.
Princeton requires students to complete at least one year of doctoral study before receiving a PhD, and lecturers must serve at least one semester before being eligible to apply for professorships or Associate Professor. This is Princeton's bottom line.
Feierman and Witten, the two bigwigs, seemed to have already planned out Shen Qi's career path for the next few years. Shen Qi had no objections; he would have to stay at Princeton for a while, at least until Ou Ye received his doctorate.
As for Shen Qi's doctoral defense, it was really just a formality. With two papers published in Top Four Journals, he could at least get a position as Associate Professor at Princeton University. A mere doctoral defense was nothing to him.
During their casual coffee conversation, the two bigwigs decided on Shen Qi's future lecturer position. If all goes well, Shen Qi will officially start working this fall.
As they chatted, Shen Qi brought up his "Shen Proximity Theorem": "I submitted my paper on 'Shen Proximity Theorem' in Banach space to <Inventiones Mathematicae> before Christmas. It's currently under review. This is my latest paper. I know the rules: it doesn't count until Princeton approves it."
Witten asked, "What are the main conclusions of the 'Shen 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, "Therefore, it is concluded that every ω* closed convex set of X* is an approximate compact Chebyshev set. I will tentatively name this conclusion 'Shen Proximity Theorem,' but the final name needs to be approved by IMU. I can only write the core summary on the blackboard; I can submit the full paper to Professor Witten and Director Feierman for review at any time."
"This proof is indeed correct." After a quick glance, Witten, an expert in Functional Analysis and space theory, acknowledged "Shen Proximity Theorem."
"<Inventiones Mathematicae>, is that right? That's fascinating, Qi. You'll have your third paper in Top Four Journals, and you've accomplished all of this in less than two years. Qi, how old are you this year?" Director Feierman asked.
Shen Qi: "22 years old."
Director Feierman nodded in approval. "Excellent."
Shen Qi and Witten drank coffee in silence, both knowing that the most remarkable person was Director Feierman.
At 22, Feierman had already been promoted to full professor at the University of Chicago; at 22, Witten was a doctoral student in the Department of the Physics Department at Princeton University; and at 22, Shen Qi was a doctoral student in the Princeton Mathematics Department.
Feierman was a child prodigy, while Witten and Shen Qi were late bloomers.
Wednesday coffee time, time to show off, and the ultimate winner in the end was Director Feierman.
Before coffee time ended, Feierman asked, "By the way, Qi, there's an international academic conference and awards ceremony at NASA in a while, the Breakthrough Prize and New Horizons Prize, have you heard of them?"
"I've heard of it." Shen Qi was pleasantly surprised. Could it be another prize?