The Youthful Days That Were Slipping Away

Publishing a paper in the Annals of Mathematics, one of the top four international mathematics journals, is a cause for celebration.

It's a joyous occasion to name a new mathematical theorem after one's own surname.

People are in high spirits when they have good news, and Shen Qi, who is experiencing double happiness, has even started walking differently lately.

A few months ago, Shen Qi was looking for a paper published by Faltings in the 1980s, but he accidentally discovered the "Muller -Manning theorem" which was not recognized by the IMU.

Shen Qi's initial intention was to try something interesting, but he unexpectedly reaped great rewards.

"My left eyelid is twitching, good things are coming~" Shen Qi hummed a little tune as he strolled through the campus of Princeton University.

Thanksgiving is just around the corner, and after Thanksgiving, Christmas is just around the corner.

After Christmas, Ou Ye and Zhou Yu'an will be coming to the United States to pursue their graduate studies.

Professor Muller said that as long as Shen Qi persists in going to the third floor of the Mathematics Department building for coffee every Wednesday, he will definitely pass his doctoral dissertation defense based on the "Muller -Shen Qi" and the paper published in the Annals of Mathematics.

In other words, if Shen Qi keeps drinking coffee until next September, he will be able to get his PhD from Princeton.

The minimum time required to obtain a PhD from Princeton is one year; that is, it takes at least one year from the day you become a doctoral student to obtain your PhD. This is a Princeton regulation.

Shen Qi obeyed the rules. "I'm just getting into the swing of things as a doctoral student, and you're already forcing me to get a PhD? That's not appropriate."

Doctoral students are still considered students, so it's a combination of research and study.

Once Shen Qi passes his doctoral dissertation defense and receives his PhD, he will need to find a job.

Shen Qi's student days are coming to an end; there are only 10 months left.

Shen Qi cherishes his soon-to-be-gone student days. He hopes to do some fun things in the remaining 10 months of his student life to commemorate his wonderful youth that will eventually pass away.

"Wow, that's a brilliant paper." Professor Lyndon Strauss Elon into Shen Qi and started chatting with Shen Qi.

"Elon, when will the second volume of your 'Number Theory Methods' be published? I can't wait to read it." Shen Qi's popularity in the Mathematics Department was growing, and his status was gradually rising. He naturally addressed Fields Medal winner Lyndon Strauss as Elon, with warmth and enthusiasm, as if he were an old friend.

Princeton's professors teach both graduate and undergraduate students, so it's common to bump into a Fields Medal or Nobel Prize laureate in an undergraduate classroom or some corner of the Princeton University. Most Fields Medal and Nobel Prize laureates are approachable, though there are a few eccentric geniuses, of course.

Whether normal or eccentric, at Princeton, where academics come first, the most effective way to earn the respect and attention of professors, students, and even janitors and librarians is to achieve academic success.

As Lyndon Strauss and Shen Qi walked and talked, Linden Strauss said, "The writing of Volume II of 'Number Theory Methods' has only just begun. I'm trying to explain the real uses of number theory, which will take some time."

Number theory is both simple and complex in most people's minds; it is elegant but not very practical.

Lyndon Strauss dedicated himself to the study of number theory from an applied perspective and made outstanding contributions.

The "Lyndon Strauss formula" explains the measure rigidity of ergodic theory and its application in number theory, for which Lyndon Strauss was awarded the Fields Medal in 2010.

The "Naming Club" is not an actual organization, but it exists in the consciousness of many scholars at Princeton University.

Theorems, formulas, conjectures, theories, systems, equations... Among the living giants of the Princeton Mathematics Department, the highest record for naming is 12, held by John Milnor, who has just retired to enjoy his later years in Europe.

The record in the History of Mathematics is held by Gauss, who has named as many as 110 theorems and formulas Gauss himself, including some physical formulas.

Shen Qi became a member of the "naming club" because of the "Muller -Shen theorem," and he became increasingly familiar with the top professors in the Mathematics Department.

"Actually, I also want to organize my research experience in number theory and talk about my shallow understanding of number theory," Shen Qi said.

"Why not, Qi? You're the one who proved the Wash Conjecture." Lyndon Strauss encouraged Shen Qi to publish an academic monograph, adding, "And you won an IMO gold medal."

"Elon, you're also following the IMO?" Shen Qi was a little surprised. A hero doesn't dwell on past glories; it's been more than four years, why bring that up again?

"I won a bronze medal representing Israel at the 1988 IMO," Lyndon Strauss revealed a secret.

"Bronze medal..." Shen Qi was very surprised. You only got a bronze medal?

"The bronze medal from 1988 is quite valuable, equivalent to a gold medal in the 21st century," Shen Qi said.

"Perhaps... I look forward to your monograph, Qi." Lyndon Strauss walked to the Spearman Hall and went inside. He had a number theory class for undergraduates today.

Shen Qi found a second interesting thing to do: publish an academic monograph specifically exploring number theory.

Publishing an academic monograph on number theory is a major project, not something that can be accomplished overnight. Shen Qi began to conceive of the idea and collect materials.

There are already too many academic monographs and textbooks related to number theory. Shen Qi doesn't want to simply write a monograph on number theory theory, as that's not interesting and even a bit boring.

"The History of Number Theory? Yes, I can start from that angle and write an interesting popular science book on number theory."

The history of number theory spans nearly two thousand years, from Diophantus to Goldbach, Fermat, Mersenne, and Riemann, and then to modern thinkers like Hardy, Ramanujan, Selberg, Hua Luogeng, and Chen Jingrun, as well as those who came to the field later, such as Wiles and Faltings... There is so much to write about.

"This popular science monograph on number theory should consist of 70% on the history of number theory and anecdotes about number theorists, and 30% on theoretical knowledge," Shen Qi set the tone for the yet-to-be-drafted "History of Number Theory."

Shen Qi's long-term ambition is to write an epic History of Mathematics, which may take ten years or even longer.

Let's start with a section from "The History of Mathematics" to test the waters, practice, and eventually write a "History of Number Theory".

Whether it's History of Mathematics or History of Number Theory, the author must be a mathematician, not a writer.

Of course, basic writing skills are essential; mathematicians must at least be able to write fluent sentences and convey meaning with clear words.

"Therefore, the proof of the 'Muller -Schen's theorem' needs to be accelerated. After completing this supplementary theorem, I will concentrate on writing <The History of Number Theory>."

While proving the "Muller -Shen approximation theorem", Shen Qi continued to lead his tutoring class, tutoring his twelve boys.

In the tutoring class, Shen Qi maintained his consistent tutoring style, starting with a question related to the History of Mathematics before discussing mathematical knowledge.

Shen Qi wrote some symbols on the blackboard: f(x), Σ, e, i

Shen Qi posed the question, "Who invented these symbols? I hope you think carefully before answering. If you answer incorrectly, I will be very angry and will not hesitate to give you a C."

f(x) represents a function, Σ represents summation, e is the base of the natural logarithm, and i represents the imaginary unit.

Mathematics Department students deal with these symbols every day, and the boys answered in unison, "Leibniz!"

"Hey, Qi, this question is too easy."

"It's impossible for anyone not to know that Leibniz invented functions and the notation for summation."

"Qi, give me some challenging questions. After all, you're the one who proved the 'Muller -Shen Theorem'."

"You have published papers in the Annals of Mathematics and the Journal of the American Mathematical Society."

The boys protested, saying that the History of Mathematics questions Shen Qi gave today were too easy, and they demanded that the difficulty be increased.