I Just Want to Be a Quiet Top Student

Shen Qi drew a figure on the blackboard, consisting of a circle and many curved lines, it looked like a big octopus.

"From the point of view of modern differential geometry, the two-dimensional Riemannian geometry is the intrinsic differential geometry of Gaussian. Combined with the graphics on the blackboard, who can give me an explanation on the two-dimensional manifold in the space of constant curvature Ways to realize non-Euclidean geometry?" Shen Qi began to discuss professional non-Euclidean geometry knowledge with students.

"I figured it out. The Gaussian curvature K of the surface is a constant α. When α is greater than or equal to 0, this abstract surface can be defined on the entire (u, v) plane." Luca spoke first.

"Then what happens when α is less than 0?" Shen Qi asked.

"The domain of definition of this surface is u squared plus v squared less than negative 4/α." Ajie answered quickly.

"Luka and Jack's answers are perfect together." Shen Qi expressed his satisfaction. Luka and Ajie's performance has always been positive and their thinking is quick.

"I have a different view on this issue." Stephen, the son of an American farmer, expressed his views not to be outdone.

"In my opinion, non-Euclidean geometry is similar to calculus. There is more than one correct answer. I think this figure on the blackboard can be explained in this way..." John, the son of a British financial tycoon, expressed dissatisfaction.

The discussion atmosphere in the tutoring class was very lively.

Students made progress in discussions and learned from others.

After the tutorial class was over, Shen Qi asked Ajie, Luka, Stephen and John to stay.

"In this non-Euclidean geometry tutorial class I took, the four of you are the most outstanding." Shen Qi appreciates outstanding students, and students who can stand out in Princeton must have something special: "Tell me, except for non-Euclidean geometry Geometry, what other subjects are you good at?"

"Coordinate geometry, metric geometry, projective geometry." Luca is a geometry fan, he is crazy about all kinds of geometry.

"Actually, my mathematics is only at an amateur level. I'm better at dating girls. If I date girls, it's a course." Luca fiddled with her hair coquettishly.

"Luka, how is your relationship with your Alabama girl?" Shen Qi asked.

When it comes to picking up girls, no one is better than Italian men. Italian men have sculptural three-dimensional silhouettes. Apart from being handsome, another skill they have in picking up girls is their thick skin.

"I haven't dated an Alabama girl for a long time, and my current girlfriend is a Colorado girl." Luca said triumphantly.

"I've never dated a Colorado girl!" Stephen from Colorado was particularly annoyed. He envied and condemned: "Italian men have the characteristics of seeing one and falling in love with the other!"

"That's the end of the girls' topic, Stephen, what about you, what do you like?" Shen Qi asked Stephen.

"Compared to geometry, I prefer discrete mathematics, and I will not give up my efforts to become an IT engineer in Silicon Valley." Once the American boy admits his death, he really does not cry when he sees the coffin.

Discrete mathematics is widely used in computer science, and Stephen, the farmer's son, wanted to develop it in this direction.

"What about you, John?" Shen Qi continued to ask.

"Non-Euclidean geometry is a course for me, and I need to learn it for credits and graduation certificates. Game theory and financial mathematical analysis methods are a kind of career for me, the career of the rest of my life." John said He realized that sooner or later he would return to the UK to take over the family's financial services company, and his study at Princeton was very purposeful.

Finally, it was Ajie, the poorest in the family, who spoke: "I also like game theory, as well as probability theory, overall planning, and computational mathematics. I like practical courses."

Shen Qi: "No one is interested in number theory, or the history of mathematics?"

"Pure number problems are useless. Can you make money? No! The history of mathematics, leave it to history lovers to study." Ajie is very down-to-earth, he only loves practical subjects that can make money.

"Well, I hope you will get good grades in the upcoming final exam." Shen Qi announced the dissolution.

These four second-year students have their own characteristics.

Italians like girls, he has a high talent for geometry, picking up girls is his main business, geometry is a hobby.

The British are extremely purposeful in learning courses that can benefit his family, step by step, and have planned a lifetime career path since he was one year old.

The son of a Colorado farmer wants to enter the IT industry to fulfill his ambitions. In his opinion, farming and raising horses has no future. Silicon Valley is the core of the future development direction.

The son of a fruit shop owner in Chinatown wants to make a fortune in order to change the family's social status and quality of life.

Today's young people are either spending time and indulging in indulgence, or working hard to make money as CEO to gain both fame and fortune.

Young people who can calm down to study pure theory are becoming rarer and rarer. Even in Princeton, where academics are paramount, hedonism, pragmatism, and utilitarianism are gradually on the rise.

Learning mathematics is not difficult, what is difficult is to train young people.

"So, the older generation of scholars like Professor Muller and Professor Faltings are the real scholars. If Princeton continues to degenerate like this, it will be a game sooner or later." Shen Qi counted, thirty years later , all the academic masters of the older generation are gone, and Princeton is over.

In the past two decades, among the 20 Fields Medal winners, only one has been trained by Princeton himself. He is Terence Tao. Terence Tao's graduate and doctoral students are studying in the Department of Mathematics of Pudong University.

Younger Filipino award winners such as Okunkov and Lynden Strauss had no experience of studying in Princeton. After they became famous, they were poached to teach and do research in Princeton.

Therefore, under the surface of Princeton's prosperity, there are crises and hidden dangers.

Shen Qi had already discovered the crisis and hidden dangers in Wangzitun, he just didn't want to talk about it.

"Thirty years in Hedong, thirty years in Hexi, Wang Zitun, you should be alerted, now start from the baby, there is still time..."

Before the Christmas holiday, Shen Qi completed the proof of the "Muller-Shen approximation theorem".

Shen Qi showed the paper to Professor Muller for review: "From the above proof, I got xα*→x0*, then x0* is the focus of {xn*}∞n=1, so there exists {xn*}∞n=1 The sub-column {xnk*}∞k=1, so that every closed convex set of X* is an approximate compact Chebyshev set."

After looking at it, Professor Muller said: "Sure enough, the rigorous proof of this supplementary theorem cannot be obtained from the Hosdev topological approach. Qi, you have used the separation method, which is very creative and has a strong logical derivation ability."

There is a certain connection between the "Muller-Shen theorem" and the "Muller-Shen theorem" recognized by the IMU, and it is also independent.

The proof of the "Muller-Shen Proximity Theorem" was basically completed by Shen Qi alone.

Professor Muller, who did not contribute much, was embarrassed to put his surname on it. He suggested: "It is more appropriate to name the new theorem 'Shen's Proximity Theorem', because I did not participate in the proof work of this theorem."

Look, this is the ideological consciousness of the older generation of scientific research workers in Pudong University.

Shen Qi strongly suggested that Professor Muller's surname be added. The two of them cooperated so happily that they don't need to care about these small details.

Professor Muller insisted not to enter the pit. He believed that "Shen's Proximity Theorem" is the most reasonable way to name it.

Unable to hold back the old man from Germany, Shen Qi revised the paper and changed the "Muller-Shen's proximity theorem" to "Shen's proximity theorem".

The paper containing "Shen's Proximity Theorem" is titled "Analysis of the Problem of Closed Convex Sets in Banach Space", which is a companion paper to the "Muller-Shen Theorem" paper in Annals of Mathematics.

"Annual of Mathematics" only publishes two issues a year, one in May and one in November, so it is called "annual".

The next issue of "Annual of Mathematics" will not be until May next year, so Shen Qi submitted the paper "Analysis of the Problem of Closed Convex Sets in Banach Space" to "Mathematical Invention". "Mathematical Invention", whose editorial office is located in Germany, is one of the four major publications, with one issue every quarter.

Another year of Christmas holidays came, Shen Qi filled up his North American version of Malibu, and did a car body cleaning and beauty.

Zhou Yu'an set off before Ouye. He was already on the flight to New York's JFK Airport and was about to land.

Shen Qi started the car and went to New York to pick up the airport.