Princeton isn't just one Fields Medal winner.

It's not uncommon for students to be taught by Fields Medal winners in the classroom.

The classroom of the Da Fanfei Award winner was basically full, and Shen Qi's functional analysis class was no exception.

Graduate students in the Princeton Department of Mathematics choose a supervisor and follow the supervisor to delve into one or two main directions.

At the same time, graduate students are required to complete the necessary credits.

For example, Yu Lei, he chose Shen Qi as his supervisor, and his graduate research direction is function theory, including real variable functions, complex variable functions and other main research content.

In addition to real variable functions and complex variable functions, Yu Lei also has to study general courses such as functional analysis, Lie groups, Lie algebra, partial differential equations, etc.

Of course, the main direction of the course should allocate a little more energy, and the other courses should allocate the learning time and dedication appropriately according to the individual's situation.

There is an intersection between functional analysis and function theory and algebra theory, and function theory and algebra theory are the main research directions of Yu Lei and Ralph.

Not only Yu Lei and Ralph came, but even Zhou Yu'an, who was about to study for a doctorate, also came.

Zhou Yu'an and Yu Lei traveled together, and they both lived in the graduate student dormitory.

The two of them stepped on the spot, and arrived at the classroom when there was still 1 minute before class.

The seats were already full, Ralph arrived 10 minutes early, and some graduate students arrived earlier than Ralph.

"Professor Shen only takes one class a month, and he is really popular. Zhou Yu'an can only sit on the ground, his main direction is differential geometry + partial differential equations, he mainly comes to Shen Qi, and he has obtained the credits of functional analysis last semester.

"Who says it's not, Xiao Qi Ge is the new winner of the Philippine Award, and he is in full swing. Yu Lei, who is also sitting on the ground, is proud, the tutor is strong, the student is strong, the tutor is the big man of the Philippine Award, and the students follow the light.

At this time, a curly-haired boy in the seat next to him gave up his position and said to Zhou Yu'an, "Zhou, you sit here." ”

"Thank you, Rachel, I'll just sit on the ground. Zhou Yu'an politely declined the offer of the curly-haired boy, he is well-known in the group of graduate students in the Department of Mathematics, he is Shen Qi's undergraduate classmate, he is doing research with Professor Figari, and is about to enter the doctoral stage.

This is Zhou Yu'an's third semester in the graduate school of the Department of Mathematics of the University of General California, and he has proved himself with his grades and has been recognized by his classmates, and some students have taken the initiative to give him up their seats.

"Brother Xiaoyu, amazing, you have made a name, you are the next little Brother Qi. Yu Lei saw it in his eyes, his chasing target was alive in front of him, Zhou Yu'an.

At this moment came a girl with a half-breed face, who hurriedly trotted all the way, math book in hand.

"Not bad for a second, just right. The girl stepped on the point more accurately, and she smiled at Shen Qi.

Shen Qi made a gesture to please take a seat, he knew this girl, the first beauty in the Department of Mathematics of the University of Pupu, she was enrolled in the Graduate School of the Department of Mathematics of the University at the same time as Yu Lei and Ralph in January this year.

Seating can only be done on the floor, and seats with chairs are full.

But the treatment of the beauties is different, and some boys give up their seats to this mixed-race girl.

The mixed-race girl refused to give up her seat to several boys, she sat directly on the ground and sat next to Yu Lei: "Hey, Yu, do you have any extra pens?"

"Yes, Heidi, happy to help you. Yu Lei handed the mixed-race girl a pen and three pieces of white paper. He used to use his laptop to record the highlights of his teacher's lectures, and he also brought a pen and paper in case he needed it.

"Thank you. The mixed-race girl smiled, she had a good impression of the good-looking Yu Lei.

Every move in the classroom, Shen Qi, who was secretly observing, saw all in his eyes, and he focused on Zhou Yu'an, Yu Lei, and Ralph.

Zhou Yu'an won the respect of his classmates with the highest academic level among his contemporaries.

Yu Lei, who has just entered school, has a handsome face, he is very popular with girls, and he is good at dealing with various types of girls.

Ralph, a native of the United States, is a bit introverted, he is very hardworking and hardworking, and he doesn't have many friends.

Shen Qi began to give lectures, and in this edition of the textbook of functional analysis, the Müller-Shen theorem on Banach space and the Shen proximity theorem were added.

Counting Walsh's theorem and Riemann's theorem, Shen Qi's name appears in two mathematics textbooks in Princeton, functional analysis and number theory.

The atmosphere in the class was lively, and the students asked a number of questions, some of which were whimsical and bizarre.

If you can let the Philippine award boss hang the blackboard, it is also a special psychological satisfaction.

"Hanging the blackboard" refers to the teacher's inability to answer students' questions and make effective answers or proofs.

Shen Qi hung up the blackboard once, when he was just a doctoral student, and he led a tutorial class, and an Arab undergraduate student asked Shen Qi how to prove the Riemann hypothesis. At that time, Shen Qi was speechless.

Riemann's conjecture was eventually proved by Shen Qi, and he never hung up the blackboard again.

"So, are you still satisfied with my answer to Banach Space, Yu Lei?" asked Shen Qi in English.

Yu Lei spoke actively in class and took the initiative to perform, and he just raised a question about the Banach space.

Shen Qi answered Yu Lei's question perfectly, and Yu Lei was very satisfied and benefited a lot.

"Yu Lei, your question is very routine and not very technical, I can answer you. Zhou Yu'an spoke Chinese and muttered quietly.

"Brother Xiaoyu, don't hit me like this, my glass heart can't bear it. Yu Lei didn't look like he was hit at all, after all, he had only been in Puda for a few months, and he was still in the learning and growth stage.

Shen Qi looked around the audience and asked, "Do you still have any questions?" ”

The mixed-race girl raised her hand: "Professor Shen, I have a doubt?"

"Speak your mind, Heidi. Shen Qi fulfilled his duties, preaching, teaching, and solving doubts.

Heidi, with delicate features, fair skin but delicate pores, should have some Asian ancestry, she said: "We all know that if one of the linear or orthogonal dimensions of Hilbert space H is infinite, then Hilbert space H must be finite-dimensional Euclidean space Rn." Conversely, if the group of maximally linear independent vectors in a finite n-dimensional Euclidean space can be the same as the maximal orthogonal basis, how can we explain that the linear dimension of the Hilbert space is equal to the orthogonal dimension and is both finite n-dimensional? Professor Shen, can you answer my doubts?

Heidi's tongue-twister-like question made the male students in the classroom curious, and they entered the same thinking channel as Heidi, waiting for Shen Qi's answer.

Yu Lei was shocked in his heart, this girl who looks like a goddess is so powerful! Princeton is really talented!

On stage, Shen Qi slapped three times in a row, and he said in a loud voice: "Heidi, our Heidi, Heidi of Princeton! Hey, Heidi, you should audition for Hollywood, I can guarantee that Heidi Lamarr's math score is definitely not as good as yours." ”

Heidi smiled and said, "Why not?"

Wow.

The boys in the classroom were screaming excitedly, most of them had heard of the legend of Hedy Lamarr, and even Hedy Lamarr was the goddess of their dreams at night.

Hedy Lamarr was once a Hollywood A-list female star, she was beautiful and captivating, and she was as famous as her contemporaries Vivien Leigh and Ingrid Bergman.

Beauty alone does not become the object of fantasy for Princeton boys.

Heidi Lamarr is a super-student, she majored in applied mathematics and communication engineering in college, she is an inventor, and she invented frequency hopping technology, which is considered the origin of CDMA.

"The Mother of CDMA" and "Mother of Spread Spectrum" Heidi Lamarr's side job is acting in movies, but she accidentally became a popular actress in Hollywood.

In Shen Qi's functional analysis class, a mixed-race girl with the same first-name as Heidi Lamarr asks a question about Hilbert's space, which is very in-depth.

Facing a female student who attaches equal importance to appearance and wisdom, of course Shen Qi can't hang the blackboard, he smiled and began to solve his doubts.