Ultimate Scholar

Li Mu smiled, then straightened his face, and continued: "Of course, I must also say that individual heroism cannot completely cover up the existence of collective heroism."

"The same goes for number theory."

"In the past, number theory was regarded as a beautiful but useless branch of mathematics, as a representative of individual heroism. At that time, number theory seemed to become lonely."

"But now, with the proposal of the Langlands program, number theory is no longer isolated, but has begun to integrate with other branches, and algebraic geometry, and group representation theory."

"From Gerd Faltings using the method of algebraic geometry to prove Model's conjecture, then to Andrew Wiles' completion of the proof of Fermat's last theorem from the Zeng Mingyashan-Shimura conjecture, and now, Li Mu By combining K-theory, modular forms, and elliptic curves, Goldbach's conjecture was finally proved—"

"So, although number theory is still a representative of individual heroism in the mathematical community, it has also been integrated into collectivism."

"And what I mean by saying this is actually to hope that you can continue to diverge your thinking in the next courses."

"The future number theory needs to be played in more fields."

"Even in the analysis of mechanics in physics, in the computational fields of biology and chemistry..."

"Then, next, I will start with a question."

Li Mu turned his head and wrote a question on the blackboard.

[In the Fibonacci sequence, are there infinitely many prime numbers? 】

Seeing this question, the students present all began to think about it.

Are there infinitely many prime numbers in the Fibonacci sequence?

The Fibonacci sequence, also known as the golden section sequence, refers to a sequence such as [1, 1, 2, 3, 5, 8, 13...], starting from the third number, and each item after that is equal to After the first two items.

The magic of this series of numbers lies in its magic, which is even reflected in nature, such as the branches of trees, the petals of lilies, and so on.

Of course, for mathematicians who study number theory, they don't care how magical this sequence is, they only care about how many prime numbers there are in this sequence.

This issue is not very hotly discussed in the mathematics community, but it is by no means unheard of. After all, this is another issue related to quality.

"In the field of mathematics, we cannot do without prime numbers, so on this question related to prime numbers, I will gradually introduce you to the basic thinking of number theory and some basic methods."

The students present also became interested, and started the class with an unsolved math problem. This kind of math class was the first time for them.

In the past, their teachers would only mention the unsolved math problems at most, but they would not explain these problems.

Therefore, raising interest brings concentration of attention.

And for Li Mu, this is also his goal.

Interest is the best teacher, and in the process, the concentration of attention is also the most important.

Of course, in the face of a large number of math rookies present, it is naturally impossible to show a lot of difficult methods, which means that he has to use entry-level methods to explain this kind of unsolved mathematical problems .

If you were the vast majority of other math teachers, you would obviously only say no to this kind of thing, because it is also a technical challenge for the teacher.

But for Li Mu, this is not difficult.

Thus, his teaching began.

The students present, following his narration, while understanding the difficulty of this problem, also unconsciously absorbed the basic knowledge of number theory.

Unknown at what time, how many people came in from the back door of the classroom.

These people are professors and teachers of mathematics at Merton College, among them are Andrew Wiles and Lucas Richter.

They didn't come here because it was Li Mu's class, but they came after hearing about what happened just now.

Seeing the crowded students in the classroom, several people couldn't help but sigh with emotion.

"As expected of this kid, so many students have come to listen to his class, and he has the same demeanor as I did back then." Wiles said with a smile.

Richter didn't refute his words, because Wiles really wasn't bragging.

In the period after he proved Fermat's last theorem, there were almost so many students who came to listen to his lectures. \b

"Let's not talk about this kind of thing, don't you think Li Mu's way of lecturing is very special?"

Richter said.

Wiles rubbed his chin, then nodded: "It's really special. He actually started with this question, giving people a feeling that he is..."

"Show off skills." Richter made a precise evaluation.

Wiles was taken aback, then nodded again and again: "Indeed, it's just showing off."

Of course, what they mean by showing off skills is not the show off of mathematical ability, but the show off of teaching methods.

The brilliance of teaching methods refers to the teaching methods that are technically difficult but also very effective.

Just like now, Li Mu started with an unsolved mathematical problem, and firstly filled the students' interest.

Normally, of course, when these students find themselves unable to understand the puzzle, their interest plummets immediately.

But Li Mu can use some simple methods to help them understand.

In this way, these professors and teachers were also attracted by Li Mu's explanation. When he finally came back to his senses, Richter suddenly said in surprise: "The things he said can be written into a paper, right?"

"It seems...it's really okay."

After a moment of silence, Wiles couldn't help but speak.

Isn't this way of teaching a bit too extravagant...?

Of course, if they knew how extravagant Li Mu was when interviewing graduate students, they probably wouldn't be puzzled by Li Mu's lecture method.

For Li Mu, this is not a luxury at all.

...

On the podium, Li Mu had already noticed Wiles and the others, but this did not interrupt his class.

During the lecture, he also gave full play to his ability to multitask, thinking about what he said at the beginning.

Number theory, with applications in other fields.

In addition, there is a problem that he has been thinking about, which is the analysis of fluid mechanics.

There is Li's space to solve the external problems, but he has been lacking another tool to solve the internal unity of the fluid.

As he said before the start, divergent thinking is needed. At this time, he is thinking about problems with divergent thinking.

Number theory is helpful to the study of statistical physics, and there is also a relationship between fluid mechanics and statistical physics.

Starting from statistical physics, deriving the direction of fluid mechanics is a niche direction, the most famous of which is deriving the fluid equation from the Boltzmann equation.

Suddenly, Li Mu's mind suddenly calmed down.

He knows!

It's the Boltzmann equation!

The key puzzle was found by him!

However, the current Boltzmann equation is not abstract enough, and this piece of the puzzle needs to be trimmed. \b

He needs to make it more abstract to summarize the different shapes inside the fluid.

In this way, he can solve the final problem of the NS equation more perfectly.

And this requires more divergent thinking.

Li Mu fell into short thoughts.

And his short thinking also caused the class to stop briefly.

The students present couldn't help but be taken aback.

They were fascinated by what they were listening to, why did they stop?

They even felt that under Li Mu's narration, they would know which direction to go to prove whether there are infinitely many prime numbers in the Fibonacci sequence.

And the current pause is like the video has reached a critical moment, and it suddenly starts buffering, making them anxious.

However, this pause was not too long, and Li Mu's narration resumed. \b

Although the students present were a little bit puzzled, they quickly forgot about this pause, and continued to think along with Li Mu's narration, returning to their interest in this number theory class.

They probably never knew that Li Mu's brief pause would leave a deep imprint on the entire mathematics and classical physics circles.

...