Li Mu smiled, then straightened his expression, 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 considered a beautiful but useless branch of mathematics. As a representative of personal heroism, number theory seemed to have become aloof at that time."
"But now, with the promulgation of the Langlands Programme, number theory no longer stands alone, but has begun to integrate with other branches, including algebraic geometry and group representation theory."
“From Gerd Faltings’s use of algebraic geometry methods to prove the Model conjecture, to Andrew Wiles’s proof of Fermat’s Last Theorem from the Zeng Mingguyama-Shimura conjecture, and now, Li Mu By combining K theory, modular form, and elliptic curves, Goldbach's conjecture was finally proven——"
"So, although number theory is still a representative of individual heroism in mathematics, it has also been integrated into collectivism."
"And what I mean by saying this is actually that I hope you can continue to diversify your thinking in the following courses."
"In the future, number theory needs to be applied in more fields."
"Even in the analysis of physics and mechanics, in the computational fields of biology and chemistry..."
"Then, 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 began to think about it.
Fibonacci sequence, are there infinitely many prime numbers?
The Fibonacci sequence, also called the golden section sequence, refers to a sequence of numbers [1, 1, 2, 3, 5, 8, 13...], starting from the third number, each item after that is equal to After the first two items.
The magic of this sequence is that it is even reflected in nature, such as the branches of trees, the petals of lilies, etc.
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 unavailable. After all, this is another issue related to quality.
"In the field of mathematics, we cannot do without prime numbers, so on this issue related to prime numbers, I will gradually introduce to you the basic thinking of number theory and some basic methods."
The students present also became interested and started the class with an unsolved mathematical problem. This kind of mathematics class was considered the first time for them.
In the past, their teachers could only mention the unsolved mathematical problems, but would not elaborate on them.
Therefore, raising interest brings concentration of attention.
For Li Mu, this is his purpose.
Interest is the best teacher, and in the process, concentration is also the most important.
Of course, facing a lot of math novices present, it was naturally impossible to show a lot of difficult methods right away, which meant that he had to use entry-level methods to explain such unsolved mathematical problems.
If it were the vast majority of other mathematics teachers, they would obviously refuse this kind of thing, because it is also a technical challenge for teachers.
But for Li Mu, this is not difficult.
So, his teaching began.
The students present followed his explanation and while understanding the difficulty of this problem, they also unknowingly absorbed the basic knowledge of number theory.
But at some point, several people came in from the back door of the classroom.
These people are all mathematics professors and teachers at Merton College, including Andrew Wiles and Lucas Richter.
They didn't come because this was Li Mu's class, but they came after hearing about what happened just now.
Seeing the classroom packed with students, several people couldn't help but sigh.
"As expected of this boy, so many students come to attend his class, he has the same demeanor as I did back then." Wiles said with a smile.
Richter did not refute his words, because Wiles really wasn't bragging in his words.
During the period after he proved Fermat's Last Theorem, there were almost as many students who came to attend his classes.
"Let's not talk about this kind of thing. Don't you think Li Mu's teaching method is very special?"
Richter said.
Wiles rubbed his chin and then nodded: "It's really special. He actually started from this issue and gave people the feeling of..."
"Show off your skills." Li Heter commented accurately.
Wiles was stunned for a moment, then nodded repeatedly: "Indeed, he is just showing off his skills."
Of course, the brilliance they are talking about is not the brilliance of mathematical ability, but the brilliance of teaching methods.
The dazzling skills of teaching methods refer to the kind of teaching methods that are technically difficult but also very effective.
Just like now, Li Mu started with an unsolved mathematical problem and first aroused the interest of these students.
Of course, under normal circumstances, when these students find that they cannot understand this problem, their interest immediately falls to the bottom.
But Li Mu could use some simple methods to help them understand.
In this way, the professors and teachers were all attracted by Li Mu's explanation. When he finally came to his senses, Richter suddenly said in surprise: "All the things he talked about can be written into a paper, right?"
"It seems...it's really okay."
After Wiles was silent for a moment, he couldn't help but say.
Is this teaching method a bit too extravagant...?
Of course, if they knew how extravagant Li Mu was when interviewing graduate students, they probably wouldn't be confused about Li Mu's teaching methods.
For Li Mu, this is not a luxury at all.
…
On the podium, Li Mu had actually noticed Wiles and the others a long time ago, but this did not interrupt his class.
While lecturing, he also gave full play to his multi-tasking ability and thought about what he said at the beginning.
Number theory, applications in other fields.
In addition, there is also the problem that he has been thinking about, which is the analysis of fluid mechanics.
There is Li's space to solve external problems, but it has been lacking another tool to solve the internal unity problem of fluids.
Just like he said before starting, he needs to think divergently. At this time, he is thinking divergently to think about the problem.
Number theory is helpful for 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 one is to derive the fluid equation from the Boltzmann equation.
Suddenly, Li Mu's mind suddenly calmed down.
He knows!
It’s Boltzmann’s equation!
The key puzzle piece was found by him!
However, the current Boltzmann equation is not abstract enough, and this puzzle piece still needs to be pruned.
He needed to make it more abstract and 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 a brief thought.
And his brief thought also brought the class to a brief halt.
The students present were all stunned.
They were listening so fascinatedly, why did they stop?
They even felt that under Li Mu's explanation, they would know which direction to take to prove whether the Fibonacci sequence has infinite prime numbers.
And the current pause is like the video suddenly starting to buffer at a critical moment, making them anxious.
However, the pause did not last long, and Li Mu's narration began again.
Although the students present were a little confused, they quickly forgot about the pause and continued to think along with Li Mu's explanation, returning to their interest in this number theory lesson.
They probably never knew that Li Mu's brief pause would leave a deep mark on the entire world of mathematics and classical physics.
…
(End of chapter)
