For Lu Zhou, taking classes with undergraduates can be regarded as a review of knowledge points.

Normally, these things would have been obvious to him, and they would have been largely unconsidered. It is only at this time that he can temporarily put aside the research itself and think about why the obvious things are obvious.

“…… As many people know, the Riemann conjecture is one of the most important and difficult conjectures in analytic number theory, and it is a hypothesis about the zero distribution of the Riemann zeta function. But few people know why the Riemann hypothesis was proposed. ”

"In fact, before the Riemann conjecture, there was a much larger proposition that has been studied by countless scholars for centuries, that is, the law of distribution of prime numbers."

As he spoke, Lu Zhou wrote a few numbers on the blackboard, looked back at the students in the classroom and continued.

"Through the most basic arithmetic theorem, even junior high school students know that each positive integer can be expressed as the product of prime factors, and if the order of the prime factors is not considered, then this representation is unique, so prime numbers have become the basic elements of positive integers."

However, the distribution of prime numbers is not as simple as its definition. It can even be said that one of the most basic tasks of the entire analytic number theory discipline is to study the distribution law of prime numbers. ”

Watching the students in the classroom gradually enter the state, Lu Zhou knew that he was almost halfway successful in this class.

Although the Riemann conjecture is a very complex problem, it is not as difficult to understand it as people think, and the real difficulty is how to solve it......

After a pause, Lu Zhou continued.

"In analytic number theory, the function π (x) is usually studied and used to represent the number of prime numbers that do not exceed x. The study of the distribution law of prime numbers is the basic task of analytic number theory, and the study of the behavior of π (x) is the central problem of analytic number theory. ”

"As for the problem of π (x), both Gauss and Legendre did a lot of numerical calculations, and conjectured that when x tends to infinity, it π (x)~x/lnx, and this conjecture was later proved to be the prime number theorem as we know it."

"Euclid's use of the elementary method to prove that there are infinitely many primes, and Euler's introduction of a product formula, these pioneers provided the possibility of analyzing and studying the problem of prime numbers, but until the 50s of the 19th century, people did not find a suitable way to prove Gauss's conjecture, until a German mathematician, published a paper entitled "On the number of primes not exceeding a given value", which opened a new way for the study of π (x)."

"Many people may have guessed who this big bull is, yes, he is what I want to talk about Riemann, and the Riemann zeta function he introduced in this paper will influence the next century and a half."

As he spoke, Lu Zhou turned to face the blackboard and wrote a line of equations on the blackboard.

【ζ(s)=Σ1/n^s】

Glancing around the silent classroom, Lu Zhou continued.

"That's it...... Doesn't that seem difficult, does it? ”

Students: "......"

MMP！

Where is it not difficult?!

In his paper, Riemann further conjectures the function he proposed, arguing that all the non-obvious zeros of ζ(s) are on a critical line. As it turned out, his vision was indeed quite far-sighted, and all the non-obvious zeros that had been obtained after extensive calculations were on a critical straight line. Unfortunately, we know that it is most likely right, but there is no way to prove that it is true. ”

"As a result, we can often get a very beautiful result with the Riemann hypothesis, but if we can't prove that the Riemann hypothesis is true, we can't prove that our result is correct."

"The reverse is also true, if we can prove that the Riemann hypothesis is correct, then thousands of mathematical conjectures that assume that the Riemann hypothesis is true will be promoted to theorems!"

"If anyone can prove the Riemann hypothesis, he will undoubtedly become the greatest mathematician of the century...... I can say this responsibly, even if the century has only just begun. ”

"Professor," at this time, a student couldn't help but raise his hand, and after getting a nod from Lu Zhou, he stood up and asked excitedly, "What if you can prove the Riemann conjecture?" ”

"This is not easy to compare, after all, my achievements are not only in the field of mathematics," looking at the student who asked the question, Lu Zhou smiled and gave an uncertain statement, "But if someone can really prove this conjecture, then his achievements in the field of mathematics will undoubtedly stand at the top of this era." ”

Next, Lu Zhou continued to talk about some research progress on the Riemann conjecture and some of its equivalent forms. Although it was all boring stuff, perhaps because of the change in the way the lecture was conducted, the students were obviously listening much more seriously than in the previous lesson.

Satisfied that he had gradually regained some of his form, Lu Zhou nodded proudly in his heart.

Time passed minute by minute, and soon it was time for class to end.

Lu Zhou glanced at the wall clock on the wall, and saw that the time was almost up, so he threw the chalk in his hand on the multimedia lectern.

"That's all for this lesson, and I just happened to have some new ideas...... Well, get out of class. ”

The classroom resounded with the sound of lala packing up the textbooks, Lu Zhou tucked the lesson plan under his elbow, nodded to the departing students who watched him leave, and then turned and walked outside the classroom.

Walking outside the classroom, Lu Zhou was about to go back to the office to record the inspiration generated during the class just now, when he was suddenly stopped by Dean Qin, who came out of nowhere.

"A very good number theory lesson!" Greeting him with a smile on his face, Dean Qin said in an emotional tone, "Even if I finish listening, I will benefit a lot." ”

Lu Zhou smiled embarrassedly and said.

"It's over. I'm ashamed to say that I haven't taught undergraduate students in a while. ”

Dean Qin said with understanding: "Everything has a sequence, it is related to the interests of the country, and of course your research is more important than teaching students. Speaking of which, have you been busy lately? ”

Lu Zhou: "Isn't it very busy, what's wrong?" ”

"That's the case, there's one thing I want to ask you about," Dean Qin coughed lightly and said, "Have you heard of the Mathematics Olympiad?" ”

Lu Zhou: "I've heard of it, but I've heard of it, is there any problem?" ”

Of course he had heard of the IMO competition, although he had not had the opportunity to participate in it.

Every year, those who win the gold medal in the IMO competition are like immortals.

For example, Schultz, whom he knew, was called by Faltins as one of the three young scholars in the world who had the best chance of surpassing him, and who had won three IMO gold medals in a row.

As for when he was asked why he signed up for two more sessions after winning the gold medal, according to him, it was because he thought it was fun......

Dean Qin smiled and said, "That's the case, didn't you hold the National High School Mathematics League last month?" The top teams from each province have already been selected, and by the national finals of the winter camp in January next year, about 30 students will be selected to enter the national training team. It's November now, and it's almost time to prepare for the exam. ”

Lu Zhou was slightly stunned, and then said with a smile: "...... You're not looking for me to be the proposer, are you? ”

Dean Qin: "This matter is not my responsibility, it can be regarded as an invitation from our Huaguo Mathematical Society, they hope that you will be the proposer of the final question." ”

Lu Zhou: "Is it appropriate for me to be the proposer?" ”

Dean Qin smiled and said: "What's wrong with this, the last question in the national finals in previous years was also an academician, you are not only an academician, but also a Fields Medal winner, if you are not suitable, then who else can be suitable?" ”

Lu Zhou: "That's okay, it's just the last question." ”

"Well, I'll leave this matter to you," suddenly remembering something, Dean Qin hurriedly added, "By the way, don't make it too difficult, if no one can do it, it won't make sense." ”

"Don't worry, I won't be too difficult," Lu Zhou said, pulling out a piece of scratch paper from the lesson plan sandwiched under his elbow, tearing off a corner and writing on it.

Seeing Lu Zhou take out the scratch paper and write, Dean Qin was slightly stunned, and then cried and laughed.

"You're not planning to do it here, are you?"

Lu Zhou: "Otherwise? ”

Dean Qin said: "This is the national finals, so you have to think about it." ”

"I've already thought about it," wrote the topic on the paper, Lu Zhou folded the scratch paper, and gently stuffed it into Dean Qin's hand, "Transfer it to the Huaguo Mathematical Society for me, this question should be fine." ”

Stunned as he looked at the back of Lu Zhou leaving, Dean Qin moved his gaze to the scratch paper in his hand and silently opened it and looked at it.

“…… Riemann zeta function? ”

Muttering something in his mouth, Dean Qin touched his chin and muttered to himself in thought.

"Can a student do this kind of question?"

However, at this moment, he suddenly seemed to think of something, and his eyes lit up slightly.

"Shhh...... Wait, this question seems to be interesting......"

Glancing mysteriously left and right, Dean Qin carefully folded the note and stuffed it into his pocket, then turned around and walked quickly in the direction of the office.