"Lao Wang, wouldn't it be a bit too hasty to let someone who is only eighteen years old come to class?" At this time, in Professor Wang's office, two people were doing opposite each other, and a professor who looked a little old said to Professor Wang a little worriedly. He is also a member of the Chinese Academy of Sciences, and is currently a professor in the Department of Mathematics at the University of Science and Technology of China. Of course, he is also one of the course hosts of this year's Hua Luogeng class, alongside Professor Wang.

"I don't think that a person who can publish an article in the Annals of Mathematics will not be qualified to teach a group of people who are at the graduate level, Brother Qiao, wait in peace!" Professor Wang seemed very calm, but his words were full of trust in Junxin.

"I'm not denying his achievements in mathematics, but I'm worried that he's too young and may have profound attainments in a certain area, but even if he has a deep research foundation on top of that, it is unknown whether he can translate it into something that students can accept."

"Brother Qiao, if you had communicated with him, you wouldn't have said that!" Professor Wang put down the teacup in his hand and said, "His research in mathematics is very deep, even more profound than you and I imagined. In the course of my conversation with him, I realized that his level had reached a very high level. As far as my research on analytic number theory is concerned, many of his ideas and research results are very inspiring to me. ”

"Maybe his lectures won't be so vivid, but not all masters are so vivid, but as long as one of so many people can keep up with his thinking, it's a harvest. You and I both know that mathematics is about talent, and who can achieve achievements in mathematics is not a genius? Didn't our original idea of holding Hua Luogeng's cram school be to pick out the one who was the most talented in mathematics? If all of them are taken care of, it will be mediocre, and in the end, the best result will be nothing more than annihilation among everyone. ”

"Well, I'll admit you convinced me!" Academician Qiao thought for a long time, sighed and nodded in acknowledgment of Professor Wang's words.

"Actually, there's no way around it!" Professor Wang sighed and said, "The most important research directions in China are concentrated in analytic number theory, ordinary differential equations, partial differential equations, etc., there is too much applied knowledge, but there are still too few studies on algebraic geometry, projective geometry, topology, etc., but since Mr. Grotendieck integrated algebraic geometry, the importance of this sub-discipline has become more and more important, and the connection with other disciplines has become deeper and deeper, and the understanding of this discipline in China is still too backward." Otherwise, I wouldn't have been able to really hire an eighteen-year-old freshman. Even if this student has already made world-class achievements, he has even become a researcher at Mizuki's Institute of Mathematics. ”

"But then again, if he wasn't a researcher at the Institute of Mathematics at Mizuki University, I wouldn't have really invited him over."

Professor Qiao nodded in agreement and said, "I didn't expect Mizuki University to have such courage to promote a first-year student as a researcher, which is equivalent to a professor level in the research system of our Chinese Academy of Sciences." ”

Professor Wang said disapprovingly: "Hasn't Mizuki always been like this? This is also a tradition of their mathematics department. Didn't Mizuki University promote my teacher, that is, Dean Hua, to the position of teaching assistant like this? Speaking of which, although Mizuki is a little more rigid, once there is the kind of person they think is worth breaking with tradition and supporting, Mizuki's courage is not something that other people can imagine. Isn't that the little guy like that? ”

Professor Qiao nodded and agreed: "It's no wonder that the Department of Mathematics of Mizuki University has just been established, and it can achieve such results. After all, the heritage is still there! ”

Junxin continued his explanation in the classroom, unaware that around him, the two members of the Chinese Academy of Sciences had a back-and-forth discussion. At this time, he was explaining the number theory of one of the foundations of his algebraic geometry.

“…… The above knowledge has been more or less understood through books or other aspects. However, what we have talked about above is the content of elementary number theory, and in the afternoon class we will start the content of the algebraic geometry part of advanced number theory, as for the textbook, there is no textbook for the time being, because these things are all sorted out by myself, and it is not a perfect system for the time being. ”

"Teacher?" A classmate suddenly raised his hand and asked.

"This classmate, please?"

"And when will we get the textbook?"

"When I'm done with my lesson, you'll probably be able to get my handouts!" Junxin is a little unsure.

"Huh? So what should we do about the exam? The student asked, surprised and worried.

Jun Xin smiled and said, "When I came, Professor Wang didn't mention to me that you would have an exam, so I didn't prepare in advance!" But since I mentioned it, I'll do a little bit about it! ”

"There are two ways to do this in this class. The first method, I will assign you a question in the first class of each week, if anyone solves this topic, I will give you full marks for this course, of course, I have been teaching here for about a month, and there is a period of holiday during the Spring Festival, which is a total of five weeks, so it adds up to a total of five questions, and any one of the questions can be solved before the exam of this subject; The second way is to take the final exam. ”

"How to choose, and it depends on your own choice, I will not interfere!"

Junxin's method comes from the way William Timothy Gowers, the famous mathematician who won the Fields Medal in '98 and studied mathematics at Princeton University. Professor Gowers uses this method of teaching in his classrooms.

However, Gools called himself an evil dragon, and jokingly called the person who could solve the problem he left behind a dragon slayer warrior, and naturally the topic left behind was very difficult. And often there is only one person in a mathematics department who can spend months solving a problem he left behind.

You must know that among the two mathematics centers in the world, the Institute for Advanced Study in Princeton is one of them, and naturally the mathematics department of Princeton University is also the top existence in the world, and the students in it are naturally the same. It is also often difficult for them to solve a problem left by Gowers, which shows the difficulty of this problem.

Junxin was taught by Professor Gowers and liked this kind of education method very much, because the people who can solve problems are all qualified to become the world's top mathematicians, and finding such talents to educate is one of the things that Professor Gowers often does.

"Well, I'll leave the first question!" Junxin's face suddenly flashed with a hint of mischief.

"Representing a number with only 1 means using only 1 to represent a natural number by addition and multiplication and parentheses, and for a given natural number n, when represented by 1, the least number of 1 is denoted as f(n). RichardK· Guy proposes a mathematical conjecture: is f(p)=f(p-1)+1 true for a given prime number p? ”