Teaching is no stranger to Junxin, during the winter vacation last year, Junxin was invited by Professor Wang Yuan of the University of Science and Technology of China to serve as a teacher in Hua Luogeng's class, which can be regarded as a person with teaching experience. However, experience is not the same as application, and students in Chinese mainland, especially those in the eighties and nineties, passively absorb knowledge far more than actively absorb knowledge, so it is generally enough to explain the knowledge points in detail step by step in class. However, European and American students are completely different, they prefer to take the initiative, in most cases, they will take the initiative to ask questions, many times the teacher only needs to explain the knowledge points a little, and a large number of questions will be raised immediately, and in the process of answering, they can also achieve the role of understanding and digesting the knowledge points.

It's not clear which way to master more things, but one thing that can be said is that the initiative of Chinese students is indeed a little worse, and Junxin himself has experienced two ways of teaching, so he naturally has a deep understanding of this.

But fortunately, this is not a formal class, and Junxin does not need to prepare for the class, in fact, his three papers are the content of his preparation. And frankly speaking, in addition to Professor Thurston's level being better than him, it was more than enough to deal with a bunch of juniors.

"In 1904, it can be said that Mr. Pang Jialai, the last encyclopedic scientist, put forward the Pang Jialai conjecture, and then, for nearly 80 years, the Pang Jialai conjecture has been the most basic assumption in topology, and it is also a problem that most topologists have been working on, but unfortunately, until now, we have not completely solved the Pang Jialai conjecture."

After his flash of inspiration, Professor Smale pioneered the opposite, starting with the high-dimensional Pong Jialai conjecture, gradually approaching to three-dimensional, and proving the five-dimensional and above-dimensional conjecture, so he won the Fields Medal. Later, topologists began to study the Ponkaleigh conjecture at lower latitudes, and Professors Donaldson, Smale, Mirno, Yau, and Thurston all contributed to this problem. ”

"With the results of the mathematicians, I began to have a new perspective on the four-dimensional Ponkaleigh conjecture. Professor Smale ...... in his paper "

"Professor Mirno, though not specifically studying this problem, has discovered manifolds in his research......"

"Not long ago, I exchanged with Professor Thurston about the leaf-like structure of three-dimensional manifolds at the professor's afternoon tea discussion, and Professor Thurston's manifold classification equation gave me a lot of inspiration, and I introduced this equation at the same time as I researched, and made certain changes to this equation to get ......"

"Professor Donaldson's work has solved my confusion and I was a little inspired by the fact that he mentioned in his research paper that four-dimensional manifold-dependent topology methods and equations were a little inspired......"

“…… After such a series of topological operations, there is such an equation expression in the four-dimensional manifold......"

…………

You want to ask a junior to understand the top research content in the industry, unless he is a biology student who can quickly figure out the meaning of the content through a large amount of information and literature. But for students of math, physics or chemistry, figuring it out is a fantasy.

Of course, Junxin didn't expect the students sitting below to understand, even if these students were nominally his seniors. However, Junxin was sure that Professor Thurston who was sitting below could understand it, and this was the main reason for his lecture.

Princeton's professional classes are generally about one and a half times, but the difference is that there is no rest time in the middle, and an hour and a half is completely course time, so Junxin does not have enough time to explain at all, so he pointed out the source of each point when he lectured, leaving only his work to deepen a little. But in the end, Junxin felt more and more as if he was making a report, and he couldn't help but feel a little depressed in his heart.

After class, Junxin was naturally invited to his office by Professor Thurston, and Junxin, who was already quite familiar with Professor Thurston's office, was not polite, and made a pot of black tea, which Professor Wiles brought from England to give to his colleagues in Princeton. After pouring a cup of black tea for Professor Thurston and himself, Junxin sat down in the armchair opposite Professor Thurston and shrunk his body completely into the chair.

"I've read the paper, there shouldn't be any problems, I'll tell Professor Faltins that all three articles will be published in the first half of next month, although it's a bit rushed, but there shouldn't be any problems." Professor Thurston said to Junxin with satisfaction.

"That's great, so that almost all topologists from all over the world will write to me asking for exchanges, so I might get a lot of questions to learn from!" Junxin nodded and said happily, "But it's really interesting, my papers in the Annals of Mathematics are published very quickly, not at all the kind of paper that takes 24 months to review!" This is true of the Modell conjecture, as is the Junshin inference of the connection between the Taniyama-Shimura conjecture and Fermat's theorem, and the same is true of these three articles! ”

Professor Thurston shook his head and said, "What's this?" The review of the editorial office of Princeton's "Annals of Mathematics" is flexible, you can't compare an ordinary paper with your papers, your papers solve major problems in the mathematical world, which has a great impact, and will naturally compress the review time, I estimate that it will only take about a week! ”

Junxin nodded, it was true. When Professor Zhang Yitang proved the conjecture of infinitely many twin primes with a difference of more than 70 million, the review time was also very short, and Professor Thurston stated a fact.

However, Junxin did not continue this topic, but talked about another topic: "If nothing else, next year's Fields Medal, you should be one of the four places, right?" ”

"Professor Mirno revealed to me that he is the current president of the International Congress of Mathematicians, and I guess eight or nine will not be far from ten!" Professor Thurston didn't prevaricate at Junxin, but nodded and said, "But I think maybe you're one of them!" ”

Jun Xin was stunned: "Me?" Shouldn't that be? ”

"Professor Mirno is campaigning for you, and he thinks you're qualified!" Professor Thurston revealed a message, "I think you can get it, too!" ”

"Fields Medal? To be honest, I think I'm still too young, and maybe it's not a good thing to win the award too early. Junxin said frankly.

"Oh? Haven't you thought about it? I knew that based on Modell's conjecture alone, the conference should have awarded you a Fields Medal, so the chances of you winning the award will be very high! ”

"Fields Medal, what mathematician wouldn't want to win this prize? I thought, of course, but I thought it would be a little later, I was too young. In fact, I was thinking that maybe I would be awarded the next 86 years, when I was 23 years old, and my age was reasonable, but I was three years younger than Professor Searle, which was acceptable and less stressful. Junxin shook his head and said honestly.

"Haha, I don't think you should think about it!" Professor Thurston smiled, "If it's just a Moder conjecture, it's nothing, but once the four-dimensional Pangjialai conjecture is published, there will be almost no problems." We mathematicians are meant to be young, and the younger the better! 19 years old, it's not impossible! ”