"Professor, I haven't seen you for a while, how are you doing?" Professor Wiles's house is the only one in his house, and the professor's wife is not at home, so it seems that something is out of the house. Junxin put the black tea he brought on the coffee table in Professor Wiles's living room and said hello.

"You don't know much less about the work mode of the Institute for Advanced Study than I do, so I won't be so busy if I don't have a teaching task." Professor Wiles replied with a smile.

Junxin nodded and replied: "The Institute for Advanced Study in Princeton is indeed a great initiative, at least it can allow people who work here not to consider any external factors, but only to consider the academic itself, to be honest, if I didn't have to go back to China, maybe I would have chosen to work in this place!" ”

"Actually, as far as I know, both Professor Dyson and Professor Mirnoe would very much like you to stay, and they can even break the tradition for you and directly grant you the title of full professor. But now it seems that you really have no intention of staying. Looks like they're going to be disappointed. ”

Jun Xin shook his head with a wry smile and said, "This is also a matter of no choice, science has no borders, but scientists have their own motherland after all." As you said, staying can be a great thing for me, but a lot of times I have to think about things that can be solved by more than just staying or leaving. ”

"Ha, it's not a big deal. I think even after you return to China, you can often see your papers. After all, it's much more convenient now than before, and if I have time, I can also go to China to see you. Professor Wiles didn't say anything about Junxin's stay or departure.

"Professor, the black tea you brewed does taste very good, I haven't drunk such mellow black tea for a long time, it looks like I'm going to come here to bother you more in the future." As for whether to return to China or stay after completing the exchange period, you must have a fixed opinion in your confidence, so you don't want to spend more time on this topic, so you take the initiative to divert the topic.

Professor Wiles smiled, "This is something I habitually do when I'm thinking about things. Black tea can improve my thinking efficiency, which is a very helpful thing for me. ”

"I wonder what the professor has been thinking about lately?" Junxin didn't make any more detours, and started today's topic directly.

"Questions about Fermat's Great Theorem!" Professor Wiles put down the cup in his hand, and said with a serious look in his eyes, "Recently, I have been collecting papers and research materials related to Fermat's theorem. ”

"So, Professor, did you gain anything?" Junxin asked.

"Actually, you should know more about this than I do." Professor Wiles glanced at Junxin with a smile and continued, "When Fermat's theorem was just coming out and being promoted, mathematicians studied it according to the traditional model of mathematical proofs, such as Euler. ”

But their proof is just the beginning. Their value is a gradual increase in the value of n, and all repetitions are eliminated. For example, Euler proved the case of n=4. In the final analysis, this is actually a kind of first changing the problem from complex to simplistic, then to a weakened theory to prove, and finally to find the final proof. ”

This method has always been the mainstream method in the research process of Fermat's theorem, and it was not until 1955 that the Taniyama Shimura conjecture proposed by Yutaka Taniyama and Goro Shimura began to change. But that's just a shift. ”

"The real change is in the work you've done in the last two years, Jun!" Professor Wiles said with a serious expression, "I think our ancestors have gone down the wrong path, or they have gone astray in the study of Fermat's theorem. Because this actually contains a problem of prime number distribution in it. In this way, in order to prove Fermat's theorem, the Riemann hypothesis must be proved before it is possible. ”

"And you solved the Moder conjecture, and then proposed the connection between Taniyama Shimura's conjecture and Fermat's theorem, which is now the Junxin inference of the internationally accepted statement. The proof of Fermat's great theorem is transferred to the ellipse curve and modulo curve that originally did not want to do with it, so that the problem of the distribution of prime numbers is cleverly crossed, so as to consider the direction of algebraic geometry, and some of the conclusions of Model's conjecture can be used to prove Fermat's great theorem, providing another possibility. ”

Jun Xin listened calmly to Professor Wiles's speech, and then said very calmly: "So, it seems that Professor you are inclined to solve Fermat's great theorem through elliptic curves and modulus curves?" ”

Professor Wiles nodded and said, "Because my major is actually the study of algebraic geometry of elliptic curves and modulus curves. There are a lot of studies on elliptic curves and modular curves themselves, so I agree with the content of Junxin's inference. ”

"Then there is no problem with the two of us going up the proof of this problem." Junxin nodded with satisfaction.

"That's why I asked you to work on proof of this conjecture. My good friend Professor Rickett once said to me that if you are to study Fermat's theorem, you are undoubtedly at the forefront of the world. I have no objection to his assertion. ”

"Thank you, Professor Beckett, for believing in me!" Junxin smiled slightly, "So how do we get started?" ”

"The Princeton Institute for Advanced Study is a very special institution, which is why I chose to work at the Institute for Advanced Study in Princeton. Because I don't have to be busy writing papers to wrap myself up, and I don't need to do research that I don't like, I have the support of my wife, and in the future, I will make proving Fermat's theorem my highest work. Everything else will revolve around this thing. Professor Wiles obviously had a plan, so he said without hesitation.

Junxin is not surprised by Professor Wiles's lonely and heroic scientific research method, in fact, it is not only the later generations of Professor Wiles who chose to do this, but also because this practice is actually the common model in the European scientific research community.

Although our people usually unite Europe and the United States, in fact, there are quite a few differences in the way of scientific research between European countries and American countries. Scientists in the Americas habitually communicate and cooperate with others after the results are produced, and then study new or higher-level results, which is commonly known as time-sensitive research. On the contrary, although they are not averse to communication, they actually prefer to publish the results of the research together after the complete research of a topic. This method is commonly known as holding back the big move.

Clearly, Professor Wiles is choosing the same approach that European scientists are using.

And the thinking of European scientists is precisely that