"Fermat's theorem?" Professor Feverman's gaze became serious when he heard the name, "Do you have any thoughts on Fermat's grand theorem?" ”

Without waiting for Junxin to answer, Professor Feverman nodded to himself and said: "Yes, no one in the international research on Fermat's theorem has thought that there would be another path before you, and your research on this theorem has already come to the forefront of the world, which is also normal." After a pause, Professor Feverman turned to Junxin and said, "Is there anything you need my help with?" ”

"Professor, I do have some opinions on Fermat's theorem, but only a very small one. I don't know enough about Fermat's theorem. Junxin shook his head and said, "To tell you the truth, "You know, although I have been studying hard during this time, for some reasons, the reserve of knowledge is still relatively insufficient. So I would like to ask you to give you your opinion on this aspect, after all, in previous studies, Fermat's theorem was studied from the perspective of number theory. Although I have studied this knowledge, it is still far from enough. ”

"Fermat's theorem?" Professor Feverman said in a trance, "Professor Faltings, Professor Phelps and others proposed to invite you to Princeton, and I almost did not raise any objections, because your Junxin inference and Model's conjecture have opened the last channel to the proof of Fermat's theorem, and you are at the forefront of the world on this issue." ”

"When I was young, I had seen this problem and fantasized about one day being able to prove this theorem, but then I went down a different path, and I was getting farther and farther away from the process of proving this conjecture. Fermat's theorem naturally became a dream in my heart. Dreams are different from ideals, ideals are achievable, but the chances of dreams being realized are still too small to be realized. ”

Jun Xin listened quietly, and did not interject, this can be regarded as a part of Professor Feverman's mental journey, and after a few years, this will be an episode in the history of mathematics.

"Speaking of Fermat's theorem, Fermat and Euler are two characters who cannot escape. Fermat pranks down that he has a brilliant idea to prove this conjecture, and Euler pushes and spreads the theorem. Almost every generation of the most prominent mathematicians has encountered and attempted to prove Fermat's theorem. But no one has been able to prove this theorem until now. In the course of three hundred and fifty years, although the n-value has become larger and larger, the hope of proving it has become more and more diminished. ”

"To be honest, you can't imagine the excitement we felt when we saw that your proof connected the directness of Fermat's theorem to the Taniyama-Shimura conjecture, and in a sense, you even opened up a new mathematical paradigm."

"At present, it seems that Fermat absolutely did not have the ability to prove this theorem back then, of course, this is my personal opinion, not a formal conclusion. Personally, I do not think that in the three hundred and fifty years since Fermat, all mathematicians, after carefully studying this conjecture theorem, will lose to what Fermat himself calls a so-called "brilliant idea", which is absolutely impossible. ”

"I think so too!" Junxin agreed. He really did not believe that Fermat could have come up with such a perfect proof of such a complex and multifaceted mathematical problem more than three hundred and fifty years ago. Although he himself said that he had a brilliant idea.

"In fact, I think Fermat thought of a similar approach at most when he saw the Pythagorean theorem, after all, the formulas of the two are relatively close, and this is the only direction Fermat can think of." Professor Feverman nodded.

"You think that's the same way, don't you?" Professor Feverman asked.

Junxin nodded, shook his head again, and said: "I have thought about this thing, but more often than not, I think that Fermat just found a special situation reasoning, such as a certain result that is pushed out in a relatively small situation." ”

"It's possible." Professor Feverman nodded approvingly, and he also agreed with Junxin's statement, which is in fact a mainstream statement in the mathematical community.

"Do you think Fermat's theorem is on my path?" Junxin asked.

"In fact, this is also a direction in which I think Fermat said he solved Fermat's grand theorem." Professor Feverman said, "This is actually very close to the formula of elliptic curves, so it is more correct to explain it by modulus curves and elliptic curves." ”

"Thank you!" Junxin is not too modest, and the elliptic curve and the modulus curve can prove Fermat's theorem, which is already a well-known thing in later generations.

"How can I help?" Professor Feverman had fully understood the meaning of Junxin's arrival, so he didn't say anything more, but asked directly.

"Actually, I do have the intention to do something about Fermat's theorem, but I lack a lot of relevant information and need further information to support it." Junxin said.

"There is no problem with this, I will coordinate the relevant materials between the Department of Mathematics and the School of Mathematics, there should be no problem, and I will ask the principal to help deal with the library's literature library, and there should be no problem. If the materials are not enough, what materials are needed, just write a list, attach the name of the paper and relevant information, and give it to my teaching assistant, I will ask her to communicate with other institutions, how about it? Professor Feverman said almost without thinking, but what he said was Princeton's greatest support.

"Thank you, Professor. But do you believe that I will be able to prove Fermat's theorem? Junxin stood up and said gratefully to Professor Feverman, who was very surprised by Professor Feverman's strong support.

"Haha, it's actually quite simple. If there are still people in this world who can prove Fermat's theorem, I think I don't know how many people I may have, but I know that no matter how many people can do this, one of them must be you. ”

"I have not lived through a single period of mathematical glory, not the time of Eulaguss in ancient times. Or the days of Hilbert and Grothendieck, I didn't experience it. But I know them very well. And I see in you the potential to make an era, come on, your achievements should not be limited to just one Fermat's theorem. I want to see where your limits lie in the future, and I hope you won't let me down. ”

"Thank you, Professor!"