Although the organizer was the Institute for Advanced Study in Princeton, in the end, the venue was changed from the Institute for Advanced Study in Princeton to the Department of Mathematics at Princeton University, which is the predecessor of the Institute for Advanced Study, which is the international equivalent of Princeton Mathematics.

The meeting was chaired by Professor Mirno, chair of the Department of Mathematics at Princeton University and tenured professor at the School of Mathematics at the Institute for Advanced Study in Princeton, world-renowned mathematician and Fields Medal winner. This is a bit embarrassing, because Professor Mirno is not an expert in number theory, or algebraic geometry. Today's topic, however, is a report proving the Model conjecture that is closely related to the two.

But Professor Mirno didn't see any difference at all, he didn't seem to be affected by these things at all, and was sitting in the first row, happily communicating with Professor Neugen, who represented the National Mathematical Society of America, who of course was also an authority on geometry.

It would be better to go a little to the right of Professor Mirno, because here is Professor Charles Feverman, a real expert in algebra.

In short, the first row is occupied by mathematicians who have already won the Fields Medal. Because of the huge influence of the Fields Medal on the American continent, mathematicians who have won the Fields Medal will always be superior in academic exchange activities on the American continent.

Sitting in the second row are some mainstream mathematicians in various fields, such as Professor Yau Chengtong, who established a branch of geometric analysis, and Professor William Thurston, who studied the classification of foliate structures in three-dimensional topology. Another example is Professor Ry-Beckett, who has made outstanding contributions to algebraic geometry.

After that, there is not such a strict distinction, and basically everyone sits back one after the other in the order of first come, first served. Anyway, Junxin didn't find any rules in the position where these people sit.

"You can begin, dear Professor Mirno." When the last student and professor sitting at the conference finally found a place to stay, the door to the large lecture hall was closed by volunteers, and a staff member walked up to Professor Mirno and whispered.

"Okay!" Professor Mirno naturally stopped talking with Professor Yau. He stood up and walked to the podium in the lecture hall. Then the lecture hall, which was still filled with the sound of conversation, fell silent for a moment.

"Good morning, colleagues, ladies and gentlemen. Sixty years ago, the famous British mathematician Mr. Modell once put forward a famous problem in number theory, which has been unsolved for 60 years because no one has been able to make a final proof, and some mathematicians even think that this is a difficult problem that cannot be solved in a short time, and that it will be a long-term work that needs to be carried out along, alongside Fermat's theorem and other problems. ”

"Sixty years after Mr. Moder put forward his conjecture, a seventeen-year-old undergraduate student from Mizuki University in China, a magical oriental country, with his extraordinary vision and talent, finally proved this difficult problem in number theory through a large number of calculations and calculations, thus bringing the study of number theory to a new level."

"Next, we have invited Mr. Jun Xin, a famous mathematician from the Department of Mathematics of Shuimu University in China." As soon as Professor Mirno's words fell, the whole hall burst into applause.

In the applause, Junxin walked briskly onto the podium, shook hands with Professor Mirno, and after a few words of whispering, Junxin stood in front of the podium and began his speech.

"Good afternoon, professors, students, and teachers. First of all, I'm going to spit out a little bit about Professor Mirno's story. ”

Junxin's unusual opening immediately attracted everyone's attention: "Anyway, I thought that as the host, Professor Feverman, who has outstanding achievements in number theory and algebra, should be the host, but Professor Mirno suddenly said to Professor Feverman: "Hey, man, he bought me with a paper that solved the four-dimensional Poincaré conjecture, so I have to go and support him." "So Professor Feverman just ceded the position of moderator to Professor Mirno."

"But what I want to say, Professor Feverman, next time we are doing a presentation on the four-dimensional Poincaré conjecture, I will definitely give you the position of moderator. Although your field of study is in algebra. ”

As soon as Junxin's words fell, he suddenly burst into laughter. As soon as Junxin started his speech, he made a joke with the two Fields Medal-level professors on the scene, which immediately attracted everyone's attention.

"Alright, Professor Mirno is probably going to draw a circle in the corner and curse me." Another chuckle, "Let's get down to business and begin the explanation of Modell's conjecture." ”

At the beginning of the twentieth century, Poincaré speculated that subgroups of rational points on elliptic curves had a finite number of generators. This conjecture was proved in 1922 by the British mathematician Louis Moder. The results proved by Mr. Moder show that although there can be an infinite number of rational points on a curve with a deficit of 1, there is a finite set of such points that can be used to construct other such points. ”

"So Mr. Moder guessed that a curve with a deficit of 2 can only contain a finite number of rational points, and that is ........."

"If this conjecture is true, it can be applied to a very wide range of Diophantine equations, of which Fermat's equation is a very important one, like ......"

Jun Xin said above, and the mathematicians below put away the smiles on their faces one by one and listened carefully.

In the '80s, when there was no such advanced equipment as computer projectors, the oldest method adopted by Junxin was to remake hundreds of copies of the paper that proved Modell's conjecture before the presentation began, one for each person who entered the room. Then Junxin passed through the oldest projector and began to explain little by little.

The Modell conjecture has been greatly studied in later studies, and even found several proof methods that are slightly different from those proved by Professor Faltins, although each has its own limitations, but it also fully explains the extent to which the Modell conjecture has been studied.

Although most of Junxin's research is geometry and other content that is relatively close to physics, he himself has a high talent in algebra, and naturally he has systematically studied the Modell conjecture, otherwise how could he be taught by Professor Wiles? Even Professor Witten's request was useless.

Junxin took this report very seriously, far exceeding the report of the International Union of Crystallography. Therefore, the explanation is very detailed, not only explaining the results, but also explaining the ideas used in each step of the content in detail. At the end of the talk, he even talked about several other ideas for proof, but it was limited to time and did not expand, even so, it was a great opportunity for these mathematicians on the scene.

"That's all I have to say about the idea and process of proving Model's conjecture, and after dinner in the afternoon, we'll continue at half past one. Thank you! ”