The work of translating the general idea into a precise essay format was not until the end of November, when it was nearly two weeks before the retreat, far more than Junxin had originally anticipated.

He thought it would be easy to think of it out of the box, but when he actually got to work, it got complicated. A lot of reasoning that seemed to be taken for granted required detailed and precise proof was the biggest reason why he spent about two weeks talking. In addition, he wrote three papers this time, and it took three times to finally completely expound the proof of the four-dimensional Pangjialai conjecture.

Of course, Junxin can also choose another method, he can not write the process of proof in such detail, just write a general direction, and then add the key equations, in this way, you can save a lot of time.

However, Junxin did not use this method, he chose the most difficult method, gave all the proofs in detail, and carefully checked them several times before he really completed the proof of this problem.

After the proof was over, Junxin let out a long sigh of relief. Immediately afterwards, I felt a burst of fatigue attacking, and then the whole person lay on the bed with his head up, and before he even had time to cover the quilt, he had already fallen asleep in a daze.

By the time Junxin woke up, it was just getting dark. Junxin looked at the weather outside and knew that he estimated that he had slept for almost two days. The sky was originally clear, but now it is full of haze, and it seems that there will be a heavy rain coming.

After a brief wash, Junxin saw that there was no movement in Ars-Alfors's room, but when he had already gone out, he didn't care. Then he went back to his room and rearranged the paper after the previous revision, and then put it neatly in the file bag and put it in the school bag. It's been a long time since I've been to class, and Junxin feels a little nostalgic for the life in the classroom.

Walk out of the Butler Apartment, cross two winding forest paths, cross a small river, and then bypass a school building - the teaching building of the physics department, and a short left turn is the Paradigm Building, where the mathematics department is located, which is also home to the mathematics department at Princeton University, the world-famous mathematics research center, and even the Paradigm Building, which was home to the earlier Institute for Advanced Study in Princeton.

As one of the world's famous mathematics centers, the Princeton Department of Mathematics actually doesn't have too many students strictly speaking, and it is estimated that Junxin got up too early in the morning, so he didn't meet a familiar mathematics student along the way, which made Junxin a little depressed.

Walking to the front of the building, the bulletin board in front of the building announced the courses of the mathematics department during the week, as well as some lectures and activities of the mathematics department during the week.

Junxin stared at the densely packed class schedule, and after finding Professor Thurston's course, he walked directly to the classroom where Professor Thurston was lecturing, no matter what grade it was. This is also a privilege that Junxin has obtained in Princeton, after Junxin finished the presentation of the Mordell conjecture, the mathematics department of Princeton University made a decision: Junxin will directly complete all the credits of all courses. In other words, Junxin does not need to take any exams now, and has already obtained all the credits. In other words, his sophomore career can actually be said to be over.

However, generally speaking, Junxin does not really want to enjoy such preferential treatment, but on the other hand, any exam in the current mathematics department is too easy for Junxin, even if Junxin is not good at mathematical logic, it is not difficult for him. So in the end, Junxin still enjoyed this treatment by default.

This kind of preferential treatment is actually a good thing for Junxin, and the courses in the mathematics department of Princeton University are not very fixed every week, of course, the number of hours is fixed. However, because there are often professors who go out to visit or participate in conferences, they basically arrange the class schedule once a week, and the courses are slightly different each week, so Junxin often chooses the courses of the teachers he is interested in according to the schedule schedule. Sometimes it's Professor Milno's classes, sometimes it's Feverman's classes, sometimes it's Professor Surston's classes, sometimes it's other professors' classes. This allows him to always have access to the courses of top scholars in various fields of mathematics, and quickly absorb the mathematical thinking and research concepts of these top mathematicians, which is of great help to Junxin, who has not yet fully formed his own thinking.

Of course, of all the professors, he took the most courses undoubtedly Professor Surston's topology course. At Princeton University, topology is a geometry course in the second semester of the sophomore year and the third year, so it is necessary to have a privilege for Junxin. Otherwise, if Junxin wants to study topology with Professor Thurston, I'm afraid he will have to wait until the next semester after Christmas.

In 1970, Thurston proposed the geometric conjecture, pointing out that the Poincaré conjecture was only a special case of the geometric conjecture. The geometry conjecture is a more powerful and general conjecture about the geometry of three-dimensional space, which holds that any space can be reduced to a few basic figures. The Proceedings of the American Mathematical Society argues that Thurston's greatness lies in his deep understanding of how to use geometric methods to understand the topology of three-dimensional manifolds.

Professor Thurston's research on the Pang-Jialai conjecture is also second to none in the world, and his geometrical conjecture is actually a series of lists of studies on the Pang-Jialai conjecture in a sense.

Therefore, Junxin's first reaction after proving Pang Jialai's conjecture was to show Professor Thurston, and even the degree of urgency was ahead of Professor Mirno.

Among the three top mathematicians in Princeton, Professor Mirno is undoubtedly the most comprehensive, he not only has a high attainment in geometry, but also has certain achievements in algebra K and other problems, which can be said to be a rare all-rounder. Professor Charles Feverman, on the other hand, was a pure algebraic mathematician, and his research on algebraic problems is among the most advanced in the world. The last professor, Thurston, was a complete topologists and won the Fields Medal for classifying the foliate structure of three-dimensional manifolds. Of course, this will not be officially seen until next year's World Congress of Mathematicians in Warsaw.

However, as for the nature of the problem of Pang Jialai's conjecture, Junxin's first reaction was Professor Thurston.