In the end, Professor Thurston did not agree to Junxin's request to be the advisor of his dissertation. Although as a professor of Junxin, it is not a big deal to be the advisor of his thesis, but Junxin's situation is indeed a bit special.

This year is 1982, which is also the day of the International Congress of Mathematicians, which also means that the Fields Medal, the highest award in mathematics, was held in Warsaw, Poland. Professor Thurston has supervised one of the winners of this year's Fields Medal. Although he is modest, he will not be presumptuous, and he knows his level very well.

In this way, he is actually qualified and capable of being a tutor for any college student or graduate student. However, in his own opinion, among these people, there is definitely no such a demonic genius as Junxin.

In the same vein, he believes that winning this year's Fields Medal is more than enough in terms of what Junxin has achieved so far. From the perspective of students and teachers, Professor Thurston still has enough confidence to think that he can be a teacher of Junxin. But in terms of the research status of mathematics, the two are equal. In the face of such a gentleman, no matter who he is, there is an inexplicable sense of depression.

Based on this consideration, in fact, no one in the entire Princeton University believes that he is qualified to be a mentor of Junxin.

Still, Princeton's top brass has taken a flexible approach out of respect for real talent. After receiving the report from Professor Thurston, President William allowed Junxin's supervisor to be vacant, but dispatched all the professors of the Department of Mathematics to form a thesis defense committee. This is the first time in the history of Princeton University.

However, this tradition was later preserved by Princeton University, and when such students were encountered in the future, it was also handled according to this convention. The next person to receive this treatment is the world-class top mathematician who was later considered to have the highest IQ in the world, the Australian-Chinese mathematician Tao Zhexuan.

Putting aside the matter of Junxin's thesis advisor for the time being, Junxin is not in the mood to pay attention to this issue anymore. He is now focused on preparing his thesis.

Mathematics is a completely logical discipline of computational tools, and all its reliance is based on a set of axioms and the inferences they prove. This is strictly adhered to, whether it is algebra or geometry, or mathematical structure or other sub-disciplines of mathematics.

In the eyes of those outside the mathematical community, the greatest success of a great mathematician is the discovery or proof of a universally recognized mathematical problem or mathematical conjecture. However, such a statement is still debatable in the mathematical community. In the eyes of mathematicians, the greatest success of a truly great mathematician is to establish a new set of mathematical paradigms that are recognized by the world.

The former is like Professor Wiles's proof of Fermat's Great Theorem and Perelman's proof of the Poincaré conjecture. The latter are none other than Gauss, Euler, Riemann, Hilbert and Grothendieck, who creatively proposed a set of methods and paradigms for mathematical research.

In fact, this is also where Junxin needs to make a choice. He comes from the future, and naturally has a complete memory of the proof of sensational mathematical conjectures, but there is not much in his memory that can help him when it comes to things that really need to build a system, after all, he is still a mathematical physicist, not a real mathematician.

He can write the answers and proofs of some of the world's most difficult mathematical problems more easily than ordinary people, but this does not mean that he has the ability to create his own mathematical paradigm, which will be a more difficult road.

In the final analysis, the proof of mathematical conjecture only shows that a person has achieved a groundbreaking result at a certain point, which may be able to lead to the development of a line, but it is relatively not so easy to affect a face. However, if you create your own mathematical system, then you will directly cross the dotted line development of mathematical conjecture, but directly target the development of surfaces and bodies.

Junxin wants to be like Euler, Gauss, Riemann, Hilbert, and Grothendieck, not just a man who proves a theorem. To do this, he needs to build his own theoretical and mathematical system. It is like Grothendieck's empirical mathematical paradigm for algebraic geometry.

Mathematics papers, whether in the past life or in this life, Jun Xin has written a lot. So even though it is a relatively special final thesis, Junxin has nothing to worry about. What he really cares about is building his own mathematical system, and this final paper, in his mind, will be the beginning of his own system.

In later generations, in addition to the well-known mathematical knowledge such as mathematical conjecture, there were also a series of theoretical mathematical systems with programmatic mathematical principles. And the most famous of the mid-term is, of course, the Langlands Program, which is the most widely circulated in the mathematical community.

The Langlands Program is a series of far-reaching ideas in mathematics, linking number theory, algebraic geometry, and reduced group representation theory. The program was first proposed by Robert Langlands in a letter to Wey in 1967. It is a set of far-reaching conjectures that predict precisely the possible connections between certain seemingly unrelated areas of mathematics. The influence of the Langlands Programme has grown in recent years, and every new development related to it is seen as an important achievement.

One of the strongest supports for the Langlands program was Andrew Wiles' proof of Fermat's theorem in the 90s of the 20th century. Wiles's proof, along with the work of others, led to the resolution of the Taniyama-Shimura-Weiyi conjecture. This conjecture reveals the relationship between elliptic curves, which are geometric objects with profound arithmetic properties, and modular forms, which are highly periodic functions derived from very different fields of mathematical analysis.

The study of the Langlands program directly led to the famous mathematicians Vladimir Drifeld, Lafvoke, Wu Baozhu and other famous mathematicians who won the highest award in mathematics - the Fields Medal for their far-reaching foresight and precise explanation of the Langlands program. Until the end of Junxin's previous life, the Langlands Program was still an important research hotspot of the mathematical system among all the basic theories of mathematics.

Thinking of this place, Jun Xin suddenly laughed, he seemed to know the direction of his next work.