"As the saying goes, there is a specialization in the art industry! Earlier, under the influence of Einstein and Yang Zhenning, I studied physics, but I didn't learn mathematics well. By the time Junxin had solved all the questions raised by Professor Lu, more than two hours had passed. Professor Lu looked at the wall clock on the wall and couldn't help but sigh.

"You are concerned about the problem of ideas, which is already looking at the problem with the thinking of a mathematician, so in my opinion, you still have a certain degree of attainment in mathematics." Junxin exclaimed. Mathematicians are not necessarily proficient in physics, but it has become a consensus in the scientific community that most physicists are proficient in mathematics. However, in the discussion just now, Junxin found that Professor Lu is not generally proficient in mathematics, especially in partial differential equations, and some of his words are inspiring to Junxin.

"After all, I'm not a math major, and I'm still a lot worse than you." Professor Lu shook his head, but he didn't dwell too much on the issue. Instead, he asked, "Listen to Professor Hu, you're going to Princeton?" ”

"Professor Hu gave me the only place in the Department of Mathematics, and I was also very curious about Princeton University, so I agreed." Junxin is a little familiar with Professor Lu's temper, so naturally he will not be modest.

"Well, Princeton, a distant memory!" Professor Lu sighed, "But Lao Hu really did not do anything wrong, Mizuki's mathematics department has just been rebuilt, and you are the only one who can be qualified to apply for Princeton!" ”

"However, it is not Professor Hu who has appointed you, but after I communicated with President William, President William repeatedly instructed me to guarantee your place, so that the Department of Mathematics is the only department that has a quota inside." Professor Lu explained.

"That's right!" Jun Xin nodded and said, "When I first proved Modell's conjecture, Professor Faltins and Professor Griffith of Princeton wrote to invite me to Princeton University, but I politely declined in the name of being a student, and only later did they have the concept of exchange students they discussed. ”

"I see, no wonder Principal William pays such attention to you." Professor Lu said with a smile.

"Can you tell me what kind of university Princeton is?" Junxin asked, even though he knew everything about Princeton, but he still wanted to know their impression of Princeton from the mouths of others.

"Princeton, what a school that people are reluctant to leave..."Professor Lu muttered, and then told Junxin about Princeton University.

Professor Lu explained in great detail, not only about the course at Princeton, but also about the general situation of the teachers at Princeton, focusing on the situation of the Institute for Advanced Study in Princeton, which is next to Princeton University. He even introduced some Chinese restaurants next to Princeton, and even compared which one of the Chinese restaurants had good food, which made Junxin benefit a lot.

After chatting about Princeton, Professor Lu took the opportunity to talk about his experience of studying at Princeton, he talked about the excitement when he saw Einstein, the joy of seeing von Neumann, and the unforgettable years when he started studying under Professor Yang Zhenning.

The topic continued to unfold, and finally Professor Lu began to tell Junxin about his research area of Yang-Mi equation.

The Yang-Rice equation, also known as the Yang-Rice theory, is a non-abelian Lee-group gauge field problem jointly completed by Professor Yang Chenning and Professor Mills in 1954. The Yang-Mills equations that emerge from this theory are a set of nonlinear partial differential equations that have not been considered in mathematics.

Many of the predictive conclusions of the Young-meter equation have been confirmed by laboratories around the world: Stanford, Tsukuba, Brookhaven, the European Institute for Particle Physics, and many others. Despite this, however, there is no known solution to their equations that describe both heavy particles and are mathematically rigorous. In particular, the "mass gap" hypothesis, confirmed by most physicists and applied in their explanations of the invisibility of "quarks", has never been mathematically satisfactorily confirmed. Progress on this issue requires the introduction of fundamentally new ideas, both physical and mathematical.

Listening to Professor Lu's explanation of the Yang-Mi equation, Jun Xin's thinking began to diverge, and he thought of the seven-thousand-year-old mathematical problem proposed by the Clay Institute of Mathematics in the United States in 2000.

In 2000, the Clay Institute for Mathematics raised $7 million, corresponding to a thousand-year-old mathematical problem for every million prizes. They are the P=NP complete problem, the Hodge conjecture, the Poincaré conjecture, the Riemann conjecture, the Young-Mills equation, the Neville-Stoker equation, and the BSD conjecture.

These questions are in the same vein as the Hilbert problem, which is about the foundations of mathematics and the foundations of physics in mathematical applications. But even thirty years later, only the Poincaré conjecture, a fundamental problem in the low-dimensional field of topology, was solved by the famous Russian mathematician and mathematical geek Grishary Perelman in three consecutive preprints of papers posted on the Internet. The other six issues remain unresolved.

Before Perelman solved the Poincaré conjecture, the first problem that could be solved in mathematics and physics was probably the Yang-Mills equation. Only some mathematicians believe that the first problem to be solved is the Poincaré conjecture, and one of the representative figures among these mathematicians is Professor Yau Chengtong.

"I think it's more likely that the Young-Mills equation will be solved first, and although you have further proved the correlation between Fermat's theorem and the Taniyama-Shimura conjecture, it may be much more difficult than the Young-Mills equation."

"I don't think so!" Junxin also replied with great interest, "Although the Yang-Meter equation is an important equation for the gauge field of quantum mechanics, I think Fermat's theorem will be solved first. ”

"Why?" Professor Lu liked this kind of discussion very much, so although Junxin raised the bar with him, his interest was even higher.

"The proof of Fermat's theorem is actually a critical step in the scientific community. The proof of the Taniyama-Shimura conjecture is the proof of the problem of algebraic geometry, which can be transformed into a proof of modular forms and elliptical lines, and the crystallization of Mr. Grothendieck's ten years of work at IHES already contains a wealth of tools and approaches, and all we need to do is to use these things rationally to be able to prove. ”

"And the Yang-meter equation, to be honest, in twenty years, I didn't see the possibility of solving it. Recently, I have been working on a professional reference book called "Mizuki University Mathematics Guide", which deals with the possible development of mathematics in the next 20 years, and I think that in mathematical physics, people will focus more on the establishment of unified theoretical models than on the old ones. ”

"Haha, it's really interesting, I'm a physics student and I'm discussing mathematics problems with you, and you, a mathematics student, actually discuss physics problems with me, this is really..." Professor Lu didn't argue with Junxin, but easily brought over the topic.