Scholar’s Advanced Technological System

The end of April.

A big thing happened in academia.

In the latest issue of the "Mathematics Annual", a full paper of 40 pages was published, and a paper on the existence of solutions to the Young Mills equation was published.

Once this news was confirmed, it immediately caused a sensation in the international mathematical and physics circles.

Discussions on this matter at the internationally renowned mathematical forum MathOverflow have exploded.

[Have you heard? The existence of the solution to the Young Mills equation was proved! ? 】

[I heard about it in the morning, but this matter is inconclusive. 】

[Isn't it conclusive to be published in the "Mathematics Annual"? The reviewer is Charles Fefferman! 】

[I have n’t finished the thesis. I do n’t know much about the theory of L-manifolds. To understand, I have to combine the paper on L-manifolds he published in 18 years. , Headache ... In short, this kind of big man's submission, even if there is something wrong, can't be picked out by ordinary people. What is the final result? Let's talk about it after the report is finished. 】

Because many new-generation mathematicians, including Tao Zhexuan and Schultz, have registered their own accounts on this website, the topical heat on MathOverflow can basically reflect the repercussions of one thing in the mathematical circle. What a sensation.

The last time such discussions had taken place, it must be traced back to two years ago, Sir Atiyah and his five-page paper ...

Hot discussions don't just happen in professional academic forums.

Even though most people don't even know how to write the Young Mills equation, they are not unfamiliar with the millennial problem.

Almost on the second day after the dissertation was published, relevant news appeared on the top pages of various news networks, and attracted countless crowds of melon eaters.

Compared to the rational discussion on MathOverflo, the reactions of Twitter and Facebook Internet users are more emotional.

[Lu Zhou? Who is the author of the paper? If I remember correctly, he solved a world-class mathematical problem only two years ago! 】

[It's the NS equation! One of the seven millennial puzzles! I remember his presentation at the Rio International Mathematician Conference that year! 】

[Challenge two millennial puzzles in a row, with only two years between ... God, how did he do that? 】

[During the period, also solved the controllable fusion? 】

[Haha, maybe a mysterious force from the East? 】

[This is crazy! 】

[……]

Although the Seven Millennium Challenges have been announced, there have been no shortage of challengers.

But few propositions on the Young Mills equation have achieved such crucial results in this field.

If it is possible to prove mathematically that a solution to the Young Mills equation exists, then the day when you want to find out what the general solution is, it should not be too far away.

Because the impact of this matter is too great, even the "Nature", which rarely pays attention to the research progress in the field of mathematics, has selected the two hundred words of the abstract part of the paper and set it "Highlight" in the new issue , And some excerpts are shown on the cover.

At the same time, in an interview with the journal of Science, Professor Fefferman, a reviewer of the paper, gave a very high evaluation of the mathematical methods used in the paper.

"Few people can reach the highest level in three or more mathematical fields at the same time. And he has not only done this, but also merged three completely different directions of partial differential equations, differential geometry, and topology. Together, a whole new mathematical approach was derived from this. "

Reporter: "Is that the magic L-manifold?"

Fefferman: "Yes."

Reporter: "But some people commented that when he proved the existence of the Young Mills equation solution, he did not create new mathematical tools based on it again. He just reused the mathematical tools created when solving the NS equation ... What do you think of this view? "

The value of a mathematical proposition is not reflected in the proposition itself, but in the mathematical methods that can be created when solving the proposition.

If this paper only uses mathematical language to tell people that a general solution to the Young Mills equation exists, but it cannot pave the way for this general solution, then even if it is an excellent result, it is difficult to achieve excellence. Level.

Fefferman: "I think this view is not objective. It is not necessary to create a new mathematical tool to reflect the value of a mathematical conjecture. It can also be a perfection of existing mathematical tools, or even just a kind of Abstract mathematical thought. "

Reporter: "Do you think he strengthened the theory of L-manifolds on this basis?"

Fefferman nodded: "Yes. It takes five years or even ten years for a theory to mature from jerky to mature, and the accumulation of countless mathematical propositions to precipitate. Few people can get it in just two years. He did it, but he did. "

"By introducing the method of L-manifolds, he successfully built a bridge between partial differential equations and differential geometry, and introduced topology ideas and methods. If I want to describe it in non-professional language, he The approach is to make the equation no longer a pure equation, but a geometry that exists in a special space. "

Reporter: "This is too abstract. Can you be more specific?"

Fefferman shrugged: "It's like making an auxiliary line on an irregular figure, and after a special change, the original complex things can be seen at a glance."

Reporter: "But I noticed that few people follow up on this research on Arxiv. Although this data may not be objective enough, if it really works, why don't anyone consider using it."

Fefferman: "The problem is very simple. You can't expect a theory that was born less than two years old to immediately become the mainstream of academia. Even Grothendieck can't do it. Not to study it in depth, even if you learn to use it. It also takes some time ... not to mention, there are certain thresholds for this method. "

Reporter: "So, how do you rate his work?"

Fefferman: "Yes ~ www.readwn.com ~ and I believe that anyone who really understands that paper will have the same idea as me."

Reporter: "The last question may have nothing to do with the Young Mills equation itself ... Of course, you can also not comment."

Fefferman smiled and said, "You ask."

Reporter: "Do you think he has the potential to become the greatest mathematician of this century?"

This is a difficult question.

After all, the 21st century has just begun.

With the reporter's eager gaze, Fefferman thought for a moment, and said, "It depends on whether Riemann's conjecture can be proved in this century. If not ..."

Having said that, he paused.

"So no doubt, it's not possible, he is already."

Recommend a seedling, "Sorry, the system is really amazing", the author is an old driver, you can eat with confidence ~