End of April.

A big thing has happened in academia.

In the latest issue of the Annals of Mathematics, a paper on the proof of existence of the solution of the Yang Mills equation was published in 40 pages.

As soon as this news was confirmed, it immediately caused a sensation in the international mathematical and physical circles.

At the internationally renowned mathematics forum MathOverflo, the discussion about this matter has exploded.

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

[I heard about it in the morning, but it's still undecided.] 】

[Publication in the Annals of Mathematics is not conclusive?] The reviewer is Charles Feverman! 】

[I haven't finished reading the paper yet, I don't know much about the theory of L manifolds, and I have to combine the paper on L manifolds he sent in 18 years to understand it, and then I have to make up for differential geometry and have a headache...... In short, this kind of bigwig's submission, even if there is a fault, it is not something that ordinary people can pick out, and what the final result will be, let's wait until the report is over. 】

Because many new-generation mathematicians, including Tao Zhexuan and Schultz, have registered their own accounts on this website, the popularity of the topic on MathOverflo can basically reflect how sensational the repercussions of an event are in the mathematical community.

The last time there was such a discussion was two years ago, when Sir Attiyah and his five-page paper were born......

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

Even though most people don't even know how to write the Mills equation, they are no strangers to the millennial problem.

Almost the day after the paper came out, the relevant news appeared on the front page of various news networks, and attracted countless onlookers from the melon-eating masses.

Compared to the rational discussion on MathOverflo, the reaction of netizens on Twitter and Facebook was more emotional.

【Lu Zhou? The author of the paper is that Lu Zhou? If I'm not mistaken, it was only two years ago that he solved a world-class math puzzle! 】

[It's the NS equation!] One of the Seven Millennium Puzzles! I remember his talk at the International Congress of Mathematicians in Rio de Janeiro that year! 】

[Challenging two millennial problems in a row, with less than two years in between...... God, how did he do it? 】

[During the period, controlled fusion was also solved? 】

[Haha, maybe it's a mysterious power from the East? 】

[It's crazy!] 】

【……】

Although since the announcement of the Seven Millennium Problems, there has been no shortage of challengers.

However, few people have achieved such key results in this field regarding the proposition of the Young Mills equation.

If we can prove the existence of the solution of the Mills equation through mathematical methods, then the day when we can find out what this general solution is should not be too far away.

Because the impact of this incident is so significant, even Nature, which pays little attention to the progress of research in the field of mathematics, has excerpted the 200 words of the abstract part of this paper, set it a "highlight" in the new issue of the journal, and some excerpts are displayed on the cover.

At the same time, in an interview with the reporter of Science magazine, Professor Feverman, the reviewer of the paper, gave a very high evaluation of the mathematical methods used in this paper.

"It's rare to be able to achieve the ultimate level in more than three areas of mathematics at the same time. And he didn't just do this, but he fused three very different directions: partial differential equations, differential geometry, and topology, and derived a new mathematical method on this basis. ”

Reporter: "Is it the magical L manifold?" ”

FEVERMAN: "Yes. ”

Reporter: "However, some people commented that when he proved the existence of the solution of the Jan Mills equation, he did not create new mathematical tools on the basis of it, but only 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 to solve the proposition.

If this paper only uses the language of mathematics to tell people that the general solution of the Young Mills equation exists, but does not pave the way for finding this general solution, then it is difficult to achieve outstanding standards, even if it is also an excellent result.

FEVERMAN: "I don't think that's objective. The value of a mathematical conjecture is not necessarily the creation of a completely new mathematical tool, it can also be a refinement of an existing mathematical tool, or even an abstract mathematical idea. ”

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

Feverman nodded: "That's right. It often takes five or even ten years for a theory to develop from jerky to mature, as well as the accumulation of countless mathematical propositions. Few people can do it in just two years, but he did. ”

By introducing the method of L-manifolds, he succeeded in building a bridge between partial differential equations and differential geometry, and introduced the ideas and methods of topology. If I were to describe it in non-technical terms, his approach would be to make equations no longer purely equations, but a kind of geometry that exists in a special space. ”

Reporter: "This is too abstract, can you be more concrete?" ”

Feverman shrugged: "It's like making an auxiliary line on an irregular shape, with a special change that makes the otherwise complex things clear at a glance." ”

Reporter: "But I've noticed that there are very few people on Arxiv who follow up on this research. While this data may not be objective enough, if it really works, why hasn't anyone considered using it? ”

Feverman: "It's a simple question, you can't expect a theory that's been around for less than two years to immediately become mainstream in academia, not even Grothendieck. Not to mention studying it in depth, even if you learn to use it, it will take a certain amount of time...... What's more, there is a certain threshold for this method. ”

Reporter: "So, you have a high opinion of his work?" ”

FEFFERMAN: "yes, and I'm sure anyone who actually reads that paper will have the same idea as I do. ”

Reporter: "The last question may not have anything to do with the Young Mills equation itself...... Of course, you can also leave it untested. ”

Peverman smiled and said, "You ask." ”

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

That's a hard question.

After all, the 21st century has only just begun.

Under the eager gaze of the reporter, Feverman thought for a moment and said: "It depends on whether the Riemann conjecture can be proven in this century." If you can't......"

At this, he paused.

"Then there is no doubt that it is not possible, he already is."

——

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