Chapter 613 This April Is Unsettled

the end of April.

Something big has happened in academia.

In the latest issue of "Annals of Mathematics", a full forty pages were used to publish a paper on the existence proof of the solution of the Yang-Mills equation.

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

On MathOverflow, an internationally renowned mathematics forum, discussions on this matter have exploded.

【Have you heard of it? The existence of solutions to the Yang-Mills equation is proved! ? 】

[I heard about it in the morning, but it's not yet settled yet. 】

[Can it be published in the "Annual Journal of Mathematics"? The reviewer is Charles Fefferman! 】

[I haven't finished reading the paper yet, and I don't know much about the theory of L-manifolds. To understand it, I have to combine the paper he published on L-manifolds in 2018, and then I have to make up for differential geometry. , a headache... In short, even if there are flaws in the contributions of this kind of boss, ordinary people can't pick out the thorns. What is the final result? Let's talk about it after the report meeting is over. 】

Because many mathematicians of the new generation, including Tao Terence and Schultz, have registered their own accounts on this website, the popularity of topics on MathOverflow can basically reflect the repercussions caused by an event in the mathematics circle What a sensation it was.

And the last time there was such a level of discussion, it had to be traced back to Sir Atiyah and his five-page paper two years ago...

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

Even though most people don't even know how to write the Yang-Mills equation, they are not unfamiliar with the Millennium Problem.

Almost on the second day after the thesis came out, relevant news appeared on the headlines of various news networks, and attracted countless people who ate melons to watch.

Compared with the rational discussion on MathOverflo, the reactions of netizens on Twitter and Facebook were more emotional.

【Lu Zhou? The author of the paper is that Lu Zhou? If I remember correctly, it was only two years ago that he solved a world-class math problem! 】

[It's the NS equation! One of the Seven Millennium Dilemmas! I still remember that his report was at the Rio International Congress of Mathematicians that year! 】

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

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

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

[This is crazy! 】

【…】

Although since the announcement of the Seven Millennium Problems, there have been many challengers.

But with regard to the proposition of the Yang-Mills equation, few people have achieved such critical results in this field.

If it is possible to prove the existence of a solution to the Yang-Mills equation through mathematical methods, then the day when we want to find out what the general solution is should not be too far away.

Due to the great impact of this matter, even "Nature", which pays little attention to the research progress in the field of mathematics, has excerpted two hundred words from the abstract of this paper, and set "Highlight" on it in the new issue of the publication , and some excerpts are displayed on the cover.

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

"Few people can reach the ultimate level in more than three fields of mathematics at the same time. And he not only achieved this, but also integrated three completely different directions of partial differential equations, differential geometry, and topology into one Together, a whole new mathematical approach has been derived on this basis."

Reporter: "Is it that magical L-manifold?"

Fefferman: "Yes."

Reporter: "However, some people commented that when he proved the existence of the solution of the Yang-Mills equation, he did not create new mathematical tools on the basis of it again, but only reused the mathematical tools created when solving the NS equation... Excuse me What do you think of this point of view?"

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

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

Fefferman: "I think this kind of view is not objective. The value of a mathematical conjecture does not necessarily have to create a new mathematical tool, it can also be the improvement of existing mathematical tools, or even just a abstract mathematical thought."

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

Fefferman nodded: "That's right. It often takes five or even ten years for a theory to develop from raw to mature, and the accumulation of countless mathematical propositions to precipitate. Few people can solve it in just two years. Do it, and he did it."

"By introducing the method of L-manifold, he successfully built a bridge between partial differential equations and differential geometry, and introduced the ideas and methods of topology. If I want to describe it in non-professional language, he The best way 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. After a special change, the originally complicated things can become clear at a glance."

Reporter: "But I noticed that there are very few people following up on this research on Arxiv. Although this data may not be objective enough, if it really works so well, why no one considers using it."

Fefferman: "This question is very simple. You can't expect a theory that was born less than two years to immediately become the mainstream of the academic world. Even Grothendieck couldn't do it. Not to mention in-depth research on it, even if you learn to use it. It also takes a certain amount of time... What's more, there is a certain threshold for this method."

Reporter: "So, you think highly of his work?"

Fefferman: "Yes, and I believe that anyone who actually reads that paper will have the same thought as me."

Reporter: "The last question may have nothing to do with the Yang-Mills equation itself...Of course, you don't have to express your opinion."

Fefferman smiled and said, "Just 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 twenty-first century has only just begun.

Under the eager gaze of the reporter, Fefferman thought for a while and said, "It depends on whether the Riemann Hypothesis can be proved in this century. If not..."

Having said that, he paused.

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