At the end of April.
Something big happened in the academic community.
In the latest issue of Annual Mathematics, a forty-page paper was published on the proof of the existence of a solution to the Yang-Mills equations.
Once this news was confirmed, it immediately caused a sensation in the international mathematics and physics community.
On the internationally renowned mathematics forum, Math Overflo, there was a huge discussion about this matter.
[Did you guys hear? The existence of a solution to the Yang-Mills equations was proven?!]
[I heard about it this morning, but it's not conclusive yet.]
[Being published in Annual Mathematics doesn't count as a conclusion? The reviewer is Charles Fefferman!]
[I haven't finished reading the thesis yet. I don't know much about the theory of the L Manifold. If I want to understand it, I have to combine it with his thesis on the L Manifold published in 2018. Then, I have to study differential geometry. What a headache … In short, the thesis of such a big name is not something that ordinary people can find fault with. I'll wait until the report is over before I know what the final result will be.]
Because many new mathematicians, including Tao Zhexuan and Schulz, had registered their own accounts on this website, the popularity of MathOverflo basically reflected how sensational this matter was in the mathematics community.
The last time there was a discussion of this level was two years ago, with Sir Atiyah and his five-page thesis …
The heated discussion wasn't just happening on professional academic forums.
Even though most people didn't even know how to write the Yang-Mills equations, they weren't unfamiliar with the Millennium Prize Problems.
The day after the thesis was published, related news appeared on the front pages of various news networks and attracted countless people.
Compared to the rational discussions on MathOverflo, the reactions of netizens on Twitter and Facebook were more emotional.
[Lu Zhou? The author of the thesis is Lu Zhou? If I remember correctly, he only solved a world-class mathematics problem two years ago!]
[It's the Navier – Stokes equations! One of the seven Millennium Prize Problems! I remember his report was at the Rio International Congress of Mathematicians!]
[Challenging two Millennium Prize Problems in a row, less than two years apart … Jesus Christ, how did he do it?]
[He also solved the controllable fusion problem?]
[Haha, perhaps it's a mysterious power from the East?]
[This is crazy!]
[…]
Ever since the seven Millennium Prize Problems were announced, there had been no lack of challengers.
However, very few people had ever achieved such a critical result in the Yang-Mills equations.
If he could prove the existence of a solution to the Yang-Mills equations through mathematical methods, then it wouldn't be too long before he could find the general solution.
Because the impact of this matter was too big, even Nature, which rarely paid attention to mathematics research, chose to highlight the 200-word abstract of this paper in the new issue of the journal. The excerpt was also displayed on the cover.
On the other hand, during an interview with a Science magazine reporter, Professor Fefferman, the reviewer of the thesis, gave a high evaluation of the mathematical methods used in the thesis.
"Very few people can reach the pinnacle of mathematics in more than three different fields at the same time. Not only did he do this, but he also fused partial differential equations, differential geometry, and topology together to derive a new mathematical method. "
Reporter: "Is it that magical L Manifold?"
Fefferman: "Yes."
Reporter: "But some people say that when he proved the existence of a solution to the Yang-Mills equations, he didn't create new mathematical tools. Instead, he only reused the mathematical tools that he created to solve the Navier – Stokes equations … What do you think of this view?"
The value of a mathematical proposition wasn't reflected in the proposition itself, but in the mathematical methods that could be used to solve the proposition.
If this thesis only used mathematical language to tell people that a general solution to the Yang-Mills equations existed, but it couldn't pave the way for finding this general solution, then even if it was an outstanding achievement, it would still be difficult for it to be outstanding.
Fefferman: "I don't think this view is objective. The value of a mathematical conjecture doesn't have to be the creation of a new mathematical tool. It can also be the improvement of an existing mathematical tool, or even just an abstract mathematical idea. "
Reporter: "You think he strengthened the L Manifold theory on this basis?"
Fefferman nodded and said, "That's right. It often takes five or even ten years for a theory to mature, as well as the accumulation of countless mathematical propositions. Very few people can do this in just two years, but he did it. "
"By introducing the L Manifold method, he successfully built a bridge between partial differential equations and differential geometry. He also introduced the ideas and methods of topology. If I had to describe it in non-technical terms, his approach is to make the equations not pure equations, but a geometry that exists in a special space. "
Reporter: "That's too abstract. Can you be more specific?"
Fefferman shrugged and said, "It's like drawing an auxiliary line on an irregular graph. After a special transformation, the originally complicated thing can be easily understood."
Reporter: "But I noticed that there are very few people on arXiv who follow up on this research. Even though this data may not be objective, if it really is that useful, why doesn't anyone think about using it? "
Fefferman: "This question is very simple. You can't expect a theory that was born less than two years ago to immediately become mainstream in the academic community. Even Grothendieck can't do this. Forget about researching it in depth, even learning to use it takes a certain amount of time … Not to mention, this method has a certain threshold. "
Reporter: "So, you have a high opinion of his work?"
Fefferman: "Yes, and I believe that anyone who really understands the thesis will have the same opinion as me."
Reporter: "Last question, it might not have anything to do with the Yang-Mills equations itself … Of course, you can choose not to express your opinion."
Fefferman smiled and said, "Go ahead."
Reporter: "Do you think he has the potential to become the greatest mathematician of this century?"
This was a difficult question.
After all, the 21st century had only just begun.
Under the eager gaze of the reporter, Fefferman thought for a bit and said, "This depends on whether or not the Riemann conjecture can be proven in this century. If you can't … "
He paused for a second.
"Then there's no doubt that it's not a possibility, he already is."
—
I recommend a novel, "Sorry, it's Awesome to Have a System". The author is an old hand, don't worry.
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