Scholar's Advanced Technological System
chapter-612

It was the end of April.

Something big happened in the academic world.

In the latest issue of the Annual Mathematics journal, a forty-page long thesis regarding the proof of the existence of a solution to the Yang-Mills equations was published.

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

This thing blew up on the internationally renowned mathematics forum "Math Overflow".

[Did you guys hear? The existence of a solution to the Yang-Mills equations has been proved?!]

[I heard about it this morning, but this is still inconclusive, right?]

[It's posted on Annual Mathematics, of course it's conclusive. The reviewer is Charles Fefferman!]

[I haven't finished reading it yet, and I don't know much about L Manifold theory. If I want to understand the 2018 paper about the L Manifold, I'll have to learn differential geometry first, what a pain in the a*s… Anyway, it's very difficult to find mistakes in a big-name thesis like this. We'll have to see what the final result is after the report conference.]

Because many of the modern young mathematicians, like Tao Zhexuan and Schultz, had their own accounts on this website, the Math Overflow trending page basically reflected the current trending events in the mathematics community.

The last time a discussion was this popular was two years ago, because of Sir Atiyah's five-page thesis…

Professional academic forums weren't the only place that blew up.

Even though most people didn't even know how to write the Yang-Mills equations, most people knew about the Millennium Prize Problem.

Two days after the thesis came out, the news appeared on various news networks and attracted countless attention from people who were in and out of academia.

Compared to the rational discussions on Math Overflow, the Facebook and Twitter crowds were much more emotional.

[Lu Zhou? Lu Zhou is the author? If I recall correctly, he solved a world-class mathematics problem two years ago!]

[The Navier–Stokes equations! One of the seven Millennium Prize Problems! I still remember his International Congress of Mathematicians report!]

[Challenging two Millennium Prize Problems in the span of two years… Jesus, how does he do it?]

[And he also solved controllable fusion?]

[Haha, maybe this is the power of Asian mathematicians?]

[This is crazy!]

[…]

Ever since the Millennium Prize Problems were announced, there had been no shortage of challengers.

However, very few people achieved worthy results regarding the Yang-Mills equations.

If someone could prove the existence of a solution to the Yang-Mills equations through a mathematical method, then it wouldn't take long before someone could find a general solution.

Because this matter was so impactful, Nature journal, which usually paid very little attention to mathematics research, selected this thesis for a 200-word highlight on their latest issue. Nature even included an extract on the front cover.

During an interview with a reporter from Science, Professor Fefferman spoke highly of the mathematical methods used in this thesis.

"Very few people are able to reach a high level in more than three areas of mathematics. Not only was he able to do this, but he also integrated partial differential equations, differential geometry, and topology into a new mathematical tool."

Reporter: "Are you talking about the magical L Manifold?"

Fefferman: "Correct."

Reporter: "But some people commented that while he proved the solution existence of the Yang-Mills equations, he didn't create any new mathematical tools, he only re-used the tools that he created during his research on the Navier–Stokes equations… What do you think about this comment?"

The value of a mathematical proposition wasn't reflected in the proposition itself, but rather it was reflected in the mathematical tools that were created when solving the proposition.

If this paper only proved the solution existence of the Yang-Mills equations using mathematical language and couldn't pave a way for finding the general solution, even though it would still be an excellent achievement, it wouldn't be outstanding.

Fefferman: "I don't think that is fair. The value of a mathematical conjecture isn't manifested in creating new mathematical tools. It can also be manifested in the perfection of existing tools, or even just in an abstract mathematical concept."

Reporter: "Do you think he strengthened the L Manifold theory?"

Fefferman: "That's right, a theory often take five to ten years to mature, and it requires the accumulation of countless corollaries and theorems.

"By inventing the L Manifold, he successfully built a bridge between partial differential equations and differential geometry and introduced topological methods. If I were to describe it in laymen's terms, he converted the equation into a geometrical object that exists in a special space."

Reporter: "That's so abstract, can you be more specific?"

Fefferman shrugged and said, "It's like drawing an auxiliary line on an irregular image. After a special transformation, the originally complicated things become simple."

Research: "But I noticed that there are very few people in arXiv who are following this research field. Even though my opinion might be misinformed, but if it is so important, why aren't people paying attention to it?"

Fefferman: "The answer is simple. You can't expect a two-year-old theory to become mainstream in the academic world. Even Grothendieck couldn't do something like this. Forget about studying the theory in-depth, even learning the theory would take a certain amount of time… Not to mention, there is a certain threshold for learning this theory."

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

Fefferman: "Yes, I believe that anyone who truly understands the thesis will agree with me."

Reporter: "One more question, it's not related to the Yang-Mills equations, and of course, you can refuse to answer."

Fefferman smiled and said, "Ask away."

Reporter: "Do you think he can become the greatest mathematician of this century?"

This was a very difficult question.

After all, the twenty-first century had only just begun.

Fefferman stared into the reporter's eyes and thought for a bit. He then said, "It depends on whether or not the Riemann's conjecture is going to be solved in this century, if not…"

He paused for a second.

"Then, there's no doubt that he already is."