Section 242

Although he can speak Cantonese, he would still be at a loss if he really had to read Chinese papers.

Of course, whether he speaks Cantonese or not is completely unimportant after he starts reading this paper.

Because he has seen the path Xiao Yi took in this paper.

"Incredible! He actually chose to prove it from a more general initial condition!"

After Xiao Yi came up with the explosion trend theory, he made an inference that using this theory can help mathematicians prove the NS equation under a more general condition. Of course, this difficulty is still quite large, so he never thought that someone could really achieve this.

More in line with the expected situation, it should be to prove the NS equation under specific initial conditions first, and then extend this proof to a more general situation.

And now, with Xiao Yi's more general proof, it can basically be extended to specific initial conditions at will.

This is also the purpose of generalized proof!

"Really? A more general proof, can he really do it?"

And next to him, there was another person sitting.

It was James Maynard.

It is already January 2024, and the new Joint Mathematics Conference is about to be held, so he came here again.

As for the annual mathematics conference of Princeton University, because there was no heavyweight report like the twin prime conjecture this time, it did not receive much attention.

However, they never expected that before the Joint Mathematics Conference, Xiao Yi would come up with such a heavyweight proof.

"Jesus! I think he should have done it. You don't know how perfect this new function space he created is!"

Tao exclaimed repeatedly, waved at Maynard, and said, "Don't you want to come and see it yourself?"

"Uh... I don't study partial differential equations much, but since it is a function space, I can take a look."

Maynard walked up.

"Hmm... Hmm?! Wait! This function space..."

As Maynard began to analyze this new function space, his eyes gradually widened.

Function space plays a very important role in mathematics. It is an important method in functional analysis and exists in many fields, not just partial differential equations. The applicable area of ​​function space can be found in almost any mathematical direction.

Of course, the scope of application varies according to the nature of different function spaces.

For example, Xiao Yi mainly studies Sobolev space in order to come up with Xiao space, which can not only be used in PDE, but in fact, it can play a role in many fields such as variational method, numerical analysis, mechanical and structural engineering, computer, etc.

Now, Xiao Yi has summarized the characteristics of various function spaces, and through various innovative changes, he has come up with this space that is perfect for analyzing NS equations. Maynard can see that it is not only very useful for NS equations.

First of all, it will definitely have a very huge effect on various PDE studies other than NS equations. In addition, considering the characteristics of this space, even if it is used in the analysis of algebraic topology, it may not disappoint mathematicians.

Maynard couldn't help but exclaim: "This new function space... is it really too perfect?"

"Yes."

Tao Zhexuan, who had already seen this, nodded and said with emotion: "It is indeed quite perfect... so perfect that it doesn't seem to be something that our current mathematics community can do."

"But we can only say that Xiao Yi can always do things that we can't imagine."

Tao Zhexuan said.

"The interval between the two millennium problems is less than two years." Maynard couldn't help but sigh at this time.

No matter what, they will not forget this key point.

The status of the Millennium Problem is unquestionable in the mathematics community.

Two years ago, mathematicians all over the world would never have thought that such a problem would be solved suddenly.

And after that, mathematicians obviously would not have thought that less than two years later, another problem would be solved.

"Two million US dollars in prize money." Maynard said.

For every problem solved, you can get a million US dollars in prize money provided by the Clay Institute.

Of course, because each problem needs to be verified for at least two years and widely accepted by the mathematical community before it can be officially awarded by the Clay Institute.

For example, Perelman's proof of the Poincare conjecture took seven years to verify. After the mathematical community basically confirmed that his proof was correct, the Clay Institute chose to officially award the award.

Of course, this is mainly because Perelman's paper was too "obvious", and mathematicians had to spend more time verifying his proof for these obvious parts.

However, Xiao Yi's proof of the mass gap problem has been recognized by the mathematical community since the International Congress of Mathematicians in 2022. It is estimated that after July this year, it will be almost two years.

Tao Zhexuan shrugged: "Yes, two million, but I think with Xiao Yi's current wealth, he probably doesn't care about this small amount of money at all."

"Yeah." Maynard said with envy: "It's really unexpected that he has such a strong ability in material research. Sometimes I really doubt whether he is really God."

These top mathematicians serve as consultants to help analyze some problems. For example, Terence Tao is also a member of the President's Science and Technology Advisory Committee and has studied AI intelligence technology for the White House.

These positions can make them quite a lot of money, but compared with the money earned by Xiao Yi who invented and created the world's top technology patents and then founded a patent company, it is still much less.

Terence Tao shrugged, then started to operate on the computer, opened his personal blog, and said: "Now it's time to post a blog."

Hearing his words, Maynard didn't know whether to laugh or cry, and complained: "You and the former US president are actually quite predestined. You both like to post things on the Internet, but he likes to tweet and you like to blog."

"Damn! Don't mention that guy to me!"

Terence Tao glared at Maynard unhappily, "He and I are not on good terms."

Maynard laughed immediately.

Once, Terence Tao commented on his blog that the former president was not suitable to be president, and then the former president responded on Twitter that Terence Tao was a failed analyst because he could not prove the Soichi Kakeyani conjecture.

The two naturally had a quarrel.

After laughing for a long time, Maynard finally waved his hand and said, "Okay, okay, I won't say anything. You should write it quickly. I guess there are many people waiting for your blog now to see what "Tao who knows a little bit about everything" thinks of this paper."

Terence Tao gave him a middle finger, then looked back at the computer screen, thought for a moment, and started typing.

...

[Who would have thought of it? Maybe I thought of it before, but I denied it in the end.

Xiao Yi actually achieved this incredible result - proving the NS equation problem from more general conditions.

Well, okay, maybe when I made the inference before, Xiao might have been doing this. After all, he developed the bursting trend theory, and with his wisdom, he certainly would not have thought of using the bursting trend theory to directly realize the generalization proof.

But I still want to express my surprise.

He really did this and achieved it.

Believe me, after doing this, perhaps the explosion trend discrimination model he made before will become more practical, and other more comprehensive models can be made from it, which can be used to help optimize the fluid mechanics model, etc. ...

...】

There are indeed quite a lot of people who follow Tao Zhexuan's personal blog, so as soon as his blog was published, it was forwarded and shared by various people. Within just a few hours, it spread throughout the mathematics community.

Those who have not read the paper can also roughly know from Tao Zhexuan's blog that Tao Zhexuan affirmed Xiao Yi's proof.

And those who have read the paper but have not understood it can realize that Xiao Yi's paper has once again reached a level that others can hardly reach.

A more generalized proof.

After learning this news, it really caused a lot of shock.

If it is a proof under specific initial conditions, then it can only be said that the problem has been solved, and it can have a greater significance for the related models under these specific initial conditions.

And now this result, as Tao said in his blog, can be used to help optimize the fluid model, etc., it can be said that its role has been directly improved by several levels.

Suddenly, those who had secretly wanted to black the PDE Industrial Alliance were dumbfounded.

No way, can it be played like this?

Just proved such a difficult problem just because of a disagreement?

How about we each take a step back, we will stop blacking, and you will also put away your proof, okay?

But obviously, unless time goes back, otherwise such a thing will definitely not exist.

So they can only bite their teeth and swallow it.

Of course, compared to these little blacks, the people on the domestic PDE Industrial Alliance side all laughed.

The result made by Xiao Yi is simply great news for them.

Not only did it effectively fight back against the rhythms of the previous period, but it can also bring an extremely huge driving force for their future development.

"I told you, Xiao Yi is amazing! Don't you know what to do with those foreign things?"

Tang Fucheng went straight to Shen Gensheng's door at HKUST and laughed.

Shen Gensheng also smiled and said with emotion: "He has never let others down. He solved such a difficult problem so quickly. He is really unique in the world."

Tang Fucheng smiled and nodded, but then he asked: "But I'm still curious. It stands to reason that his papers are all public. Why don't foreign countries set up their own PDE industrial alliance?"

"It's very simple." Shen Gensheng smiled. As a physicist specializing in rare earths, he has a deep understanding of China's industry.

"Because our industry is the world's number one, and we also have the most complete industrial chain in the world."

"If you want to train a model, you first need a lot of data, all kinds of different data, and only our country can provide data in various fields to train the model."

"As for foreign countries, if they want to do it, they have to discuss who should control the organization first, and then consider how to get the data."

"No matter what happens in the end, the model they train will not be as good as our model. I don't need to say more about what the market will choose at that time?"

Tang Fucheng was stunned. He didn't expect the reason to be so simple.

But then, he also sighed slightly: "After all, it depends on Xiao Yi to come up with it first."

Shen Gensheng nodded: "Yes."