So he was happy to let Tao Xuanzhi realize this.

"What you said makes me want to communicate with him. If he is also concerned about the prime number problem, I don't know if he will see our paper and what his evaluation will be." James Maynard said with a smile.

For people like them, too much energy has been spent on the study of prime numbers. Who doesn't want to be the first to solve those problems that have puzzled people for hundreds of years?

"Yes, Professor Zhang, maybe you can help me contact Qiao Yu. I am very interested in his idea. If possible, maybe we can cooperate."

Tao Xuanzhi suddenly spoke.

He just made some simple deductions in his mind based on what Zhang Yuantang said, and suddenly found that Qiao Yu's idea was indeed possible to succeed.

He still didn't know how Qiao Yu solved some problems, but there was no doubt that this was a brand-new mathematical idea.

A more unified mathematical expression makes the proof process of number theory clearer. It is no longer necessary to build a complex system for a specific problem and use different types of modal spaces to represent different problems...

Qiao Yu is ambitious! He wants to construct a unified theory of mathematics in his own way. Tao Xuanzhi even suspects that Qiao Yu wants to replace the Langlands program. Yes, just use his modal space theory to build one.

Replacement.

This does not seem impossible, because although Qiao Yu's method is also abstract, it is not as difficult to understand as Langlands' program.

In particular, the geometricization of number theory problems can make some obscure number theory problems more intuitive in the modal space.

"I can ask that kid, although he is only sixteen years old... How should I put it, he doesn't resist communication, but he has his own way of choosing collaborators."

Zhang Yuantang said with a strange expression.

In fact, ever since he learned about Qiao Yu's subject, he has been paying attention to the related progress. Of course, the result surprised him.

"Paranoid?" Harvey Guth, who had been silent on Qiao Yu's issue, asked.

He knew the least about Qiao Yu. He had only heard about some things that happened at the World Congress on Algebraic Geometry, so he had not expressed his opinion just now.

"It's not paranoia. To be precise, it should be self-confidence. I think he probably thinks he can complete this project on his own. So when he chooses collaborators, he likes to choose people who are closer to him than to the subject.

Helpful people."

Zhang Yuantang shook his head and corrected himself.

Well, this is understandable, and it can even be said that geniuses generally have this confidence.

Tao Xuanzhi also laughed and joked: "Indeed, if the main framework can be proved by itself, the rest will be detailed verification work, and it does not require skilled collaborators.

But I'm looking forward to what kind of results he can produce. Professor Zhang, you may make me unable to sleep well for a while, especially considering that someone can really solve many complex number theory problems at once."

Zhang Yuantang smiled and did not answer.

Not only him, but the other two people also felt a sense of urgency.

If someone really proves a series of difficult problems about prime numbers in an unprecedented way, this is not entirely good news for many mathematicians who have been studying prime numbers.

After all, no one wants to be a backdrop. If you don’t believe it, you can ask Sam and Frank.

"It's okay, let's ask first. I have never had any contact with Qiao Yu. It might be rude to send him an email rashly. Please, Professor Zhang."

Tao Xuanzhi thought for a while and said.

Zhang Yuantang smiled and nodded in agreement.

Discourtesy is just an excuse, these geniuses are proud.

…

Huaxia, Yanbei University.

At this time, Qiao Yu was indeed doing work that the professors on the other side of the ocean were concerned about.

He can ignore the verification work, but there are some tasks he needs to do first.

What Qiao Yu is doing at this time is to transform a series of problems he intends to solve using the modal space framework from classical expressions into modal space expressions.

For example, the classic expression of the twin prime conjecture is that there are infinite pairs of prime numbers (p, p+2), among which the prime numbers p and p+2 are both prime numbers.

Then the expression in multimodal space must be transformed into three questions.

1. In the modal space M, there are infinite pairs of modal points (r_p, r_p+2), such that the modal distance d_m (r_p, r_p+2) satisfies the fixed constraints.

2. The modal density function ρ_m(r) accumulates to infinity in the modal space region that satisfies the twin prime condition.

3. The distribution of twin prime pairs forms equally spaced points on the modal path Γ, and shows periodicity and symmetry in the modal space.

To put it simply, a classic number theory problem is decomposed into three geometric problems.

If he can prove these three geometric problems in modal space, it means that he has completed the proof of the twin prime conjecture.

Of course, the premise is that his axiom system of generalized modal number theory can be widely recognized by the mathematical community, and it can be proved that this axiom system can indeed convert between geometry and number theory, and always maintains verifiability.

But then again, there are people who do the verification work, and he is the only one who does the transformation work himself.

After all, transforming the problem requires an extremely clear understanding of the axiom system and extremely high mathematical insight.

In the same way, the same steps are required to solve the Riemann Hypothesis. First, convert the classical expression into a geometric expression under this framework, decompose the problem, and then prove it one by one.

This step actually went very smoothly.

Even the transformation of the Riemann Hypothesis is simpler than the Twin Prime Conjecture.

Moreover, in the classic interpretation, all zero points are distributed on a line. The distribution in the modal space is on a hyperplane.

Of course, the completion of the conversion does not mean that the problem will be solved immediately. There are still many things to be defined to achieve this step.

For example, geometric tools such as modal density, convolution, etc. In short, after geometricizing the problem and modalizing it, Qiao Yu will know what tools are needed to solve the problem, and then go to the framework to prove and transform them one by one.

Qiao Yu didn't think what the professors opposite him thought, or even what Director Tian and Mr. Yuan thought. He had no intention of building the entire theoretical framework first.

His plan is to build it on demand.

To determine what tools are needed to prove the upper bound conjecture, first derive the required tools in the form of theorems, and then prove the problem.

Then we will look at what new tools are needed for the twin prime number conjecture, and then proceed to the next stage of derivation, and then start to prove...

The advantage of doing this is naturally that it can publish the most articles, and others can't even say that he is doing nothing.

Whether it is adding new tools or solving new problems, it is the favorite content of the mathematics world. Even the Langlands Program is also composed of many sub-conjectures.

This is actually the reason why Qiao Yu has no interest in appraising funds. After all, even if he gets the grant, the money is not in his personal account.

Instead, it will be transferred to the account of the research center, and then a sub-account will be divided below. When money is needed, it can be transferred directly. Not to mention that the funds allocated to pure mathematical theory are generally not much.

Mainly because of reputation. But Qiao Yu feels that he is not so anxious to seek fame. There is no need to be so anxious to build the framework and benefit the mathematics community.

After all, China's research progress in theoretical mathematics is far behind that of the West. After his new axiom system is fully contributed, there is a high probability that it will be the first to use it in some cutting-edge proposition proofs.

After completing these basic tasks, Qiao Yu stretched out and planned to ask other people about their work progress on WeChat.

Yesterday, he specially created a group chat and brought Qiao Xi, Xue Song and Chen Zhuoyang into a discussion group to facilitate his assignment of tasks.

Then he saw a new email notification appeared in his work mailbox, and it was Professor Zhang Yuantang's email, so he subconsciously clicked on it.

Even though he is somewhat famous in the mathematics community now, he doesn't actually exchange many emails on weekdays.

The main reason is that there is a lot of email communication within Professor Li’s research group at Huaqing.

As for other big bosses, they only occasionally send emails to discuss some issues. This is not only because everyone is busy, but also because Qiao Yu has not developed the habit of communicating by email.

"Qiao Yu:

We met in person. Today I was fortunate enough to be invited by Professor Xuanzhi to discuss his latest article "New Progress in Large-Value Estimation of Dirichlet Polynomials" with Professor Guth and Professor Maynard, and I felt that I gained a lot.

I remembered that when I was at Yanbei, you once said that you were very interested in the prime number problem, so I recommended this article to you. The article has been published on the preprint platform arXiv, and the authors are James Maynard and Harvey Guth.

After discussing the article, I mentioned to three professors the axiom system of generalized modal number theory that you are trying to construct. Professor Tao Xuanzhi was very interested after hearing this.

In recent years, Professor Xuanzhi has also been trying to combine the analytic theory of prime numbers with the extreme value principle in combinatorial number theory to study the characteristic relationship between prime number distribution and modular form, and to search for properties similar to prime numbers in general sequence and functions.

And has made many achievements. For example, he developed the genetic sieve method to analyze the role of sieve method in complex sets, especially for constructing prime number sets with specific properties.

He is also committed to promoting the Polymath project, reducing the distance between prime number pairs from 70 million to less than 600. Therefore, he hopes to establish cooperation with you and jointly discuss the geometricization of prime number problems.

If you are also interested, please let us know the convenient time or communication method.

Looking forward to seeing you, and wishing you Shunqi!

Zhang Yuantang."

After quickly scanning the letter, Qiao Yu subconsciously opened the web page and searched for the names Tao Xuanzhi, James Maynard, and Harvey Guth...

Yes, Qiao Yu is not only a layman in mathematics, but also a layman in academia. He really doesn’t know many big figures in mathematics.

However, he knew that if he could invite Zhang Yuantang casually and ask Professor Zhang to write this letter to him specifically, he must be a big shot in the mathematics community.

This is indeed the case.

A quick search revealed two Fields Medalists. There is also one who, although he has not won the Fields Medal, seems to have a fairly low status in the world of mathematics.

The most important thing is that they are different from the Fields Medalist whom I met at the World Algebraic Geometry Conference last time. Both Tao Xuanzhi and James Maynard are still very young.

Tao Xuanzhi has just turned fifty this year, and James Maynard is even younger, still one year short of forty.

Qiao Yu could tell that Tao Xuanzhi was very active in the mathematics community. Last year, he teamed up with more than 60 mathematicians to develop questions and launched FrontierMath, a mathematical benchmark used to test the mathematical ability of artificial intelligence.

Simply put, FrontierMath is an original question bank. The benchmark contains hundreds of original and extremely challenging mathematical problems, covering the main branches of modern mathematics, such as number theory, real analysis, algebraic geometry, category theory, etc.

Then let the most advanced AI go to the question bank to answer the questions...
To be continued...