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Berlin, Germany.

About fifteen years ago, the International Mathematical Union established its headquarters in this historic city.

The headquarters is located in the city center.

The stated purpose of establishing the headquarters is to keep pace with the times, improve the organization's operational efficiency, and enhance its support capabilities for global mathematical collaboration.

Of course, having a headquarters can be useful in many situations. At least it provides a place to store files on various funded projects.

The reason for setting up its headquarters in Berlin is that it can receive funding from the German Federal Ministry of Education and Research and the Berlin State Government.

In recent years, as China's influence in the mathematics community has grown, the number of Chinese faces at the headquarters here has also been increasing.

After all, the proportion of Chinese mathematicians in the council, the highest governing body of the alliance, is increasing year by year.

With more people, there is naturally more say. In particular, Chinese mathematicians have always been very united when dealing with foreign countries in recent years.

The reason was actually that those who were not united were all kicked out. This is naturally thanks to Qiao Yu, although he is currently only a senior member of the International Mathematical Union and does not hold any official position within it.

However, most of the Chinese mathematicians who are able to enter the Council of the International Mathematical Union and its various branches have made outstanding contributions to the study of Georg algebraic geometry.

Therefore, when expressing opinions internationally, people often have no choice but to blindly follow the lead of others.

Especially when there are controversies, they often have to rely on Qiao Yu to speak on their behalf.

Qiao Yu also stated on more than one occasion in public that while Chinese mathematicians can fully discuss their opinions internally, they must remain united when expressing them externally.

A few years ago, two prominent figures in the Chinese mathematics community actually got into an argument at a high-level mathematics forum over some trivial research matters.

It caused quite a stir at the time. It was even more talked about than the falling out between Yuan Longping and his disciple Tian Yanzhen.

The result was also very touching.

It is said that Qiao Yu, along with two of his students, meticulously reviewed all the papers authored by these two academic giants, starting from their doctoral studies...

Then Qiao Yu even wrote to the editorial offices of two first-tier journals to discuss the matter. As a result, two papers by each of the two big names were taken down.

One of them had a very good chance of becoming an academician, but that chance was dashed because of this incident.

Since then, almost all Chinese mathematicians have been exceptionally polite to their own people when they are abroad.

After all, this can't be called making an example of someone; it's more like making an example of someone else...

Even the Committee on Mathematical Standards, one of the three standing committees of the International Mathematical Union, is no exception.

It's important to know that the Mathematics Standards Committee is definitely the most discordant of the three standing committees, and arguments often occur between them.

Mathematicians from different countries and with different academic backgrounds come here and, in most cases, they are unwilling to compromise on mathematical research methods, educational methods, and the standardization of symbols.

After all, this represents whether the research results of a group of people are recognized by the world.

The core members of this year's Mathematics Standards Committee consist of eighteen members. Among them are five Chinese mathematicians, a record high.

In addition, China currently has one temporary representative and two observers.

In the development of a series of mathematical standards, in addition to the core members of the committee, these representatives and observers are also important.

Especially when it comes to international cooperation.

Unfortunately, if the standards are set too outrageously, it might lead some people to form their own schools of thought and stop participating in the alliance...

Of course, it's impossible to follow the ideas of any one country completely. In many cases, it even involves politics and power struggles.

After all, the influence of the academic community, especially the basic science community, is extremely important to many self-important major powers.

This is often how power and influence are accumulated.

When a group of people who possess cutting-edge knowledge need the recognition of these major powers, their thoughts and opinions will naturally become biased.

Specifically, in the case of China, it's roughly this: China couldn't compete in the past, and now China is too lazy to compete.

Qiao Yu pioneered the axiomatic system of generalized modalities, which, along with Qiao algebraic geometry, has largely unified mainstream mathematical notation.

For the new generation of young people willing to devote themselves to the study of algebraic geometry, the axiomatic system of generalized modalities is almost a required course.

Although mathematicians from different regions still use different symbols to represent the same concepts, this type of mathematician is becoming increasingly rare.

The Generalized Modal Axioms will be formally incorporated into the Standard Reference Theorem set at the International Congress of Mathematicians in 2030, with the number ICM-2030-Thm6.18.

From that time onward, it signified that the mainstream mathematical community worldwide had recognized the generalized modal axiomatic system's unification of numerous mathematical symbols.

Therefore, if there is no internal competition, the Mathematical Standards Committee has become a place for many mathematicians in China to build their seniority.

To some extent, Qiao Yu's existence was a painful blow to many ambitious mathematicians of his time in China.

Or, to put it another way, it can be directly extended to the global mathematics community.

After all, when someone has a precipitous lead in the industry, it makes everyone else look dim and insignificant.

Many mathematicians even suspect that when future generations look back on the development of mathematics in the next century, they will probably only remember Qiao Yu's name.

Even top-tier mathematical geniuses like Peter Schultz and Tao Xuanzhi, who are highly regarded in the Western mathematical community, can probably only be categorized as "other".

It's not because Qiao Yu solved the century-old problem of the Riemann Hypothesis, but because the influence of the generalized modal axiomatic system is so profound.

With the help of this system, many mathematical research institutions around the world have made great progress in their research on many difficult problems in recent years.

For example, a team has already proven the Four Color Theorem using the Cho's algebraic geometry method. However, the paper is currently under review.

However, according to the reviewers, the chances of it being approved are very high.

Qiao Yu was originally one of the ideal reviewers, since the method he pioneered was used, but unfortunately, Qiao Yu rejected it outright.

For other mathematicians, being able to review papers on such difficult problems is itself an affirmation of their abilities.

At the same time, they can also be the first to access and verify new methods that interest them.

But for Qiao Yu, reviewing manuscripts is just asking for trouble.

This is probably one of the reasons why Yuan Zhengxin and Tian Yanzhen felt that Qiao Yu was having too easy a time recently.

However, everything was about to change from this point on.

... Zhu Zhengze arrived at the headquarters of the International Mathematical Union early in the morning.

This building is located in the center of Berlin. It belongs to the Erstrasse Institute for Applied Analysis and Stochastic Research.

As members of the Mathematics Standards Committee, mathematicians certainly don't have time to sit in an office like ordinary people.

However, the committee also has many miscellaneous tasks to handle, such as coordinating and guiding academic activities.

These miscellaneous tasks are highly specialized, and ordinary people simply cannot handle them, so a rotation system was adopted.

Each committee member is required to spend some time here every four years to complete routine administrative tasks and make professional decisions.

For the next two weeks or so, it was Zhu Zhengze's turn to be on duty.

After sitting down in his office and making himself a cup of tea, Zhu Zhengze opened his email.

Although I have to work on the committee, as a doctoral supervisor, I can't completely ignore things at the university.

Fortunately, with the internet so readily available these days, most issues can be resolved via email.

Furthermore, the International Mathematical Union recently replaced the office computers of its three main committees and secretariat with Huaxia's Taiji series computers.

With the help of the updated meeting system that supports multi-dimensional presentations, it is easier to hold small meetings online, and information security can also be improved.

Adding holographic reality would make it even more realistic. The only inconvenience is the time difference.

However, Berlin's daylight saving time is only six hours different from China's.

He arrives at the office promptly at nine o'clock every morning, which is three o'clock in the afternoon in China, making communication quite convenient.

Zhu Zheng opened his email as usual and immediately saw the title highlighted in red.

He glanced at the sender and saw that it was an email from Academician Tian. He immediately opened the email.

There's no way around it; Tian Yanzhen's current status in the Chinese mathematics community is truly unique.

Not only because he was considered by many to be just one step away from winning the Fields Medal, but also because he had a student named Qiao Yu.

In China, it's not a big deal to offend those who do mathematical research, but you absolutely cannot mess with the big shots in the Huaqing and Yanbei line.

Zhu Zhengze thought this was a good idea. Because he was part of the Yanbei faction and belonged to the vested interests.

Yenbei University also played a role in his selection to the committee.

Therefore, they naturally have even greater respect for someone like Tian Yanzhen, a big shot from their own school.

"Professor Zhengze: The attachment contains Qiao Yu's latest research findings. You need to carefully study it in conjunction with the letter from Tao Xuanzhi that sparked widespread discussion recently. It would be best to hold an impromptu meeting to discuss it. Feel free to call me anytime if you have any questions..."

The email contained only a few short sentences.

But that was enough to gain Zhu Zhengze's attention.

After all, Tian Yanzhen made it very clear that the attachment contained Qiao Yu's latest research results!
The open letter that Tao Xuanzhi forwarded to his blog some time ago has been the subject of much discussion in the mathematics community.

As far as he knew, several mathematical research institutes had already begun to tackle the problem of viscosity terms.

After all, partial differential equations have always been a popular area of ​​mathematical research.

If Qiao Yu's method is indeed valid, it could not only solve the Navier-Stokes equation problem, but also unify equation processing methods in multiple fields, and even provide new numerical simulation methods.

For example, it can restructure Navier-Stokes partial differential equations in a completely new way, transforming previously unmanageable nonlinear terms into computable geometric invariants.

To reiterate, the greatest significance of solving a difficult mathematical problem is not the solution itself, but rather the creation of many novel mathematical methods and tools for future generations, allowing the discipline of mathematics to continue to advance.

For many mathematicians, the greatest wish in their lives is probably to make mathematics truly relevant to the real world.

While this is work that physics needs to do, what if we could truly use mathematics to systematically take over the real world?

Zhu Zhengze couldn't bother with other emails at this point. He took a deep breath and downloaded the attachment directly.

Good heavens, a whole bunch of formulas piled up together. Each formula only has a brief explanation of one or two sentences.

For those who haven't studied the generalized modal axiomatic system and Georg algebraic geometry, looking at these formulas is probably no different from reading a book without words.

Fortunately, Zhu Zhengze began researching this field six years ago. Currently, Huaxia is one of the most in-depth researchers of Georg algebraic geometry.

His paper, “Serre Duality Theorem for Q-Condensed Layers and Cho's Cohomology,” was directly selected as a core reference for the ICM-2030 conference report, and he was invited to give a 60-minute presentation at that mathematics conference.

Another paper, "The Rigid Theorem of p-adjournals and the Quantumization of Langlands Correspondences," has been listed as essential reading for doctoral students in arithmetic geometry by many mathematics schools, including Yanbei, Huaqing, and Princeton.

This is also why he joined the Mathematics Standards Committee.

Although Qiao Yu has not focused on mathematics in recent years, many mathematicians like Zhu Zhengze have been helping him advance and enrich the entire theory.

In particular, the standardization process is inseparable from the efforts of countless mathematicians like Zhu Zhengze, who are in their prime.

Therefore, once the attachment was downloaded, Zhu Zhengke, who was focused on thinking, got into the zone much faster than Tian Yanzhen.

This is clearly an extension of the thinking that followed Qiao Yu writing that letter to Tao Xuanzhi.

From the first formula given by Qiao Yu, we can tell that Zhu Zhengze was working on solving the problem of viscosity terms.

Moreover, the way they think remains as unconventional as ever...

Zhu Zhengze was also pondering this problem during this period. Of course, Tao Xuanzhi made this letter public to involve more mathematicians and pool their wisdom to solve this difficult problem.

But at this moment, Zhu Zheng felt that his thinking was still too traditional!
From Reynolds number analysis to boundary layer approximation, then regularity estimation, and attempts to perform singular perturbation expansion...

However, Qiao Yu completely rejected these traditional approaches and instead took a different path, directly parameterizing the viscosity term geometrically.

A more specific explanation is that Qiao Yu directly reinterpreted the viscosity term in the traditional Navier-Stokes equations.

A fiberized neighborhood centered at x is created on the manifold, so that the viscosity coefficient is no longer a fixed constant, but dynamically coupled with the local geometry...

This step allows the original equation to be directly transformed into a system of recursive equations of an infinite-dimensional Lie algebra, with each recursive level corresponding to a vortex structure of different scales...

In this way, if a certain solution is required, the process directly proceeds to the Nth term, which automatically includes the Nth-order nonlinear effect...

Zhu Zhengze was completely stunned after only seeing about half of the formula!
Honestly, at this moment he couldn't imagine what kind of brain could come up with such a way to simplify the complex and solve this problem that he thought would plague the world for at least another century!

Well, even though he hadn't finished reading it yet, just by looking at this thought process, he was already convinced that Qiao Yu had definitely solved the problem he had just raised himself!
Is this some kind of self-questioning game? (End of Chapter)