Scientists, or intellectuals, are a very special group. They may not have a lot of wealth, but in a sense, a large part of the growth of wealth in this society is based on the efforts of these people.

If we must make an analogy, they are like the engine of social wealth growth. They do the most tiring work in areas that people cannot see.

Just like after a normal family buys a car, except for maintenance or repairs, no one would deliberately open the car hood every day to see what the engine looks like.

Yes, everyone knows that the engine is important, but no one bothers to take a look at it when nothing happens.

Because most ordinary people don't know how the engine works or its principles. They just need to know that the thing can still be used and is not broken.

Mathematicians are like the engines of academia. They do the hardest and most tiring work. In fact, most of the time, everyone's attention to the mathematical community is limited to whether there are any good tools that can be used.

Even for the same scientific research funding application, the research funds for mathematics are less than those for other sciences.

Such as physics, chemistry... After all, the latter requires various experiments. Laboratory investment and various instruments require money...

So in a sense, mathematicians don't have many bright moments.

After all, only a few people can create the ultimate romance with a pen and a piece of paper.

Most people can actually become famous if they can make some improvements based on other people's research results.

Yes, in fact, there is no need for Chen Zhuoyang to feel ashamed.

Because the nature of mathematical research determines that major breakthroughs are uncommon.

Ninety percent of mathematicians' jobs are to refine existing theories or solve local problems. Of course, this does not mean that these seemingly inconspicuous results are unimportant.

Because these accumulations may give those geniuses a sudden flash of inspiration.

Various reasons also determine that for most mathematicians, being able to give a 60-minute report at an important meeting is already the highlight of life.

After all, this is not a branch venue, and the time given is very long. And there are really many people here today, and it even seems to be more people than at the last World Congress on Algebraic Geometry.

Fortunately, Qiao Yu has become accustomed to being an opinion leader among the crowd.

"The distribution of prime numbers is one of the core issues in number theory research, and its spacing problem has always been an unsolved mathematical problem. In actual research, mathematicians have proven that the upper bound of the prime number spacing can be restricted within a specific range.

Professor Zhang Yuantang's pioneering work reduced the upper bound of this distance to 70 million, and through the efforts of mathematicians around the world, it was reduced to 246. What I want to report today is based on the axiom system of generalized modal number theory, a

New geometrization methods to solve related problems.

By mapping the prime distribution into modal space, and using geometric tools such as modal density functions, modal paths, and modal convolution, we demonstrate that the bounded distance between primes can be further reduced to an upper bound of 6..."

It starts with a simple introduction.

First of all, let everyone know how this work is carried out. Without the cooperation of Lot Dugan, this aspect will be very troublesome.

Because the abstract "Based on the axiom system of generalized modal number theory, a new geometric method is derived" can make countless people in the audience confused.

But let’s not talk about all of them now, at least more than 80% of the participants will not be confused.

Because after the publication at noon yesterday, the organizer, who had been prepared for it, had already started to move.

More than two thousand papers that had been printed out in advance were distributed through the hosts of each session before dinner.

At least every registered member of the Mathematical Society has a copy. If there is no interest in this proposition, the paper will be given directly to those who are interested.

Some people directly borrowed the paper and printed a copy.

Hotels that hold such academic conferences will thoughtfully arrange printing services. Of course, if the internal staff is too busy, there will also be dedicated personnel who will send them outside for printing.

Although one night may not be enough for all participants to fully understand the paper, at least most people already know the general concept and have a preliminary understanding.

At the same time, sixty minutes is already the longest time for an academic report at a top conference, but it is actually not enough for Qiao Yu to introduce the generalized modal space framework to everyone. So after briefly talking about the abstract,

Qiao Yu immediately entered the state.

"...The modal path Γ is a continuous curve in the modal space, which is used to describe the distribution trajectory of prime numbers in the geometric space. In order to reduce the modal point spacing, the following optimization construction of the path is required:

As you can see on the big screen, this formula, where T is the path period, is used to ensure that the path has a periodically repeating structure in the modal space."

"It can be seen from the above that the curvature and distribution of the path Γk are driven by the local high-value area of ​​the modal density function ρM(r), and Γk passes through the local extreme point of the modal density function, ensuring path coverage in high-density areas.

The modal path has geometric symmetry. Assuming symmetric mapping: M→M, it satisfies:

Through the above optimization structure, the high density, periodicity and symmetry of the modal path Γ can be guaranteed..."

…

"Do you understand?" Zhang Yuanling, who was deep in thought, was interrupted by a heavy line beside him.

First he nodded slightly, then shook his head.

Well, it doesn't actually interrupt his train of thought, it can only be said to interrupt his idea of ​​further exploration.

To be honest, I didn’t fully understand it!

But this can't be blamed on him. In fact, Zhang Yuanling believed that at least 90% of the people at the meeting could not understand what Qiao Yu was talking about at this time.

It’s not that everyone’s level is not good enough, or their understanding is not good enough. The main reason is that what I’m talking about today is too special. It’s a brand new theoretical framework, and it’s only been one night that everyone has been exposed to this framework.

Before you fully understand the framework built by Qiao Yu, you can imagine how difficult it is to understand the content of this paper.

So while listening to the report, Zhang Yuanling kept recalling some conclusions and theorems in another paper.

For example, knowledge points such as the definition of modal space, modal density function, construction of modal paths, modal convolution formulas, etc...

Then use these unfamiliar knowledge points to deduce what Qiao Yu is talking about. These have to go through a very complex transformation process in the human brain.

It was easy to talk when you were young, but as you get older, your brain is not as flexible as it was when you were young.

"You don't understand either, so I feel relieved. After all, I have reviewed his ideas before." Zhongxing said in a joking tone.

It's a joke indeed.

If Zhang Yuanling knew at that time that Qiao Yu could complete this axiom system to this extent in more than two months, he would not have questioned anything at all and directly approved it.

But now it can only be said that it was a miscalculation!

"Tian Yan is so lucky that I don't know how to describe it." Zhang Yuanling said nonchalantly.

He knew that Chongzhongxing had no ill intentions. The two of them had a good relationship, and they had discussed it together in private yesterday. If Chongzhongxing came to review Qiao Yu's project document, there would definitely be doubts.

It can only be said that Zhang Yuanling was quite unlucky this time.

"Hey...it's not just good luck. After all, he is at Yanbei University." Zhongxing sighed.

Zhang Yuanling was silent.

Yes, probably only Yuan Zhengxin has the qualifications to say that Tian Yan is really lucky, and even Yuan Zhengxin is a little bit worse.

The reason is naturally the siphon effect of prestigious schools.

When more than 80% of the competition students and candidates in the society, as well as the parents, regard Yanbei and Huaqing as their first choices, other prestigious schools want to compete with these two schools for the best seedlings. Indeed, It's too difficult.

Especially a youngster like Qiao Yu who is already in his prime at the age of sixteen.

Although Shuangdan University is also a famous school and its School of Mathematics is ranked among the best in the country, it is still a little behind compared to Yanbei and Huaqing.

Seeing that Zhang Yuanling did not speak, Zhongxing sighed and said: "Hey... those were two papers yesterday. In the next at least thirty years, I think we can look forward to China having a say in the world of mathematics."

Zhang Yuanling smiled, but the smile was not so cheerful.

Just listening to the second half, it is obvious that this is a compliment, but since he is an old colleague, of course he can understand the meaning of it:

At least in the next thirty years, there is no need to consider challenging the status of Yanbei and Huaqing in the Chinese mathematics community...

Whatever ambitions you have, you can put them aside for now. These are all conceivable.

With this realization, Zhang Yuanling suddenly thought of a possibility and couldn't help but said: "Old Shen, what do you think about next year's Fields Medal..."

Zhong Xing was stunned for a moment, then shook his head slightly and said with emotion: "This... shouldn't be possible, right? After all, he is still too young, he will only be seventeen next year.

But we can look forward to that time in 2030. He will only be 21 years old at that time. But one thing I am sure of is that he will definitely be considered for many awards next year."

Zhang Yuanling nodded, indeed... seventeen years old, this age is too young.

This is definitely one of the situations that the International Mathematical Union jury needs to take into account.

Seventeen years old really allowed Qiao Yu to win the prize. How many years will he rule the world of mathematics? Not to mention that every year there are many candidates who are stuck at 40 years old. If they exceed 40 years old, they will never have a chance.

Moreover, the Fields Medal Jury Committee should consider leaving some expectations for the future... If Qiao Yu really wins the award next year, the topic of the youngest Fields Medal winner will probably be completely ended.

This also made Zhang Yuanling somewhat emotional. Who could have imagined that one day, the reason that prevents a mathematician from winning the Fields Medal is that he is too young?!

After all, this thing is too outrageous.

"So, Professor Zhang, after this meeting, I think you can choose a time to chat with Qiao Yu... Besides, he withdrew the project on his own last time, so it actually has little to do with you."

Zhongxing looked at the young man on the stage who was still talking with a complicated expression and said casually.

Zhang Yuanling thought for a while, then nodded inconspicuously, and said: "Let's finish the paper first. It's always a bad idea to rush into it. There must be common topics."

Zhong Xing also nodded. He could understand Zhang Yuanling's concerns. They were all decent people, so they couldn't completely lose face, right?

…

In the front row, Yuan Zhengxin didn't care much about what Qiao Yu said. After all, he had read the paper countless times and had communicated with Qiao Yu.

The narration at the report meeting also followed the paper, and Qiao Yu's thinking was clear at every step.

If you have this time, why not mention more of his students.

"Yesterday you said that Qiao Yu had already told you about the idea of ​​this paper?"
To be continued...