Great Country Academician

At the MathoverFlow International Mathematics Forum, the paper Xu Chuan posted on the arxiv preprint website can be said to be the most popular topic in the past two days.

However, what is slightly different from the previous situation is that there are almost no top mathematicians among the people participating in the discussion this time.

Although most mathematicians are relatively "aloof", especially many older generation mathematicians who are older, they do not often use mobile phones and computers, let alone surfing the Internet.

But in any case, when faced with such a major issue as the Millennium Problem, and the person who disclosed the paper is still the semi-recognized first person in the mathematics community today, many top mathematicians in the past would basically stand up and express their opinions.

However, this time, the top leaders in the entire mathematics community seemed to have collectively lost their voices, with almost no movement.

Even Professor Terence Tao, the ‘surfing assistant’ who loved to express his opinions online in the past, did not appear this time, nor did he update his blog or Twitter.

This strange situation has also caused a lot of discussion and attention on major mathematics forums and websites.

After arxiv was restored, most people who paid attention to this matter also downloaded the paper. Regardless of whether they can understand it or not, at least they still have to 'pretend' online.

[By the way, what happened to Professor Xu’s paper? Can you give me an accurate answer? 】

[Professor Tao has not come out, and there is still no message. 】

[Wait a minute, a proof paper at the level of the Millennium Problem cannot be determined in a short while. Professor Tao didn't come out, maybe he was reading a paper. My friend is from the University of California. He said that Professor Tao has canceled the course for the next week. 】

[I downloaded and read the paper published by Professor Xu on arxiv. This paper seems to have nothing to do with the Riemann Hypothesis. I did not see any research ideas about the critical zone in it. 】

[The people above are just pretending to understand. The research direction of Xu’s thesis is the Riemann Hypothesis. 】

[I also read Professor Xu’s paper. He seems to have not followed the critical band research method, but has opened up another new path, returning the Riemann function to the π(x) prime number counting function, and then doing the equivalent Research looks like. 】

【? ? Give up the research idea of ​​critical zone? Does he think this road is dead? 】

【impossible! Critical band compression is currently the best way to advance the Riemann Hypothesis. I know that the idea of ​​regressing the π(x) prime number counting function has been studied a long time ago, but it doesn't work at all. It is more difficult than the critical band idea. big! 】

【Who knows? Top experts like them may have their own ideas. 】

The discussion on the MathoverFlow International Mathematics Forum is quite heated.

Some people think that many mathematicians have not spoken out, which is undoubtedly because they are not optimistic about Professor Xu's paper.

Others are on the supportive side and believe that the papers published by Professor Xu have been strictly confirmed based on his usual practice. If they are not 100% sure, they will not make the papers public.

This group of people is quite large. After all, Xu Chuan's good academic reputation has brought him many fans over the years.

Of course, more people are still silently waiting for news.

After all, it’s only been a few days?

The verification of this millennium mathematical problem is calculated in months or even years.

At a time when discussions are intense in major mathematics forums and online, as well as in major mathematics institutions or universities, a brand new paper has been quietly published on the arxiv preprint website.

"Each set of Jensen polynomials with the same "degree", except for the offset 0+N≤δ(X)≤1-1/2·N, all satisfy the requirements of the Riemann Hypothesis! 》

This is the title of the paper, and it is also the brand-new achievement Xu Chuan has made these days.

As for this title, he got the 'equivalent' answer by shrinking the Riemann function ζ back to Jensen's inequality and then studying it through subsigma algebra.

In 1927, Polya proved that the Riemann Hypothesis, a conjecture about the zero-point distribution of the Riemann zeta function, is equivalent to the zero-point distribution of another type of function - in other words, as long as a certain zero-point distribution of the other type of function is proved. These properties are equivalent to proving the Riemann Hypothesis.

Simply put, the zero-point distribution properties equivalent to the Riemann hypothesis can be studied through the Jensen polynomials associated with the Riemann zeta function.

As long as the offset and zero point number of the Jensen polynomial are expanded, the same result as the zero point distribution of the Riemann zeta function can be obtained.

Jinling, at the foot of Purple Mountain.

Xu Chuan, who had not seen the sun for more than a month, walked out of the villa.

The weather was still hot in mid-to-early October, but with the Purple Mountain at its back, the temperature at the foot of the mountain was not so hot that people couldn't even go out.

At the entrance of the courtyard, the unique Hongqi car was waiting quietly.

"Professor, where are you going?"

Opening the car door, Xu Chuan got in the car and replied smoothly: "Let's go to the Sichuan-Hai Materials Research Institute first."

If Brother Fan Pengyue hadn't been reporting information to him non-stop, to be honest, he would have almost forgotten that he had a materials research institute under his name.

This time, it was also because Brother Fan reported on the latest research progress in the direction of batteries. After four years of hard work by the lithium battery department of the institute, lithium-sulfur batteries finally made new breakthroughs.

This news was delivered by Senior Brother Fan Pengyue two days ago, but at that time he was completing the final steps of the Weak Riemann Hypothesis paper, so he ignored it.

Now, after the paper has been uploaded to the arxiv preprint website, he finally has time to go to the Sichuan-Hai Materials Research Institute to see what is going on.

To be honest, lithium-sulfur battery technology has not made breakthroughs until now, and in Xu Chuan’s opinion, it is a bit slow.

After all, as early as four or five years ago, he led a team at the Sichuan and Hai Materials Research Institute to successfully develop artificial SEI films.

This achievement directly solved the problem of the generation of lithium dendrites in lithium batteries, and the registered profession also brought him billions of funds.

The emergence of artificial SEI films has also triggered changes in the lithium battery industry. It can be said that countless companies or groups have swarmed into this field.

Although there are only two types of lithium batteries as a whole, 'lithium metal batteries' and 'lithium ion batteries', in fact, they can be divided into many series and types.

For example, the most common lithium-ion battery generally uses lithium alloy metal oxide as the positive electrode material, graphite as the negative electrode material, and uses a non-aqueous electrolyte.

According to the different lithium alloy metal materials of the positive electrode, it can be divided into lithium cobalt oxide batteries, lithium manganate batteries, lithium nickel oxide batteries, lithium iron phosphate batteries, and so on.

Batteries are an extremely huge market. From various electronic products such as mobile phones and computers to aerospace and other top fields, it can be said that no one can do without batteries.

A capitalist who doesn’t want to take a bite of such a huge market cake is not a qualified capitalist.

Four or five years have passed, and on the basis of artificial SEI films, countless different models and types of lithium batteries have been extended around the world.

The capacity and battery life of some lithium batteries have even exceeded those of the 'carboxymethylcellulose-lithium fluorocarbon' lithium battery developed by Xu Chuan himself.

This has also led to the Chuanhai Institute of Materials, a laboratory that initially became famous in the battery field, to come to an end.

If it weren't for the core artificial SEI film that no one can shake for the time being, and the high-temperature superconducting materials that still support its business, it is estimated that its existence is like a meteor streaking through the atmosphere, shining for a while, and then ending in glory.

Of course, this is also related to Xu Chuan not focusing his research and energy on the Sichuan-Hai Materials Research Institute.

For this research institute established a few years ago, except for leading the team to complete the artificial SEI thin film technology and high-temperature copper-carbon-silver composite superconducting materials, he has almost never taken care of other things.

But let it go, the general research direction of the Chuanhai Institute of Materials has always been formulated by him.

For example, this breakthrough lithium-sulfur battery technology, the lithium-air battery still being developed in the laboratory, the research and development of superconducting materials, and a series of technologies such as the synthesis of starch and carbon compounds from carbon dioxide are all directions designated by him personally.

It's just that the time required for these technological breakthroughs may be a bit beyond his imagination and planning.

Originally, Xu Chuan thought that after the completion of artificial SEI thin film technology, lithium-sulfur batteries would be completed in two or three years at the latest.

As a result, it has been four or five years since then, and there have been some changes.

If only one laboratory at the Chuanhai Institute of Materials was researching this, it would be nothing. Four or five years would be nothing.

Now in the battery industry around the world, it can be said that those with investment are almost all researching lithium-sulfur batteries and lithium-air batteries. After all, lithium-sulfur batteries and lithium-air batteries are phased development steps of lithium-ion batteries.

As a result, in four or five years, no company in the world has heard of a breakthrough in this field.

In the field of lithium battery research, the speed of major laboratories and enterprises is much slower than Xu Chuan imagined.

At the same time, when Xu Chuan rushed towards the Chuanhai Materials Research Institute, as expected, topics related to the Riemann Hypothesis were detonated again.

Less than half an hour after Xu Chuan posted the proof paper of the weak Riemann hypothesis on arxiv, mathematicians around the world once again turned their attention to this preprint website.

Fortunately, the Los Alamos National Laboratory, which is responsible for managing and maintaining the website, responded immediately and added all the backup servers. This way it could barely maintain the influx of traffic and allow many Scholars can see relevant papers as soon as possible.

At the same time, at the MathoverFlow International Mathematics Forum, the sound of discussion came like a tsunami.

【arxiv! Professor Xu! Proof of the Weak Riemann Hypothesis! 】

【ah? 】

【God! It’s unbelievable, it’s only been a few days? ! 】

[Judging from the time of his previous upload, the interval between the two proofs of the weak Riemann hypothesis is less than a week! Only six days and nine hours to be exact! 】

【His~! Isn't this too fast? 】

【Isn’t it right? The paper Professor Xu uploaded to arxiv is not about the study of Jensen polynomials and π(x) prime counting functions? 】

[I suggest you study mathematics carefully before coming here. 】

[The Jensen polynomial is named after the Danish mathematician Jensen's study of it. It has the same zero-point distribution properties as the Riemann hypothesis, that is, the zero points of the Jensen polynomial are all real numbers. In other words, as long as you can prove that the zero points of the Jensen polynomial are all real numbers, you have also proved the Riemann Hypothesis! 】

[If I remember correctly, this equivalent proposition seems to have been even more difficult to deal with than the Riemann Hypothesis itself for a long time. 】

[Yes, because there are infinite groups of Jensen polynomials - distinguished from each other by so-called "degrees", and each group has infinite numbers - distinguished from each other by so-called "offsets". To solve It is probably more difficult than the Riemann Hypothesis on the current basis. 】

[At least the Riemann Hypothesis has been proved by the critical band contraction method, which has also pushed it to No(T)\u003e0.4N(T). 】

On the MathoverFlow mathematics forum, related discussions are extremely intense.

However, most of the topics focused on the proof that Xu Chuan could complete the weak Riemann hypothesis so quickly and the route and direction of his research.

As for the correctness of this paper itself, not many people discuss and study it.

After all, after the emergence of the paper proving the weak Riemann hypothesis, scholars who still have time to surf the Internet are basically 'stupid students' who cannot understand the paper.

Those experts who can understand the paper are basically immersed in the paper at the moment.

On the other side, in the United States, California, in a villa not far from the University of California, Los Angeles.

Terence Tao, who was immersed in studying the Riemann Hypothesis using the tools created by Xu Chuan, was suddenly awakened by the ringing of his cell phone.

Frowning, he picked up the phone from the desk beside him. It was his assistant calling. He slid his finger across the screen and answered the call.

"Wyatt, didn't I tell you not to disturb me if you have nothing to do?"

On the opposite side, the female assistant's voice came quickly.

"Sorry, Professor Tao, this is what you ordered. On arxiv, Professor Xu, who you asked me to follow, uploaded a new paper."

Hearing this, Tao Zhexuan was stunned for a moment, and his breathing became faster. He quickly asked with a trace of luck: "What is Professor Xu's thesis about?"

"As for the Riemann Hypothesis, judging from the title of the paper, it seems to be a proof paper for the weak Riemann Hypothesis."

After hearing these words, Tao Zhexuan was silent for a while, then threw away the pen in his hand, fell to the back of the chair, and stared silently at the original color wooden door not far away.

Just when the female assistant almost thought the call had been hung up, Terence Tao said, "Please transfer the paper to my mailbox."

"Okay, Professor"

After hanging up the phone, Tao Zhexuan stared at the ceiling of the study room silently for a long time, with a complicated expression on his face.

He originally thought that his speed was fast enough. In this week, he used the tools and papers to continue to study the breakthrough of the Riemann Hypothesis and had some results.

It can even be said that he has seen the weak Riemann hypothesis. Give him another month, maybe he can solve this problem.

However, in just one week, that person had already solved the weak Riemann hypothesis.