Great Country Academician

Chapter 698: Challenge from the world’s top mathematicians!

Just as Fefferman thought, at this moment, arxiv has been directly squeezed and paralyzed.

Just when Xu Chuan uploaded his paper to Arxiv, within an hour, the arxiv preprint website was directly overwhelmed by the huge traffic pouring in from all over the world.

Although judging from the time when the Riemann Hypothesis was proposed, it has only been more than 160 years since Bornhard Riemann proposed it in 1859. It is not the longest among the many conjectures in the mathematical world. There are many conjectures about its further past.

For example, Goldbach's conjecture was proposed as early as 1742. It has been nearly three hundred years, but it still has not been solved.

But in the mathematics world of the 21st century, if you want to say which mathematical conjecture has the greatest impact on mathematics, there is no doubt that it is the Riemann Hypothesis!

Research around it has greatly promoted the development of analytic number theory and algebraic number theory, and a series of important problems and conjectures in the fields of function theory and number theory are also directly dependent on the solution of the Riemann Hypothesis.

Not only that, there are more than two thousand formulas linked to this, waiting for the fate of 'sublimation' or 'fall' together.

It can be said that after Xu Chuan posted his paper on the arxiv preprint website, almost the entire mathematical community was attracted to it.

At the same time, discussions on this matter have exploded on the famous international mathematics forum MathoverFlow.

【arxiv! Professor Xu from China uploaded a proof paper on the Riemann Hypothesis! 】

【WTF? what's the situation? 】

[What a fart, arxiv crashed again. 】

[Requesting a paper! Is there anyone who has downloaded the paper? Please! 】

[Don’t beg, you won’t understand even if I beg. 】

[Shrimp and pig heart, but those who have downloaded the paper are probably chewing on it now. Let’s wait for arxiv to recover. 】

[If I remember correctly, this is the first scholar to claim that he has made a major breakthrough on the Riemann Hypothesis? Starting from the pheasant professor Opeyemi Enoch of Nigeria, and then to Mr. Sir Michael Atiyah, from civilian science to the Philippine Prize winner, there are too many. What is the result? None were successful. 】

[It’s different this time. The one who published the paper this time is the famous Professor Xu! There is nothing wrong with the paper he published on arxiv! 】

[But can he guarantee that he will not make mistakes throughout his life? impossible! The Riemann Hypothesis is too difficult, let alone proving it. Even if you make a small breakthrough on it, it will be enough for you to win the Fields Medal. The critical band method has only been able to break through No (T)\u003e Just 0.35N(T), which is the achievement of the last century. 】

[I remember that there was a mathematician who expanded it to No(T)\u003e0.4N(T)? 】

[It is just a public paper and has not been fully certified by the mathematics community. 】

[Ahem, you are mistaken upstairs. Professor Xu is not promoting that he has proved the Riemann Hypothesis this time. The paper he sent seems to be looking for another way to shrink the critical band. 】

【.】

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

There are those who believe it, and there are those who question it, including those who are famous mathematicians such as Terence Tao.

The existence of the Riemann Hypothesis is extremely rare in the mathematical world.

A mathematical conjecture is closely related to the fate of more than two thousand mathematical propositions. It is like an apple tree growing in heaven, covered with various red fruits.

But the world of mathematics exists in the human world, and its existence can only be said to be elusive.

Of course, although for a century and a half, mathematicians have failed to succeed in their efforts to climb the towering peak of the Riemann Hypothesis, there are many various achievements that have been born as a result.

For example, the most famous prime number theorem is a result derived from this.

This is also one of the reasons why countless people have discussed it. It is too difficult to solve it.

Countless people have tried, but none have succeeded.

The heated discussion does not only occur on international mathematics forums. Putting aside those netizens who discuss the matter on forums and on the Internet, the one who is most concerned about this matter is the mathematics community itself.

It can be said that some scholars who have obtained first-hand papers are currently studying and reading them with concentration.

University of California, Los Angeles, California, USA.

Tao Zhexuan has canceled all today's schedule and is sitting at home reading the paper Xu Chuan sent him via email.

Unlike others who downloaded it on the arxiv preprint website, he can be said to be the second person to receive this paper together with Deligne.

At this moment, he was very glad that he had heard the news that Xu Chuan was studying the Riemann Hypothesis, and made a special call to learn about the situation and get first-hand papers.

Otherwise, given the time difference between the United States and China, by the time he finds out, arxiv may be paralyzed.

Pushing up his glasses, Terence Tao was immersed in the paper in his hand.

It was not an easy task for him to fully understand the proof paper of more than one hundred pages. He had to skip two days of classes and activities and spent nearly two days to thoroughly read the paper.

"It's kind of interesting, it seems to be a road that's been rarely studied."

"He did not study how to further compress the critical zone, or choose the most difficult left translation route of the right boundary to break through, but contracted it back to Jensen's inequality, and then studied it through subsigma algebra."

"Is this a regression of the π(x) prime number counting function?"

Staring at the last article of the paper in his hand, Tao Zhexuan muttered to himself.

At first, he thought it was a proof of the Riemann Hypothesis, but later after reading some of the content and title of the email, he found that it was not, but related to the weak Riemann Hypothesis. Later, after printing out the paper and reading it, he discovered that the paper in his hand was a preparation for solving the weak Riemann hypothesis.

However, it is more of a comprehensive proof paper than a tool.

Because in this paper, he saw many problems and directions that have not been broken through in the mathematics world, and gave the answers in it.

Although these problems are not very famous, their influence in their respective fields is not small.

For example, the problem that the integral inverse transform is difficult to converge at the jump of the π(x) function will be solved. After being solved, the Fourier transform function will be raised to a whole new level.

Although Professor Xu did not continue to expand in the paper, from his perspective, he can naturally see the hidden scope of advancement behind it.

Putting the paper in his hand on the table, Terence Tao took off his glasses from the bridge of his nose, gently rubbed his aching eyes, closed his eyes and thought.

In fact, judging from the paper, Professor Xu has not yet solved the weak Riemann hypothesis. But he gave a tool, or path, to the answer.

For a top mathematician, especially one who has researched in the field of analytic number theory, facing this paper is undoubtedly like a strong man who has been hungry for three days and sees a big cake in front of him. Same.

Instinct urges them to take this tool and follow the next path to find the weak Riemann hypothesis and solve it.

Tao Zhexuan didn't quite understand why he had pushed the progress to this point without first solving the weak Riemann hypothesis before releasing it together.

Is he really not worried about others taking advantage of his achievements and taking the lead in solving this problem?

Is he really that confident in himself?

Not worried at all that others might go ahead of him and take away this share of glory that must belong to him from his hands?

Or does it mean that he doesn't really care about these things anymore?

After all, as a scholar who has solved three millennium problems, perhaps the weak Riemann hypothesis is just that for him.

After thinking for a while, Terence Tao opened his eyes again, pursed his lips and took a deep breath.

No matter what Professor Xu thought, he wanted to give it a try.

Try using this tool to make a breakthrough on the weak Riemann hypothesis, and go down this path and give it a try.

He would not go or bother to compete for such an honor.

but!

There is a competition with Xu Chuan to see who can solve this problem first, but this is what he cares about.

Tao Zhexuan knows very well that he is definitely at a disadvantage on this road, because this tool and this road were proposed by Xu Chuan, and there is no doubt that the founder will have a deeper understanding.

But he wanted to see who could solve this problem first. I also want to take a look and see how big the gap between the two is.

After all, no genius is not proud!

Meanwhile, on the other side.

At Princeton University, in Pierre Deligne's office, Edward Witten and Charles Fefferman were together.

Thanks to Professor Deligne's prompt, both Witten and Fefferman downloaded the paper from arxiv as soon as possible and printed it out.

"You mean Xu Chuan has discussed this idea with you before?"

In the office, Witten looked at Deligne in surprise, holding a cup of coffee in his hand.

Deligne nodded and said, "About a month ago, he asked me for some of Grothendieck's manuscripts and papers, and we talked about some things in this regard."

Hearing this, Fefferman looked over in surprise and asked in surprise: "You mean this result was made by him in the past month?"

Deligne: "That's probably not the case. Regarding the research on the Riemann Hypothesis, I think he should have had ideas for a long time. Maybe he has been doing research intermittently in his daily life. He may have only recently determined his ideas and direction."

After listening to this explanation, Fefferman understood a lot.

It would be hard for him to believe that he could produce such a 'shocking' result within a month.

However, for scholars like them, it is normal to study some well-known conjectures in their daily life.

Take the seven millennium problems, for example, they are there. Whether you are a scholar in this field or not, it can be said that almost all of them have seen and studied these conjectures.

Of course, it is one thing to have seen and studied it, but it is another thing to be able to find ideas and methods.

"Speaking of which, he has even perfected his tools and ideas. Why not prove the weak Riemann hypothesis and then publish it?"

After chatting for a while, Fefferman suddenly looked at Deligne and asked curiously.

Deligne thought for a while, shook his head and replied: "I don't know, maybe I can't wait? Do you want to share this joy with us?"

Fefferman smiled and said, "Old friend, I just got some news from Terence Tao. I wonder if you are interested?"

"What?"

Fefferman said with interest: "Use Professor Xu's tools and ideas, continue along his ideas, and do research on the weak Riemann hypothesis and the Riemann hypothesis to see if we can get ahead of him. solve this problem!"

Hearing this, Deligne frowned slightly, glanced at him, and said, "Is this okay?"

Hearing this, Fefferman quickly shook his head and said with a smile: "No, no, no, we don't mean what you think. We just want to give it a try and see if we can stay ahead of him."

After a slight pause, he continued: "In other words, we want to have a not-so-equal competition with him. Tao has already found some friends. Regardless of whether we can succeed, we just want to see everyone's performance in this field. With speed and insights, maybe it will bring us some other ideas or results.”

"Isn't this interesting?"

"Want to come together?"

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