Chapter 192 Xu Huoqi Theorem

Chapter 192 Xu-Hodge Theorem

The day after the lecture, a luxurious review team consisting of six Fields Medalists officially began to review the paper.

At the same time, top journals in the mathematics community also came to the door.

Editors or editors-in-chief of major journals such as Annals of Mathematics, New Advances in Mathematics, and Acta Mathematica Sinica came to the door with gifts, with only one purpose, that is, to ask Xu Chuan to publish this paper proving the Hodge conjecture in their journals.

This is probably one of the rarest situations in the mathematics community, where high-ranking journals chase mathematicians.

For an ordinary mathematician, it is undoubtedly very difficult to publish an article in a top journal such as Annals of Mathematics.

Academia actually has quite a lot of unspoken rules.

In the academic circle, it is not simply about how awesome your article is in mathematics or how much donations you make. Each journal (especially the top journals) has its own circle. As long as there is a circle, there is a way of speaking for people in the circle.

If your article does not conform to that way of speaking, and your academic contribution is not rare, rejection is a very normal result.

As for how to enter this circle, it has something to do with mentors, schools and other aspects.

For example, the Annals of Mathematics is jointly operated by Princeton University and the Institute for Advanced Study.

For mathematicians of the Princeton School, this is the most accessible top mathematics journal.

Otherwise, there wouldn't be so many people eager to go to top universities like Princeton to study and teach.

For normal people, this is the fastest way to get in touch with the top academic circle.

Of course, for Xu Chuan, it doesn't matter whether there is a circle or not.

To forge iron, you must be strong yourself. With his academic achievements, no journal will refuse.

For these journals that come to the door, Xu Chuan has no intention of dealing with them.

If there is no accident, he will probably choose to submit the proof paper of the Hodge conjecture to the Annals of Mathematics.

On the one hand, it is the relationship between the Annals of Mathematics and Princeton. On the other hand, he has had many cooperative relationships with the other party before, and the cooperation is quite pleasant.

Moreover, the Annals of Mathematics is also one of the four great journals, and it will not humiliate this paper.

Maybe in the future, he can establish his own top journal, but now he does not have such ability.

It is not so easy to establish a top journal. From operation to review and editing, to contributors and social influence, it takes a very long time to improve bit by bit.

He is not qualified now. Even if he establishes a journal, no one will submit articles.

At his current age, it is most important to focus on learning and breakthroughs.

And he does not have this mind now. When these journals come to him, it is when his paper is being reviewed by six Fields Award bigwigs.

After the report meeting, the proof of Hodge conjecture formally reviewed the paper. Xu Chuan was busy dealing with various questions raised by these bigwigs, and he was almost busy every day.

This is completely different from the last time to prove the Weyl-Berry conjecture.

When proving the Weyl-Berry conjecture, there were more than ten days of review time. He was only a little busy in the first few days, and the proof paper was smoothly understood by the bigwigs of the review group. It can be said that it is quite free.

And this time, he was so busy with the Hodge conjecture that he wanted to split himself in two.

At the same time, the news that he proved the Hodge conjecture also spread across the ocean to the other side of the earth.

Due to the fact that the paper has not been fully verified by the mathematical community, the official media did not report it on a large scale, and only briefly mentioned it in daily news.

But even so, it was still noticed and dug out, posted on the Internet, and aroused heated discussions among many people.

[After a year, the top scorer of the college entrance examination made another move, this time challenging the Hodge conjecture among the seven millennium problems! ]

[Fuck, no way? ! ]

[What is the Hodge conjecture? I have never heard of this thing. ]

[The person above, you just need to know that this is a very awesome mathematical problem. ]

[I searched Baidu and found that the problem is called 'On a non-singular complex projective algebraic variety, any Hodge class is a rational linear combination of algebraic closed chain classes'. What the hell is this? I know every word, but I can't understand it when it is put together. ]

[The most difficult to understand question among the seven Millennium Problems. Without a postdoctoral degree, you can't even understand the question. ]

[Big brother is awesome. ]

[It hasn't been proved yet, and it hasn't passed the peer review, but they opened the red wine to celebrate. If it is proven wrong in the end, it will be a slap in the face. ]

[The above person is really sour grapes. In addition, that is not called red wine, it is called champagne! Please read with me: xiang xiang bin benzene. ]

[What he said is not wrong. The peer review has not passed yet. It's interesting to celebrate so early and be slapped in the face in the end. ]

[Hehe, he conquered mathematicians all over the world at the report conference. Even Pierre Searle said that this is an excellent achievement, but he couldn't conquer you guys who don't even understand what the question means. This is really interesting. ]

The discussion on the Internet is getting more and more heated, but it has no impact on the mathematical community.

As early as when Xu Chuan posted the paper on arxiv, the mathematics community had already experienced a collective earthquake.

The end of this report meeting is just to add fuel to the flames.

Before the peer review is completely completed and the dust settles, the domestic mathematics community and formal media will definitely not publicize it on a large scale.

However, it is certain that major media from CTV to Renren Daily to New Youth and other media and newspapers are already prepared.

Once the dust settles, this huge propaganda machine will be launched for this.

Not only the media, the proof of the Hodge conjecture has been officially paid attention to by the upper political circles.

Except for a few people, others do not know what kind of changes this attention will bring to the country.

This represents not only a mathematical conjecture and a Fields Medal, but also represents the world's top academic level.

And China has been lacking such a scholar for a long time.

Xu Chuan, who is far away in Princeton, is not aware of the domestic comments. He is busy with peer review at this time.

It has to be said that the mathematics community is really a place where crouching tigers and hidden dragons are.

Although his two mentors, Deligne and Witten, had verified his thesis in advance, many imperfect parts were still found during the review.

Among them, the problem raised by Professor Faltings from Germany was the most serious and required time-consuming modification.

This expert who once used algebraic geometry to prove the Model conjecture raised a rather tricky question about the use of projective clusters in the thesis.

This is a place that Deligne, Witten and himself had never noticed.

It must be said that the mathematical ability and rigor of this old man from Germany are really admirable.

Of course, if it was just a question, it would not be so.

But this old man not only raised the question, but also gave two almost completely different ways of modification.

Although all roads lead to Rome, two completely different methods can be given for such top mathematical problems, which shows that the old man's mathematical strength is really strong.

In fact, this is exactly the case. In the entire algebraic geometry community, since his ancestor Grothendieck passed away, Faltings is now vaguely known as the first person in the algebraic geometry community.

Considering the status of algebraic geometry in today's mathematics, it is not an exaggeration to say that he is the number one in today's mathematics.

In fact, many people do not understand this evaluation.

Because Faltings' contribution to the mathematics community is not too well-known. Perhaps the most familiar thing is that he proved the Model conjecture.

But there are people in the mathematics community who are as famous as the Model conjecture or even more famous.

For example, Professor Deligne proved the Weil conjecture, Professor Wiles proved Fermat's Last Theorem, Perelman proved the Poincaré conjecture, and so on.

If you look at it from this perspective, Faltings does not seem to be ranked.

But the mathematical community's recognition of a person's mathematical ability does not only come from proving a certain mathematical conjecture.

Although this does account for a large proportion, the tools and methods in proving mathematical conjectures, the number of mathematical achievements and the contribution to the mathematical community are more critical.

And this old man is the one who created the tools and methods. He almost perfectly found a way to combine algebra and analysis, and created great value with it.

For example, he had previously obtained arithmetic algebraic geometry using methods, and this achievement was applied by Professor Andrew Wiles to the proof of Fermat's Last Theorem, accounting for a considerable proportion.

This time, relying only on the two methods proposed for a problem, Xu Chuan experienced the old man's powerful but almost completely different mathematical ability and talent.

In today's mathematics, if one mathematical problem after another is like a mountain.

Ordinary mathematicians solve problems by either climbing snow-capped mountains or walking through grasslands and finding a shortcut to bypass them.

When Faltings faced this mountain, he directly flattened the mountain with a bulldozer or blew it up with a bomb.

He would not use skills to do this, he did it completely with strength, he was a power player.

It's very ignorant to say this, but it is Xu Chuan's greatest experience with this old man.

This conceited and arrogant old man from Germany, for the use of mathematical tools, only relying on two solutions to a problem opened the door to a new world for him, which made him feel deeply.

After spending a few days and referring to the opinions of some reviewers who raised questions, Xu Chuan successfully completed the revision of the paper.

Fortunately, this problem was not so fatal, and it did not cause nearly a year of trouble like Wiles who proved Fermat's Last Theorem.

With the revised paper, Xu Chuan found Professor Faltings again and handed him the paper.

The old man did not look surprised that he could complete the revision of the paper so quickly, as if it should be so. He reached out and took the paper and read it.

Until the revised paper came into his eyes again, the arrogant German old man flashed a trace of surprise in his eyes, sat up straight, and became serious.

After more than ten minutes, Faltings put down the paper in his hand, looked up at Xu Chuan, and said lightly: "Congratulations, you have completed the revision of the paper. I have no other opinions or questions about the part I am responsible for reviewing."

"Deligne's evaluation of you is correct. You are indeed one of the best mathematicians in the world, not inferior to Schultz, and there is hope to surpass me."

After a pause, the old man continued: "Of course, there is only hope."

Hearing this, Xu Chuan almost suffocated.

It is rumored that this old man has a bad character. There is nothing wrong with his arrogance. He is simply the king of the kings.

However, he knows some rumors about the best mathematicians mentioned by Faltings.

The old man also commented on Peter Schultz: "He is one of the three best mathematicians I have ever seen in my life, and there is hope to surpass him."

Many people in the mathematics community know about this rumor.

They speculated who the other two people were. Some said it was Grothendieck and Jean-Pierre Serre; others said it was Deligne and Terence Tao.

However, Faltings never responded to this matter directly.

But no matter what, the fact that this arrogant old man made such an evaluation shows the excellence of the person involved.

Now he has also received such an honor: "There is hope to surpass him!"

For this evaluation, Xu Chuan really didn't know whether to be angry or laugh, and finally had nothing to say.

It can only be said that in the realm of pretending, he is really far inferior to this big guy, and it is even difficult to look at his back.

After all, he himself is not a very good pretender.

Time passed day by day. In the third week after the peer review began, the review team composed of six Fields Medals spent more than 20 days to finally complete the review of the six-part paper.

In the Institute for Advanced Study in Princeton, Xu Chuan received a call and came to the office of Charles Fefferman, the director of the Department of Mathematics at Princeton University.

The hidden NPC of Princeton University had a bright smile on his face and gave Xu Chuan a big hug.

"Congratulations, the proof of the Hodge conjecture has passed peer review."

"From today, the Hodge conjecture will be officially promoted to a theorem, and we now have a perfect tool that can construct any H object from geometric objects in a purely algebraic way."

On the other side, Professor Camilo de Lellis, the editor-in-chief of Annals of Mathematics, also smiled and congratulated: "Dr. Xu Chuan, your paper will be published in the next issue of Annals of Mathematics."

"At the same time, we will also publicize this great success in advance so that more people will know about it. "