After returning to the dormitory with questions from Deligne, Xu Chuan locked himself in this room of less than twenty square meters.

Although Deligne told him that there was nothing wrong with the core of the thesis, only the minutiae at issue, he did not dare to relax in any way.

Not to mention him, Wiles, who proved Fermat's conjecture, had been plagued by a 'minor problem' for eight months.

And for mathematics, or for science, rigor is the most necessary thing. Any science that is problematic is unscientific.

Therefore, before formally submitting the paper and holding a math report meeting, he should make the paper as perfect as possible.

.......

More than 10 days had passed since Xu Chuan had revised and perfected the problems that his two supervisors had checked in the proofs of the papers, and he had posted them on the Arxiv website.

Whether it is their own attention or the word of mouth of friends, anyway, the vast majority of scholars who pay attention to the Hodge conjecture or the seven millennial problems, or the people who eat melons on the Internet, already know the news.

For the more than 100 pages of papers that are hung on the ARXIV preprint website, almost all of them have been downloaded.

Unfortunately, not everyone can read the 100-plus pages.

In other words, the number of people who can read the more than 100 pages of the paper is only a very small part.

The vast majority of people don't even understand the most basic algebraic cluster and group mapping tools.

Therefore, there is a constant debate on the Internet, especially in the mathematical community, on a professional forum:

[Hi, did you read the paper on arxiv that proves Hodge's conjecture?] Is there anyone who knows how to come out and explain whether Hodge's conjecture has been proven. 】

[I read it, but I don't understand it at all.] 】

[Incredible, is there really any hope of solving the Hodge conjecture?] 】

[You think too much, this is one of the seven millennial problems, and it is only Pongala's conjecture that has been solved so far, this is still the joint efforts of countless people for a century, and Perleman also stood on the shoulders of giants to solve the three-dimensional Ponga conjecture. And what about Hodge's conjecture? Not to mention the shoulders of giants, now there is not even a ladder. 】

[What's more, isn't the implication of such an important proof paper thrown on a spammy website like arxiv? 】

[But the person who proved this paper was the winner of the Cafford Prize in Mathematics and Astronomy, the genius boy Xu Chuan, who had solved the Weyl-Berry conjecture before, and he had a habit of throwing the paper on the Arxiv website before.] 】

[But the Weyl-Berry conjecture and the Hodge conjecture are not at all a level problem, the former is not well-known in the mathematical community, while the latter is the problem of the century.] More importantly, how long is it until he solves the Weyl-Berry conjecture today? It's less than two years, right? In two years, one of the seven millennial problems has been solved, do you believe it? 】

[I remember that it took Professor Wiles seven years to solve the Fermat conjecture, and it took Perleman eight years to prove the Poincaré conjecture, and less than two years to solve the Hodge conjecture, is this possible?] Perhaps soon the paper will be proven to be seriously flawed by the mathematical community, and the Hodge conjecture is still on the top. 】

......

There is no peer review on ARXIV, and if the paper above has been verified, then no one knows whether it is correct or not.

Regarding the proof paper of Hodge's conjecture thrown by Xu Chuan, everyone is also talking about it.

Some felt that the Hodge conjecture was hopefully solved, after all, the person who uploaded it was a genius mathematician, a favorite to win the Fields Medal, and even a Fields Medal winner, after all, he only had to wait a while before the Fields Medal was reached.

It's November 2017, and it's only eight or nine days before the International Congress of Mathematics will be held in August next year.

Of course, many more people do not believe that the Hodge conjecture has been solved.

Whether it's in terms of time, or age, or anything else, this is a bit unreliable.

The Seven Millennium Problems are not unsolved, but no one will believe that one of them can be solved in less than two years.

Time is too short.

Moreover, the provenance is unbelievably young.

According to the algorithm of the Chinese lunar calendar, it will be two months before he reaches the age of twenty, and even if he has solved a world-class mathematical conjecture before this, not many people think that he can continue to solve a millennial problem.

After all, the vast majority of people are skeptical of people who are too young, whether academics or other fields.

This is almost the same in any country.

In addition, it has been confirmed that no journal in the mathematics community has received the submission of this certification paper.

In other words, the young scholar did not formally submit his paper to a mathematical journal other than throwing his paper on Arxiv.

For today's academia, this does not in any way feel like a formal solution to a major conjecture.

So many people are wondering if this is a joke.

In addition to the arguments, there are many people who are expecting a response from Princeton or the proveners of the paper.

After all, this is Hodge's conjecture, the Seven Millennium Problems.

Such a major conjecture, no matter what, the prover should come out and explain it.

At the very least, a press conference should be wanted.

If the Hodge conjecture is to be fully confirmed, it is the duty of the prover to explain his theory and answer all doubts.

Unless, this is just a big joke that the young scholar is playing to the world, with his reputation and the future.

However, many people are still willing to believe this young scholar on this point. After all, he had already solved a world-class problem before.

Therefore, the mathematical community is waiting for the convening of the report meeting, and even many mathematicians have contacted Princeton University, hoping that Xu Chuan can stand up and deal with the doubts of the outside world.

It's just that Xu Chuan, who will be there, is not aware of these things, and at this time he is repairing his paper and solving the problems raised by Professor Deligne and Professor Witten when they check the paper.

.....

After locking himself in his dormitory for five days, Xu Chuan finally finished revising his thesis.

In fact, there are not many questions raised by the two mentors, Deligne and Witten, and there are only two questions + three suggestions in total.

It's just that in order to solve these problems perfectly, he has repeated each idea many times.

And after solving the problem perfectly, he rechecked the paper twice, which took several days.

To be honest, in a proof paper that is more than 100 pages long, the two top math experts have only checked two problems, which shows how excellent this paper is.

With the revised paper, Xu Chuan found two supervisors, and after verification and discussion, the three of them finally confirmed the perfection of the proof-proof paper.

At the same time, the long-awaited response from the outside world has finally arrived.

In the afternoon of the same day, Princeton University's official website was updated with an important piece of information about the math conference.

In five days' time, next Monday, Princeton University will hold a math presentation by Xu Chuan on a paper proving Hodge's conjecture.

With the announcement of this conference information, the entire mathematical community was boiling.

From the appearance of the proof paper of the Hodge conjecture on the Arxiv website to the presentation of the proven, the mathematical community waited for 20 days.

Such a long period of time, which was unprecedented in the past, also made the outside world's skepticism about this paper reach its peak for a time.

But now, all the doubts and discussions will come to fruition.

Mathematicians who were interested in this have bought plane tickets one after another.

.....

With the updated information on Princeton's official website about math conferences, numerous mathematicians began to flock to Princeton.

This kind of quiet town is gradually becoming lively.

Regarding the proof report of Hodge's conjecture, Xu Chuan actually didn't care much.

Whether it is the convening of the seminar, the arrangement of foreign scholars, or the media reporters, as well as the party and dance party after the presentation, Princeton University helps.

The only thing he had to do was to prepare his presentation materials and think ahead of the questions that many mathematicians might ask at the presentation.

Even if the two masters, Deligne and Witten, had already helped to prove the paper beforehand, he could still face some fatal or unexpected questions in front of mathematicians from all over the world at the presentation.

So he had to make more preparations before the briefing.

Time passed day by day, and soon it came the day before the briefing.

In the Rockefeller Residential Academy, Xu Chuan put down the ballpoint pen in his hand, got up and went into the kitchen and took out a bottle of yogurt from the refrigerator, and before he could take a sip, there was a knock on the door.

Curious as to who had come to look for him at this point in time, he opened the door to the dormitory, and the person standing at the door made him stunned for a moment.

"Teacher, Dean Rong, Academician Zhang, why are you here?"

Standing at the door were Chen Zhengping, the tutor of Nanjing University, Rong Zhizhuan, the dean of the School of Mathematics, and Zhang Weiping of Sun Moon University.

"What, aren't you welcome?" Academician Zhang Weiping of Sun Moon University asked with a smile.

Xu Chuan was slightly stunned for a moment, then he reacted, quickly let go of the door, welcomed the three of them into the dormitory, and said, "Quick, please come in." ”

"You kid really made a big deal this time, proving Hodge's conjecture, the seven millennial problems, tsk, I've never heard you say you're working on this before."

The three of them stepped into the dormitory, and after looking at the room, Dean Rong Zhi of the School of Mathematics of Nanjing University, looked at Xu Chuan with a smile and sighed.

Xu Chuan smiled and said, "I was inspired by chance, so I tried to study this aspect, as for whether it can really prove the Hodge conjecture, we have to wait for the conclusion of the mathematical community." ”

Hearing this, Rong Zhizhuan shook his head with a smile and said, "You, you are still so modest, and you haven't changed at all during the time you have lived abroad. ”

After a pause, he continued, "Before you come here, we went to see Professor Deligne, and he has a very high opinion of your paper. And he and Witten have verified it, and there is nothing wrong with it. ”

On the side, Chen Zhengping interjected: "Tomorrow's report meeting, how are you going?" ”

Xu Chuan: "There must be preparations, and I have already thought about everything that can be considered here, but I just don't know what kind of questions others will ask tomorrow." ”

Nodding, Chen Zhengping took out a thin stack of rolls of paper from his pocket and came over.

"Here are some ideas from some mathematics professors in China who have studied your proof paper, and there are ideas and suggestions in it, which may bring you some help."

Hearing this, Xu Chuan was stunned for a moment, and hurriedly took the roll of paper, opened it and looked at it.

He really didn't expect Chen Zhengping to bring him such a gift. There is no doubt that this is quite precious.

Rong Zhizhuan said on the side: "You have to thank Academician Zhang Weiping Zhang for this, he took the lead in opening a small seminar in China, and invited some top mathematics professors at home and abroad to help discuss it." ”

Xu Chuan was stunned again, looked at Zhang Weiping, and sincerely thanked: "Thank you." ”

Zhang Weiping waved his hand and said with a smile: "With your current mathematical ability, these ideas and suggestions are nothing to you. ”

.......

The group of three didn't stay in the dormitory for long, said hello, gave a gift, and left without even drinking hot tea.

After all, tomorrow the proof report meeting of Hodge's conjecture will begin, and everyone knows how busy Xu Chuan will be.

The next day, at two o'clock in the afternoon.

The Alexander Auditorium at the Institute for Advanced Study in Princeton was crowded.

In addition to the scholars who were invited to participate in this academic presentation, there were many mathematicians from the university and students who came with their supervisors.

In particular, the number of mathematicians and mathematics students from China even accounted for nearly one-fifth of the entire seminar, and most of them were students who came to see the world with their tutors.

There were so many people attending the lecture that the Alexander Auditorium, which can accommodate more than 500 people, could not sit down, and many of those who did not get a seat had to sit or stand in the corridors.

】

Standing behind the curtain of the auditorium, Xu Chuan sat steadily on a wooden chair with some smiles on his face.

The calm demeanor made the staff on the side a little curious, and asked with a smile: "You don't look nervous at all." ”

Xu Chuan joked: "That's because you didn't see how fast my heart was beating." ”

The staff smiled and said: "This is different, I have worked here for many years, and I have seen a lot of outstanding young heroes, no matter who they are, before they come to the stage to make a report, they almost have to rely on various means to suppress their excitement." ”

"Even Schultz initially relied on constant deep breathing to regulate his emotions, not to mention a proof report of such a major conjecture."

After a pause, the staff member looked Xu Chuan up and down, and then said, "You look much calmer, I don't see much nervousness from you." ”

Xu Chuan smiled and said, "Coming to the stage to report is not more difficult than proving a mathematical conjecture, is it?" ”

Hearing this, the staff member also laughed, opened his mouth, and was about to say something when another young staff member trotted in.

"Mr. Xu Chuan, it's already one fifty-five, and the preparations outside have been made, do you need to prepare anything else here?"

Xu Chuan stood up and said, "Thank you, I'm ready." ”

With that, he walked towards the stage outside.

......