After returning to the dormitory with questions from Deligne, Xu Chuan locked himself in this room of less than 20 square meters.
Although Deligne told him that there was no problem with the core of the proof paper, and that the problems were only some details, he did not dare to relax in any way.
Not to mention him, Wiles, who proved Fermat's conjecture, was troubled by a "little problem" for eight months.
And for mathematics, or for science, rigor is the most necessary thing. Any science with problems is unscientific.
Therefore, before officially submitting this paper and holding a mathematics report meeting, he must make the paper as perfect as possible.
.......
When Xu Chuan revised and improved the problems that the two tutors checked in the proof paper, more than ten days had passed since he posted the paper on the arxiv website.
Whether it's their own attention or word of mouth from friends, most of the scholars who pay attention to the Hodge Conjecture or the Seven Millennium Problems, or the people on the Internet, already know the news.
For the more than 100 pages of papers posted on the arxiv preprint website, almost all of them have been downloaded by those who have access to them.
But unfortunately, not everyone can understand this more than 100 pages of paper.
In other words, only a very small number of people can understand this more than one hundred pages of paper.
Most people cannot understand even the most basic algebraic variety and group mapping tools.
Therefore, there are constant debates on the Internet, especially in the mathematics community, on a certain professional forum:
[Hi, have you read the paper on arxiv that proves the Hodge conjecture? Can anyone knowledgeable explain whether the Hodge conjecture has been proven? 】
[I saw it, but I couldn’t understand it at all.]
[Incredible, is there really any hope of solving the Hodge conjecture? 】
[You are thinking too much. This is one of the seven millennium problems. It has only been solved by Poincare's conjecture. This is the joint efforts of countless people over the past century. Perleman is also standing on the shoulders of giants.
The three-dimensional Poincare conjecture was solved only last week. But what about the Hodge conjecture? Not to mention the shoulders of giants, there is not even a ladder now.]
[More importantly, if such an important proof paper is posted on a junk website like arxiv, isn’t the meaning still obvious? 】
[But the person who proved this paper is the winner of the Craford Mathematics Prize and the Astronomy Prize, the genius boy Xu Chuan. The Weyl-berry conjecture that he has solved before must still be certain, and he has also lost the paper before.
The habit of going to the arxiv website.】
[But the Weyl-berry conjecture and the Hodge conjecture are not problems at the same level at all. The former is not famous in the mathematics world, while the latter is a problem of the century. More importantly, how long has it been since he solved the Weyl-berry conjecture today?
It’s been less than two years, right? In two years, one of the seven millennium problems has been solved. Do you believe it?]
[I remember that it took Professor Wiles seven years to solve Fermat's conjecture, and it took Perleman eight full years to prove the Poincare conjecture. It took less than two years to solve the Hodge conjecture. This is
Is it possible? Perhaps this paper will soon be verified by the mathematical community as having major flaws, and the Hodge conjecture will still be high.]
...
There is no peer review on arxiv. If the above paper has not been verified, no one knows whether it is correct.
Everyone was also talking about the paper proving the Hodge conjecture that Xu Chuan threw up.
Some people think that the Hodge conjecture has hope of being solved. After all, the person who uploaded it is a genius mathematician and a popular candidate for the Fields Medal. It can even be said that he is the Fields Medal winner. After all, he is far away from the Fields Medal.
The Erz Prize just needs to wait for a while.
It is already November 2017, and there are only eight or nine days until the International Mathematical Congress will be held in August next year.
Of course, more people do not believe that the Hodge conjecture has been solved.
No matter from the perspective of time, age, or other aspects, this is somewhat unreliable.
The seven millennium problems are not unsolved, but one of them can be solved in less than two years. No one would believe it.
time is too short.
Moreover, the prover is so young that it is unbelievable.
According to the calculation of the Chinese lunar calendar, it will take two months to reach the age of twenty. Even if he has solved a world-class mathematical conjecture before then, not many people think that he can continue to solve a thousand-year-old problem.
problem.
After all, most people are skeptical of people who are too young, whether they are scholars or in other fields.
This is almost the same no matter which country you are in.
In addition, according to confirmed information, no journal in the mathematics community has accepted the submission of this proof paper.
In other words, apart from posting his paper on arxiv, this young scholar has not formally submitted it to a mathematics journal.
To today's academic community, this does not look like a formal solution to a major conjecture.
So many people are wondering if this is a joke.
In addition to discussions, many people are looking forward to a response from Princeton or the prover of the paper.
After all, this is Hodge's conjecture, the seven millennium problems.
No matter what you say about such a major conjecture, the prover should come out and explain it.
At least, a press conference should be required.
If you want to completely confirm the Hodge conjecture, the prover is obliged to explain his theory and answer all questions.
Unless, this is just a huge joke played by this young scholar on the whole world, a joke on his own reputation and future.
However, many people are still willing to believe this young scholar on this point. After all, he has already solved a world-class problem before.
Therefore, the mathematics community is waiting for the convening of the report meeting, and many mathematicians have even contacted Princeton University specifically, hoping that Xu Chuan can stand up and respond to the doubts from the outside world.
It's just that Xu Chuan doesn't know these things at this time. At this time, he is revising his thesis and solving the problems raised by Professor Deligne and Professor Witten when they checked the paper.
.....
After locking himself in the dormitory for five full days, Xu Chuan finally completed the revision of his thesis.
In fact, the two instructors Deligne and Witten raised not many questions, only two questions and three suggestions in total.
It's just that in order to solve these problems perfectly, he conceived and repeated each one many times.
And after he solved the problem perfectly, he re-checked the paper twice, which took several days.
To be honest, in a proof paper that is more than 100 pages long, two top mathematics experts only checked two problems, which shows how excellent this paper is.
With the revised thesis, Xu Chuan found two supervisors. After verification and discussion, the three of them finally confirmed the perfection of the proof.
At the same time, the long-awaited response from the outside world finally arrived.
That afternoon, Princeton University’s official website updated an important mathematics conference information.
Five days later, that is, next Monday, Princeton University will hold a mathematics lecture. The lecturer is Xu Chuan. The lecture content is a proof paper of Hodge's conjecture.
With the announcement of this conference information, the entire mathematics community became excited.
From the time the proof paper of Hodge's conjecture appeared on the arxiv website to the time when the prover held a relevant report meeting, the mathematics community waited for twenty days.
Such a long period of time was unprecedented in the past, and it also caused the outside world's doubts about this paper to reach its peak.
But now, all doubts and discussions will come to an end.
Mathematicians who were interested in this matter bought air tickets one after another.
.....
As the mathematics conference information was updated on Princeton University’s official website, many mathematicians began to flock to Princeton.
This quiet town gradually became lively.
Xu Chuan actually didn't worry about the report on the proof of Hodge's conjecture.
Whether it is the convening of the lectures, the arrangements for external scholars, the media reporters, or the evening parties and dances after the lectures, Princeton University helps.
The only thing he had to do was to prepare his report materials and consider in advance the questions that many mathematicians might ask at the report meeting.
Even if the two masters Deligne and Witten had helped with the proof paper beforehand, at the report meeting, facing mathematicians from all over the world, he might still face some fatal or unexpected problems.
question.
So he had to make more preparations before the report meeting was held.
Time passed day by day, and soon it came to the day before the report meeting.
In Rockefeller Residential College, Xu Chuan put down the ballpoint pen in his hand, stood up, went into the kitchen and took out a bottle of yogurt from the refrigerator. Before he could take a sip, there was a knock on the door.
Somewhat curious about who came to find him at this time, he opened the door of the dormitory and was stunned for a moment by the person standing at the door.
"Teacher, Dean Rong, Academician Zhang, why are you here?"
Standing at the door were Chen Zhengping, a tutor from Nanjing University, Rong Zhizhuan, dean of the School of Mathematics, and Zhang Weiping from Sun Moon University.
"What, aren't you welcome?" Academician Zhang Weiping from Riyue University asked with a smile.
Xu Chuan was stunned for a moment before he realized what was happening. He quickly opened the door and welcomed the three of them into the dormitory, saying: "Quick, please come in."
"You guys have really come up with something big this time, proving Hodge's conjecture and the seven millennium problems. Gee, I've never heard you say that you are researching anything in this area before."
The three of them entered the dormitory. Dean Rong Zhi Zhuanrong of the School of Mathematics at NTU looked at the room, looked at Xu Chuan with a smile and sighed.
Xu Chuan smiled and said: "I was inspired by chance, so I tried to research this aspect. As for whether it can really prove Hodge's conjecture, we have to wait for the conclusion of the mathematical community."
Hearing this, Rong Zhizhuan smiled and shook his head, saying: "You are still so humble. You haven't changed at all during the time you have been living abroad."
After a pause, he continued: "Before you came here, we went to see Professor Deligne, and he spoke very highly of your paper. And he and Witten have verified it, and there is nothing wrong with it.
question."
On the side, Chen Zhengping interjected: "How are you preparing for tomorrow's report meeting?"
Xu Chuan: "I'm sure I'm prepared. I've thought about everything I can think of, but I just don't know what questions others will ask tomorrow."
Nodding, Chen Zhengping took out a thin stack of roll paper from his pocket and came over.
"These are some thoughts of some domestic mathematics professors after studying your proof paper. They contain ideas and suggestions, which may be able to bring you some help."
Hearing this, Xu Chuan was stunned for a moment, quickly took the roll of paper, opened it and started reading.
He really didn't expect that Chen Zhengping would bring him such a gift. There is no doubt that it is quite precious.
Rong Zhizhuan said from the side: "You have to thank Academician Zhang Weiping for this. He took the lead in holding 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 said sincerely, "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 three of them did not stay in the dormitory for long. After saying hello and giving them a gift, they left without even drinking hot tea.
After all, tomorrow the report meeting on the proof 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 Alexandria Auditorium at the Institute for Advanced Study in Princeton was packed with people.
In addition to the scholars invited to participate in this academic report, there are also many private mathematicians and students who came with their tutors.
In particular, mathematicians and mathematics students from China accounted for nearly one-fifth of the entire seminar, and most of them were students who came with their instructors to see the world.
There were so many people attending the lecture that the Alexandria Auditorium, which could accommodate more than 500 people, could no longer hold any seats. Many people who did not get a seat could only sit or stand in the corridor.
】
Standing behind the scenes of the auditorium, Xu Chuan sat steadily on a wooden chair with a smile on his face.
The calm demeanor made the staff on the side a little curious, and asked with a smile: "You don't seem nervous at all."
Xu Chuan joked: "That's because you didn't see how fast my heart was beating."
The staff member smiled and said: "This is different. I have worked here for many years and have met many outstanding young people. No matter who they are, they almost have to resort to various means before going on stage to give a report.
Suppress your excited emotions."
"Even Schultz relied on constant deep breathing to regulate his emotions at the beginning, let alone 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 in you."
Xu Chuan smiled and said: "It's not more difficult to give a report on stage than to prove a mathematical conjecture, is it?"
Hearing this, the staff member also laughed and opened his mouth. When he was about to say something, another young staff member trotted in.
"Mr. Xu Chuan, it's already 1:55, 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."