It had been a week since Lu Zhou posted his thesis on arXiv. Most people who paid attention to Goldbach's conjecture had heard the news.
Some people were amazed by the "Group Structure Method", some people were in disbelief, and some people were dismissive of the fifty pages. This was because it was not easy to understand the entire proof process.
Other than those who were proficient in the "Yin and Yang, Four Symbols, Five Elements, and Eight Trigrams" method, very few people in the field of analytic number theory studied Goldbach's conjecture.
For example, people who studied the large sieve method were not necessarily proficient in the circle method, and vice versa. Other than the mainstream choices, there were some methods such as the density method and trigonometric summation, which were even more unpopular.
But in the Group Structure Method used by Lu Zhou, not only could one see the shadow of the sieve method, but one could also see the circle method and even the group theory.
Because of this, let alone verifying the correctness of the thesis, there was a certain threshold for understanding the thesis.
Of course, the general view of the number theory community was relatively optimistic. After all, Lu Zhou had already won the Cole Prize in Number Theory and solved many problems in number theory, especially in the field of prime numbers.
Because many professors mentioned this matter in their lectures, the discussion gradually spread from the academic circle to some campus BBS.
It wasn't just the scholars who were interested in this area that were talking about this matter. Even the mathematics students from major universities were talking about this thesis.
On a foreign mathematics forum that was famous for predicting the Fields Medal, a discussion began because of this.
[Okay! I know he has solved the twin prime conjecture and Polignac's conjecture, but our professor said in class that Goldbach's conjecture is not on the same level as them. It's like the Ivy League and the Super Bowl. Although they are both football, they are not on the same level. To put it bluntly, I don't believe that his thesis is correct. There must be a problem somewhere. I think it will be overturned soon.]
[So who is your professor?]
[James Maynard! The winner of the 2014 SASTRA Ramanujan Gold Prize! A candidate for the 2018 Fields Prize! I think his opinion is more authoritative.]
[Oh, that Maynard. I've heard of him before. I think he's the Englishman who researched the spacing of prime numbers? It was said that after Zhang Yitang calculated 70 million, he had been challenging the twin prime number conjecture. He had been preparing for a whole year, but in the end, he was beaten by someone else. He was so angry that he burned his entire manuscript? (laughing)]
[Hehe!]
[My opinion is the opposite of yours. Our professor thinks that the Group Structure Method will become a very promising analytical number theory tool.]
[Oh? Who is your professor? With all due respect, not everyone has the ability to review analytical number theory, especially in the field of prime numbers.]
"Tao Zhexuan."
[…]
…
There was no peer review on arXiv, so the correctness of the thesis could not be determined. There were many opinions on whether or not this mathematical problem could be proven.
However, everyone knew that the mathematics community would not wait too long for this dazzling research success.
The second week after Lu Zhou uploaded the thesis, the Princeton Institute for Advanced Study posted a conference announcement on their website.
Next Monday, Lu Zhou would be at the Princeton Institute for Advanced Study lecture hall. He would be giving a one-hour report on the Goldbach's conjecture.
After this announcement came out, all of the debates about the correctness of the thesis turned into discussions about the report itself.
Many people doubted the correctness of the thesis mainly because they did not understand the Group Structure Method and the arXiv thesis did not have a peer review. If it was posted as a report in a place like the Princeton Institute for Advanced Study, a lot of questions would undoubtedly be answered during the Q&A session.
Because of this, Lu Zhou was particularly serious about preparing for the next few days. He did not let down his guard because of the recognition from the system.
The key to proving a mathematical conjecture was logical self-consistency, but it still needed to be recognized by peers. This was fundamentally different from a subject test. There was no standard answer that could be used as a reference. As the person who proved the conjecture, he had the obligation to explain his theory and answer all questions.
Lu Zhou did not dare to let go of even the smallest details. A lot of traps were often hidden in "obvious" problems.
Not to mention him, even Wiles, who proved Fermat's last theorem, was stumped by these small problems. He was stuck on an "obvious" but problematic problem for almost a year. If it were not for his friend's encouragement, he would have admitted defeat.
When Lu Zhou finished his work, he could not help but feel emotional.
He did not feel this before, but now he realized how useful it was to have a student.
When he was going to give the report on stage, he would give it to the student as a reference point. He would then draw out the parts that he did not understand, and the parts that would be difficult for him would be obvious.
Unfortunately, even though Professor Deligne lent him a PhD student to be his advisor, Professor Deligne's advisor wasn't theoretical, but rather, he was only helping him with the PowerPoint presentation.
Even if Lu Zhou wanted to ask him what part of his thesis did he not understand, he would just be muddled.
This was because his research direction was algebraic geometry. He did not know anything about the circle method or the sieve method …
…
Time quickly passed by, and it was finally the day before the report.
With the influx of mathematicians, even the quiet town of Princeton became lively.
Princeton was very attentive to mathematicians from all over the world.
According to the arrangement of the Princeton Institute for Advanced Study, the mathematicians who were invited to this report were arranged to stay at the Princeton Hotel across from Palmer Square.
If everything went well, not only would there be an academic conference during the day, but there would also be a celebratory dinner filled with champagne and food at night.
However, Lu Zhou did not have time to think about these problems. For him, every second before the report was precious.
The next afternoon, the No.1 lecture hall at the Princeton Institute for Advanced Study was packed.
In addition to the scholars who were invited to the conference, there were also some uninvited students. Some of them came with their supervisors, some of them studied in Princeton, and some of them even drove here from New York or Philadelphia.
Although they did not receive the specific time of the conference, some of them still managed to grab a seat.
As for those who came late, some simply sat on the aisle on both sides of the seats, and some even stood in the corner or outside the corridor, standing together with the reporters who had rushed over after hearing the news.
The report would officially start at two o 'clock and end at three o' clock. Depending on the number of questions and the content of the questions, it might be extended.
If everything went smoothly, after the report, the Princeton Institute for Advanced Study and the editorial department of Annual Mathematics would organize a panel of four to six people to review Lu Zhou's thesis. Finally, they would summarize the review opinions and decide whether or not his thesis would pass.
It could be said that the success of this thesis depended on whether or not Lu Zhou could explain his Group Structure Method.
Lu Zhou stood in the backstage of the lecture hall and looked at the time on his phone. He then took a deep breath.
Only five minutes left.
This was the tenth time he looked at the time on his phone.
He could not remember how many times he took a deep breath to adjust his heart rate.
Before this, Lu Zhou learned from Professor Deligné about the number of people attending the conference.
Without considering the people who volunteered to attend, there were more than 150 invited scholars. Some of them were from Paris, some were from Germany, and some were from his home country.
Other than people from the mathematics community, there were also media reporters from all over the world.
Soon, he would stand in front of the world and solve this century's problem.
Suddenly, a staff member from the Institute for Advanced Study walked into the preparation room and spoke to Lu Zhou in a respectful voice.
"Mr. Lu, it's almost time. Are you ready?"
Lu Zhou did not answer the question immediately.
Lu Zhou turned around and looked at the mirror. He reached out and adjusted his tie.
He took a deep breath and looked at himself in the mirror. He then smirked.
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