A lot of things could happen in the time it took to drink a cup of coffee.
While Lu Zhou was lying on his bed and his consciousness was in the system space, at the University of Montreal, Canada, thousands of kilometers away from Princeton, British mathematician Andrew Granville was browsing arXiv.
This was one of the things he did every day. Sometimes it was after his morning run, sometimes it was before he went to bed.
Although most professors liked to give the job of keeping track of the latest research progress on arXiv to their PhD or master's students, Granville liked to do it himself.
Although the quality of the theses on arXiv was not peer-reviewed, many new people had put forward some very creative ideas that were very inspiring … It was just that they were not perfect.
Granville roughly looked at about ten theses and yawned. He was about to get up and go to sleep.
However, at this moment, he suddenly received an alert from a website on his personal page. It was from two tags that he followed — analytic number theory and prime number problems.
Glanville frowned. His obsessive-compulsive disorder made him click on the notification.
However, after he saw the title of the article, he could not help but smirk.
[Any even number greater than 2 can be expressed as the sum of two prime numbers.]
Isn't this the Euler statement of Goldbach's conjecture?
Generally speaking, this kind of thesis would be thrown into the "general mathematics" section. However, he had already blocked this section.
Granville did not know why this thesis would trigger an alert. However, he guessed that it was probably a bug on the website or the staff was negligent.
He shook his head and was about to close his laptop to sleep when he suddenly noticed the name of the author.
Then …
He was stunned.
Lu Zhou?
Winner of last year's Cole Prize in Number Theory?
Proof of Zhou's conjecture, twin prime number conjecture, and Polignac's conjecture?
Does this mean … he proved Goldbach's conjecture this year?
WTF？！
Granville was stunned and instantly woke up!
His sleepiness was swept away, but he didn't move. Instead, he sat on the chair and stared blankly for half a minute.
Then, he looked at the calendar and confirmed that it was already May, not April 1st.
The thesis had a total of more than fifty pages, but compared to the amount of information contained in the title, this was nothing.
"He actually solved Goldbach's conjecture … This is impossible."
Granville muttered to himself as he opened the thesis and read the abstract line by line.
Then, he spent the whole night reading this thesis …
…
On the other side of the Atlantic Ocean, at the École Normale Supérieure in Paris, there was a lecture on the weak Goldbach's conjecture.
The speaker was naturally the prover of this conjecture, Harold Helfgott.
"… The circle method ends in the weak Goldbach's conjecture. We can prove that any odd number greater than 7 can be expressed as the sum of three odd prime numbers, but it is difficult to generalize it to even numbers."
"Of course, my proof is far from perfect. There's still a lot of room for improvement. But if everyone here is interested in studying this problem, I suggest that you change your way of thinking and reconsider this problem. "
The lecture came to an end.
Next was the Q&A session.
There were not only professors and researchers from the École Normale Supérieure sitting here, but there were also students.
After a long time, a young man stood up to speak.
"Professor Helfgott, how long do you think it will take to solve Goldbach's conjecture?"
Helfgott thought for a bit and replied, "It depends on whether our tools to solve the problem are existing or unprecedented. In fact, if possible, I even hope that it will never be solved. Look at what we've got? We've improved the ancient sieve method, created the circle method, the density method, etc … I'm not being greedy, but maybe we can get more treasures from this conjecture. "
The lecture ended.
There was a round of applause as Professor Helfgott walked out of the lecture hall.
He did not stay here for long. He carried his briefcase and walked toward his office.
He pushed open the door and walked to his seat. However, before he could sit down and drink some water, his student walked toward him with a surprised look.
"Professor! I saw a thesis on Goldbach's conjecture on arXiv! "
Helfgott placed his briefcase on the table. His expression did not change as he said in a slow voice, "Amos, I've told you many times, you have to read articles on arXiv selectively. There is only one Perelman, and there will only be one. You should read the classics that I gave you, not the trash that has not been peer reviewed. "
Mathematics and computer science were different. For the computer industry, a difference of two months could mean a difference of a century. Therefore, many people liked to fill in the gaps first, and that was why they frequently used arXiv.
As for mathematics, to be honest, there was not much meaning in just one idea.
Amos looked helpless. He knew that his boss did not like arXiv, but he still tried to explain, "But professor, the author of this article is the winner of last year's Cole Prize in Number Theory! It can't be that his thesis is trash, right? "
Helfgott was slightly stunned. He looked very surprised.
It was not because of the Cole Prize in Number Theory. For people like him, this kind of title was like a fleeting cloud. However, he knew who the winner of last year's Cole Prize was. Because at the academic exchange conference at the University of California, Berkeley, the young man from China left a good impression on him.
But …
Why would such a major conjecture be on arXiv?
Helfgott felt like he had to treat this thesis seriously. He could not miss such a major achievement because of his bias against arXiv.
He took out his glasses from his pocket and immediately said, "Print out the thesis for me."
"Okay, professor!"
Amos returned to the computer energetically and started the printer.
After a buzzing sound, the 50 pages of A4 paper were sent to Helfgott's hands.
Professor Helfgott pushed his glasses and took out a pen from the pen holder. He began to read the contents of the thesis line by line.
Time slowly passed by.
Amos waited for a long time, but he did not get the reaction he expected.
Finally, he became a little anxious and could not help but ask in a low voice.
"Professor, is he right?"
"… I'm not sure." Professor Helfgott shook his head and put down the pen in his hand. He said carefully, "But I don't find any obvious problems."
The proof of such a major conjecture could not be concluded in a short period of time. Not only did he need time, but so did his colleagues who were researching in this area.
Professor Helfgott leaned back in his chair and closed his eyes. He pondered for a while.
After about five minutes, he finally opened his eyes. It seemed like he was talking to his student Amos, but it also seemed like he was talking to himself.
You've already exceeded your reading limit for today. If you want to read more, please log in.
Login
Select text and click 'Report' to let us know about any bad translation.
