Translator:Henyee TranslationsEditor:Henyee Translations
A lot could happen in a second.
While Lu Zhou was laying in bed, immersed in the system space, British mathematician Andrew Granville was browsing arXiv at the University of Montreal which was located thousands of miles away from Princeton.
This was one of the daily habits that he would sometimes do after his morning run or sometimes before going to bed.
Although many professors liked to delegate the work of stalking arXivs latest research to masters or PhD students, Granville liked to take this matter in his own hands.
Although the papers on arXiv had not been peer-reviewed, many people had come up with new and creative ideas. They were inspirational albeit not perfected.
Granville roughly scanned through a dozen or so theses, he yawned and was about to go to bed.
Suddenly, on his profile, he got a notification from the website. It was from the two categories he followed: analytical number theory and prime numbers.
Granville flinched. His OCD prompted him to open the notification.
Once he read the title of the article, his mouth was wide open.
[Any even number greater than 2 can be expressed as the sum of two prime numbers.]
Isnt this Eulers statement of Goldbachs conjecture?
Normally speaking, this type of thesis would be in the general mathematics section which would then be blocked by Granvilles settings.
Granville did not know why this thesis gave him a notification. He thought that the website must have malfunctioned.
He shook his head and was about to turn off his laptop and go to sleep when he suddenly noticed the name of the author.
He was stunned.
The winner of the Cole Prize in Number Theory?
Solver of Zhous conjecture, twin prime conjecture, and prime number?
This means that Did he solve Goldbachs conjecture this year?
Granville was instantly awake!
His sleepiness instantly went away and he sat in his chair for half a minute.
Then, he looked at the calendar to confirm that it was not April Fools Day.
A fifty-page long thesis was normal for a conjecture of this size.
I cant believe he solved Goldbachs conjecture No way.
Granville opened the thesis and started reading.
He spent the entire night reading the thesis.
On the other side of the Atlantic, in cole Normale Suprieure, a lecture on the weak Goldbachs conjecture was going on.
The lecturer was Helfgott.
The limit of the circle method is the weak Goldbachs conjecture. We can prove that any odd number greater than 7 can be expressed as the sum of three prime numbers, but it is difficult to generalize it to even numbers
Of course, my proof is far from perfect. There is a lot of room for improvement. If anyone in the audience is interested in this problem, I recommend you change your mind and research something else.
The lecture came to an end.
Next was the question and answering session.
There were both professors and students from cole Normale Suprieure attending this lecture.
After a long time, a young man spoke.
Professor Helfgott, how long do you think until Goldbachs conjecture is solved?
Helfgott thought and said, It depends on whether or not the tools used to solve the conjecture exists or not. In fact, I hope it is never solved. Look at what we have received? In order to solve this conjecture, we invented the sieve method, circle method There is much more to be gained researching this problem.
The lecture ended.
The crowd erupted in applause and Professor Helfgott left the lecture hall.
He did not stay there for long. Instead, he carried his briefcase and walked toward his office.
When he opened the door and before he could sit down, his student walked over with a horrified look.
Professor! I saw a proof of Goldbachs conjecture on arXiv!
Helfgott placed his briefcase on the table and did not change his expression as he said calmly, Amos, Ive told you, you have to be more careful when reading theses on arXiv. Theres only one Perelman. You should look at some classic publications that Ive given you, not ones that havent been peer-reviewed.
Mathematics was different than computer science. For computer science, two months could be a century. Therefore, many people liked to first publish before they prove. Hence, they used arXiv frequently.
However, for mathematics, publishing without peer review meant nothing.
Amos had a helpless expression. He knew that his boss did not like arXiv but he still tried to explain, But Professor, this thesis was written by the winner of Cole Prize in Number Theory! Surely his paper is legit.
Helfgott froze and he had a surprised expression.
Not because of the Cole Prize award because he had met many people that had won the Cole Prize. It was because he knew who won the Cole Prize in Number Theory last year. He was there at Berkeley and the young Chinese man left a good impression on him.
Why would he submit such a major conjecture on arXiv?
Helfgott changed his attitude. He felt that he should treat this thesis with caution. He could not ignore such a major discovery due to prejudice against arXiv.
He took out his glasses from his pocket and said, Bring me the thesis.
Amos went to the computer with enthusiasm and printed the thesis.
The printer quickly printed fifty warm pages which were then delivered to Helfgott.
Professor Helfgott adjusted his glasses and took out a pen as he started to read the thesis line by line.
Time slowly passed by
Amos waited for a long time.
Finally, he was a little anxious and he could not help but ask, Professor, is he correct?
I dont know, said Professor Helfgott as he shook his head. He then placed the pen down as he said, But I havent found a mistake yet.
It was impossible to verify a major conjecture in a short amount of time. Helfgott needed time and friends that were in this field.
Helfgott leaned back in his chair and closed his eyes as he started to think.
After five minutes, he opened his eyes and said to Amos.
He used a brand new method, I can see signs of the sieve method, and residual of the circle method Of course, the most interesting part is the introduction of his own theoretical framework. I have seen similar ideas in Zellbergs thesis. As for whether or not his proof is correct, I cant make a decision yet. I need someone elses opinion