Scholar’s Advanced Technological System

A cup of coffee is enough for a lot of things to happen.

As the ark returned to its bed, lying flat, conscious of entering the system space, British mathematician Andrew Granville was browsing Arxiv's web page at the University of Montreal, Canada, thousands of kilometres from Princeton.

This is one of the things he must do every day, sometimes after the morning run and sometimes before bed.

While most professors prefer to throw their peer research updates on Arxiv to doctoral or master's students in the lab, Granville likes to do it personally.

While the quality of the paper on ARXIV without peer review is uneven, many new people have come up with some very creative ideas that are very instructive… just not perfect.

Looking roughly at about ten papers, Granville hit an arrears and was about to get up to bed.

However, at this point, his personal page suddenly received alert from a website and came from two tags of his concern - Parsing Mathematics and Argumentative Problems.

Granville frowned and the obsessive-compulsive disorder prompted him to turn on the reminder.

However, after seeing the title of the article, he could not help but leave the corners of his mouth alone.

"Any even number greater than 2 can be expressed as the sum of the two primes"

Isn't that what Goldbach thought of Euler's statement?

Generally, this kind of paper would be thrown into the "general math” section, which he'd set aside a long time ago.

Granville doesn't know why this paper triggered a reminder, but it's probably the website that bugs or staff missed it.

Shaking his head, he suddenly noticed the contributor's name as he was about to close his laptop to sleep.

Then…

He was stunned.

Lu Zhou?

Last year's Cole Mathematics Award winner?

Proof of weekly speculation, twin count speculation, Polynesian speculation?

What does this thesis mean… this year he proves Goldbach's assumptions again?

WTF?!

Granville suddenly shrugged, and suddenly sober!

The original difficulty swept away, but instead of moving, he sat in a chair for half an hour.

He then looked at the calendar and confirmed that it was May, not April 1.

The paper consists of more than fifty pages, but this is nothing compared to the amount of information contained in the title.

“It is impossible to solve the Goldbach conjecture…. ”

With a whisper in his mouth, Granville opened the paper, followed the abstract of the paper and looked down line by line.

Then, this paper, he watched all night...

……

On the other hand, far across the Atlantic, a lecture on the proof of the weak Gothenbach conjecture is being given by the Paris high school teacher.

And the speaker, naturally a testament to that assumption, Harold Helfgott.

“… at the end of the circle, weak Gothenbach speculates that we can prove that any odd number greater than 7 can be expressed as a sum of three odd primes, but it is difficult to extend it to even numbers. ”

“Of course, my proof is far from perfect, and there is plenty of room for improvement. But if all of you are interested in studying this issue in depth, I would suggest that you reconsider it in a different way. ”

The lecture concludes.

The next step is to ask questions.

There are not only professors and researchers of Parisian high school teachers sitting here, but also students.

After a long wait, a young man stood up and spoke.

“Professor Helfgott, how long do you think it will take to resolve the Gothenbach conjecture? ”

Helfgott thought about it and replied: "It depends on whether our tools to solve the problem are available or unprecedented. Actually, if I could, I would even hope that it would never be resolved. Look what we've got. We've improved old screening methods, created round and density methods, etc. … Not that I'm greedy, but maybe we can get more treasures through this proposition. ”

The lecture is over.

A round of applause was raised and Professor Helfgott was sent out of the reporting room.

Without making more stops here, he took the briefcase and walked in the direction of the office.

Pushing the door open, he walked to his position, but before waiting for him to sit down for a sip of water, his students walked towards him in surprise.

“Professor! I saw a paper on Goldbach's guess on Arxiv! ”

Helfgott put the briefcase on the table, his expression didn't change much, and he said, "Amos, I've told you many times, the article on Arxiv has to be selective. There's only one Perelman, and there's probably only one, and you should see the classic journals I drew for you, not the bad ones without peer review. ”

Unlike mathematics and computers, for the computer industry, an idea is two months away, which could mean a century away. So a lot of people like to take the pit first, then add it up before using ARXIV more often.

And mathematics, honestly, with just one idea, really doesn't make much sense.

Amos's expression was helpless, and he knew his boss didn't like Arxiv, but he tried to explain: "But Professor, the author of this article was the winner of last year's Cole Theory Award! It's impossible that his thesis is a mess, too. ”

Helfgott was slightly stunned and very surprised.

Not because of the name of the Cole Prize for Mathematics, but because such a name is already cloudy for people like him. But last year's Cole laureate, he knew whose it was. Because at the academic exchange at Berkeley, California, that young Chinese man made a good impression.

Just...

Why is Arxiv still on this big speculation?

With a slight finishing touch, Helfgott felt he should treat the paper with caution. Such a significant achievement must not be missed because of prejudice against Arxiv.

He took his glasses out of his pocket and immediately said, "Print the paper for me. ”

“Yes, Professor! ”

Amos returned to the computer with great energy and started the printer.

With a buzzing sound, the 50 pages of hot A4 paper soon arrived in Helfgott's hands.

Professor Helfgott pushed glasses and pulled a fountain pen out of the pen barrel, looking at the contents of the paper line by line.

Time goes by.

Amos waited a long time and did not wait for the reaction he was expecting.

Finally, he was in a bit of a hurry and couldn't help but whisper.

“Professor, is he right? ”

“… I'm not sure.” Professor Helfgott shook his head, dropped the pen in his hand and said with caution, "but I did not find any obvious problems. ”

Proof of this great speculation is also unlikely to be concluded in a short period of time, not only by his time, but also by his peers who are studying this direction.

Leaning on the chair, Professor Helfgott closed his eyes and pondered for a while.

About five minutes later, he finally opened his eyes, like talking to his student Amos, and talking to himself.

“… he applied an entirely new method, where I could see the shadow of the sieve method, and the closed-orbit integral and residual theorem, which are obviously traces of the circle method… Of course, the most remarkable thing is that he introduced the concept of mass theory in his own theoretical framework. I've seen similar ideas in Professor Zelberg's thesis, but not so pure. As for whether he proved it or not, I don't dare to make a decision. I need to ask others for their opinions...”