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

Just when Lu Zhou returned to the bed and lay flat on his back, and his consciousness entered the system space, at the University of Montreal in Canada, which is thousands of kilometers away from Princeton, the British mathematician Andrew Granville (Andrew Granville) Granville) is browsing Arxiv's web page.

It's one of the things he does every day, sometimes after his morning run, sometimes before he goes to bed.

While most professors like to leave the work of keeping track of the latest research progress of their peers at Arxiv to Ph.D. or master's students in the lab, Granville likes to get his hands dirty on it.

While the quality of the papers on Arxiv, which has not been peer-reviewed, has been mixed, many newcomers have come up with some very creative ideas that are very inspiring...... It's just not perfect.

After a cursory look at about ten papers, Granville yawned and was about to get up and go to bed.

However, at this moment, he suddenly received an alert from a website on his personal page, and it happened to be from the two tabs he was concerned about - analytic number theory and prime number problems.

Granville frowned, his obsessive-compulsive disorder prompting him to click on the reminder.

However, after seeing the title of the article, the corners of his mouth couldn't help but twitch.

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?

In general, such papers would be thrown into the "General Mathematics" section, which he had long since set up and blocked.

Granville didn't know why the paper triggered the alert, but he thought it was probably a bug on the site or an oversight on the part of the staff.

Shaking his head, just as he was about to close his laptop and go to sleep, he suddenly noticed the name of the contributor.

And then......

He froze.

Lu· Zhou？

Winner of last year's Cole Number Theory Prize?

Proof of the Zhou-style conjecture, the twin prime conjecture, and the Polygnac conjecture?

The meaning of this paper is...... This year he proved the Goldbach conjecture again?

TF？！

Granville was momentarily stunned, and instantly sober!

The original sleepiness was swept away, but he did not move, but sat in his chair for half a minute.

Then he looked at the calendar and confirmed that it was May, not April 1.

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

"The Goldbach conjecture was solved...... That's impossible. ”

Whispering to himself, Granville clicked on the paper and followed the abstract of the paper, line by line.

Then, he read the paper for a night......

……

On the other side, on the other side of the Atlantic, the École Supérieure de Paris is giving a lecture on the proof of the weak Goldbach conjecture.

And the speaker, of course, was the provator of this conjecture, Harold Helfgot.

“…… The end of the circle method is in the weak Goldbach conjecture, where we can prove that any odd number greater than 7 can be represented as the sum of three odd primes, but it is difficult to generalize it to even numbers. ”

"Of course, my proof is far from perfect, and there is still a lot of room for improvement. But if all of you here are interested in delving into this issue, I suggest you think differently and reconsider it. ”

The lecture came to an end.

Next, there is the Q&A session.

There are not only professors and researchers from the Ecole Supérieure de Paris, but also students.

After waiting for a long time, a young man stood up and spoke.

"Professor Hellgot, how long do you think it will take to solve the Goldbach conjecture?"

Helfgot thought for a moment and replied, "It depends on whether our problem-solving tools are existing or unprecedented. Actually, if I could, I even hoped it would never be resolved. See what we've got? We improved the ancient sieving method, created the circle method, the density method, and so on...... It's not that I'm greedy, but maybe through this proposition, we can harvest more treasures. ”

The lecture is over.

The audience burst into applause and sent Professor Hatchgort out of the lecture hall.

Without staying here long, he carried his briefcase and walked in the direction of the office.

Pushing open the door and walking towards his place, his student walked up to him with a look of surprise on his face.

"Professor! I saw a paper on Arxiv about the Goldbach conjecture! ”

Helfgot put the briefcase on the table, his expression did not change, and said in an unhurried voice, "Amos, I have told you many times that the articles on Arxiv should be read selectively. There's only one, and probably only one, Perelman, and you're supposed to be reading the classics I've given you, not some unpeer-reviewed dross. ”

Mathematics is different from computers, and for the computer industry, an idea (idea) is two months behind, which can mean a century of difference. Therefore, many people like to occupy the pit first and supplement it later, so they will use Arxiv frequently.

And mathematics, to be honest, just an idea, really doesn't mean much.

Amos looked helpless, he knew that his boss didn't like Arxiv, but he still tried to explain: "But Professor, the author of this article is the winner of last year's Cole Number Theory Prize!" It can't be that the paper he wrote is also dross. ”

Helfgot was slightly stunned, his expression very surprised.

It's not because of the title of the Cole's Number Theory Award, which is already a floating cloud for people like him. But last year's Cole Prize winner, he knows who's it. Because at the academic exchange meeting at the University of California, Berkeley, the young Chinese left a good impression on him.

It's just that......

Such a significant conjecture proves, why is it still on Arxiv?

With a slightly adjusted expression, Helfgort felt that he should be cautious about the paper. Such a major achievement should not be missed because of the prejudice against Arxiv.

I took out the strap of my glasses from my pocket, and I saw him immediately say, "Print out the paper for me." ”

"Okay, Professor!"

Amos energetically returned to the computer and turned on the printer.

With a buzzing sound, soon the 50 pages of A4 paper, which were still hot, were delivered to Helfgot's hands.

Professor Herbgert pushed his glasses, pulled a pen from the pen holder, and examined the contents of the paper line by line.

Minutes and seconds passed.

Amos waited a long time, not for the reaction he was expecting.

Finally, he waited a little anxiously, and couldn't help but ask in a whisper.

"Professor, is he right?"

“…… I'm not sure. Professor Helfgort shook his head, put down the pen in his hand, and said in a cautious tone, "but I didn't find any obvious problems. ”

It is impossible to make a conclusion in a short period of time to prove such a major conjecture, not only for him, but also for his colleagues who are studying this direction.

Leaning back in his chair, Professor Hatchgot closed his eyes and pondered for a moment.

After about five minutes, he finally opened his eyes, as if he were talking to his student Amos, and as if talking to himself.

“…… He used a completely new method, and I could see the shadow of the sieve method on it, and I could also see the traces of the closed orbit integral and the remainder theorem, which were clearly circular methods...... Of course, the most amazing thing is that he introduced the concept of group theory into his theoretical framework. I have seen similar ideas in Professor Zelberg's paper, but not so pure. As for whether he proved it or not, I dare not say for sure, I need to ask the opinions of others......"

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