The top student must be diligent.

Chapter 87: Excitement in Mathematics
"He did?"

Hearing what Bombieri said, Deligne, who had been taking a nap with his eyes closed, opened his eyes, turned his head and asked.

“In my opinion, he did.” Bombieri nodded and exclaimed: “These are definitely two very beautiful papers.”

"Each step is very detailed. Although I read it quickly, I am basically sure that they are all correct."

"And just as we had said at the beginning, he has a mathematical mindset that most other mathematicians don't have. At every critical step, he is always able to make progress in ways that we can hardly imagine, and every time he makes progress, it is always so efficient that it is hard to imagine before watching, but after watching, you will only be amazed."

"It makes me wonder, is it possible that the brain structure of these young people is different from ours?"

Bombieri's praise made Deligne raise his eyebrows, "That's really a very high evaluation."

"You will understand after you watch it." Bombieri said with a smile.

Deligne laughed: "Anyway, you just read it and got the result. It's enough to know that his conclusion is correct."

He hadn't looked at it just now, just waiting for Bombieri to tell him the result.

Bombieri immediately shook his head and said, "No matter what, I still recommend you to read his paper, even if it is just to appreciate a piece of art made of mathematical words."

"Really?"

Hearing what Bombieri said, Deligne became interested: "Then it seems I really need to take a look at it as soon as possible."

“You won’t be disappointed,” Bombieri said.

Deligne nodded and decided to take some time to read it over in the next few days.

At this time, the originally quiet small coffee shop gradually became noisy, and many mathematicians from the Princeton Institute for Advanced Study had finished reading.

Discussions gradually began, with some exclamations.

"He was definitely right. I couldn't find any mistakes, and his process was very detailed and easy to follow."

"Yes! I think so too. He is right."

Finally, several people came to Bombieri and asked, "Professor Bombieri, do you think those two papers are correct?"

Bombieri smiled and replied: "My conclusion is the same as yours, it is absolutely correct."

……

Oxford university.

"Yes, yes, that's right." James Maynard looked at the paper on the screen while holding a pen in his hand to do calculations according to the contents of the paper.

His eyes were filled with excitement.

【MQ^5/2R^3/x^(115)……】

【x^(1/3)/M^(1/3)≤N3≤x^3/7+……】

"Then we can see that for every <1 and A>0, there exists a constant C>0 such that for x>2, there exists Σ_(1≤q≤x^θ)E(x;q)≤Cx/log^Ax!"

"The Elliott–Halberstam conjecture has been perfectly proved!"
"Perfect!"

"It's so perfect!"

As a mathematician who regards number theory as his lifelong pursuit, James Maynard is very happy to see any great achievements in number theory.

Even though it was not something he had researched himself, he was still happy with it.

Suddenly, the indignation he had felt towards Xiao Yi for playing Fermat's tricks a few days ago was calmed down. For the sake of these two papers that made him applaud -

Of course I forgive him!
Excited, he immediately took out his cell phone and called Terence Tao, a senior researcher and good friend of his.

Terence Tao.

Soon, the call came through.

Just when he was about to speak, Terence Tao on the opposite side spoke first.

"Hey! James, have you read those two papers by Xiao Yi?"

"I can't believe that the problem we have been studying for so long has been solved so suddenly!"

"There is also the theory in the first paper that combines far-Abelian geometry and automorphic forms. Hmm... In the paper, Xiao Yi named this theory [Etale Algebraic Cluster Automorphic Theory]. I took a quick look at this theory and was surprised to find that the Polymath project we once worked on will be able to achieve a breakthrough directly!"

"The only regret is that Xiao Yi has already proved the Elliott-Halberstam conjecture, and he has directly solved the prime number gap problem into 6..."

"Ha, this can't be said to be a pity, it should be said to be a good thing!"

"besides……"

Just as Tao was about to continue speaking, he suddenly realized something and asked, "James, why aren't you talking?"

James Maynard said helplessly: "You have been talking all the time, how can I speak?"

“Ahahaha~” Tao laughed awkwardly, and then said, “Okay, okay, you go first, you go first.”

Maynard said helplessly again: "But you have already said everything I wanted to say."

"Ah, this..." Tao Zhexuan paused for a moment, and finally asked: "How about...you continue to listen to me?"

"Okay, go on." Maynard sighed.

Tao didn't hesitate and started talking right away: "Also, using the Etale algebraic variety automorphism theory, maybe we can make more achievements in prime number problems, such as the x^2+1 prime number problem."

Maynard: "Why not consider twin primes? We are now within 4 of the final answer."

"Hmm... Because I thought about it roughly, and finally I can conclude that the limit of Etale algebraic variety automorphism theory is 6. If we want to improve it to the level of [less than 3], we may still need to think of ways from other angles."

"So, why don't we study the application of this theory in other areas!"

"That's the really unfortunate thing."

Although it is a pity that we cannot go further and directly prove the twin prime conjecture.

But the undeniable fact is that -

This jewel in the crown of number theory has been officially pushed to the number 6 thanks to Xiao Yi's achievements!

……

The influence of the two papers continues to grow, more and more mathematicians have read them, and more and more mathematicians have expressed great recognition of them.

Some mathematicians even began to believe that these two papers could be regarded as one of the biggest breakthroughs in mathematics this year, and that Science should include this in its year-end selection.

There are quite a few mathematicians who agree with this view, and there is absolutely no opposition. Even the editor-in-chief of IHES, Bergeron, has come out to say that when "Science" begins to select the top ten most important breakthroughs in the scientific community this year, he will definitely vote for the [Etale Theory of Automorphism of Algebraic Clusters].

Of course, there are also quite a few mathematicians who are making a fortune in silence.

These mathematicians are looking forward to Xiao Yi's two papers because Xiao Yi's theory will help them achieve major breakthroughs in their own projects, or even complete them directly!
(End of this chapter)