Chapter 235 Surprising Evaluation

If the core idea of ​​the minimum quadratic non-residual estimation of modulus prime numbers in the group construction method comes from the large sieve method, then the part of the idea of ​​Fourier analysis of the function on the circle in Helfgott's paper is just For his theory plump branches and leaves.

This "99%" work started before he went to California to listen to the lecture last year, and it has now ended. The remaining 1% is the inspiration that keeps most people out of the door of truth.

And now, this piece of the puzzle has been held in Lu Zhou's hands.

Before Charles Fefferman finished the class, Lu Zhou packed his things quietly, just as he came quietly and left quietly.

The old professor standing on the podium just glanced at the direction he was leaving, a smile appeared on the corner of his mouth, and then continued to teach his number theory class in that slow voice as if nothing had happened.

Back at the apartment, Lu Zhou picked up the pen and wrote on the paper.

The emerging ideas are like diabetes insipidus, which cannot be stopped!

I finished writing the fifth page eloquently, then the sixth page, and the seventh page...

Time passed by every minute and every second.

The wall clock on the wall passed noon and then turned to dusk until the sky outside the window gradually darkened.

When Lu Zhou reached the end of the sixteenth page, he finally stopped the slightly trembling pen tip in his hand and looked at the research results in front of him.

"...and then this introduces Bombieri's theorem, which is obvious a few dozen lines down the line...and you're done!"

Taking a deep breath, Lu Zhou leaned back on the chair, exhaled the pent-up air in his chest, and finally let out a smile from his frowning brows.

Further down, it is the solution to Goldbach's conjecture.

From now on, his boat is truly sailing into an unknown sea.

Still, he believes he can do it.

This gratuitous but unshakable belief is probably the same feeling that Andrew Wiles felt when he looked at Fermat's last theorem after completing the proof of Taniyama-Shimura's theorem.

When a tool is completed, fulfilling the mission of the tool is just a matter of going along with the flow.

Goldbach's conjecture, which has gathered the strengths of everyone's research for nearly two hundred years and has been studied by several masters of algebra, has finally come to this point.

There is no pride in Lu Zhou's heart, only honor.

It is an honor that he will cap this building.

After thinking about the unspeakable feelings for half a minute, Lu Zhou took out his mobile phone and sent a text message to his mentor Deligne and his friends in Princeton, telling them that his project had entered a critical stage, and he planned to Retreat and study for a while, so that they don't have to worry.

Then, he turned off his mobile phone and completely sealed himself in this small room of more than ten square meters...

We have reached this point, and if everything goes well, it shouldn't take too long.

If it doesn't go well...

Then he won't come out!

...

The design of the Institute for Advanced Study in Princeton is very interesting. The restaurant and the lecture hall are designed together. During the lunchtime lectures and biweekly seminars, people sitting here can even listen while eating.

At the same time, the coffee machine here is also free to use.

Sitting in the corner of the restaurant, Deligne looked at the paper in his hand meticulously.

As an academic editor of many journals such as "Annual of Mathematics" and "Chronicle of Mathematics", he usually has very little free time, so he usually puts the review time in an hour after lunch.

Unless it is a particularly interesting paper, he generally will not bring it back to the office, or take it out to discuss research with other professors.

Sitting opposite Deligne with a dinner plate, Professor Edward Witten greeted with a smile and asked.

"Why haven't you seen your new doctoral student recently?"

Among all the doctoral students recruited by Princeton recently, Lu Zhou can be said to be the one Witten admires the most, especially the talent in mathematics and physics he showed at the CERN report meeting made him seem to see himself in his youth. He has always regretted not being able to take it under his wing.

CERN recently canceled the experiment on the 750GeV energy region. He has always wanted to talk to the young man about the idea of ​​the characteristic peak, but unfortunately, he has never had the opportunity.

Professor Deligne didn't take his eyes off the paper, but simply replied: "He took a leave of absence recently."

Witten: "Leave?"

"Well," Deligne nodded, and casually replied, "He's studying Goldbach's conjecture, and I just granted him a two-week leave."

"Goldbach's conjecture..." Witten's expression was slightly surprised, but it didn't change much. "This is really an interesting proposition. I thought he was working on the standard conjecture in your research group."

While making a mark on the thesis paper, Professor Deligne said casually: "I invited him, but he was not interested, and I didn't force it. For this kind of genius, force him to do one thing Instead, it is better to let him develop freely in the direction he is interested in."

At this moment, the mobile phone placed on the table vibrated suddenly.

Seeing the text message reminder, Professor Deligne reached out to pick up the phone and looked at it, his eyebrows twitched suddenly.

【Dear Professor Deligne, I am your student Lu Zhou. The thing is, my research has entered a critical stage, and I need to retreat for a period of time, maybe a month, maybe... I don't know. In short, before the end of this year, I will give you a satisfactory explanation. 】

Although he didn't see what was written on the phone screen, he could see the changes in his old friend's expression. Edward Witten smiled and continued to ask, "Do you think he can succeed?"

Professor Deligne put down the phone expressionlessly.

After thinking for a moment, he suddenly sighed, shook his head and said.

"I don't know, I just don't agree with his research methods. Closed research is not a good choice, and the worst result may even lead him into a dead end. Even if he asks for leave to attend lectures and exchange meetings , I'm all for him, and I can even help him apply for funding. But until now, as far as I know, his leave is just to lock himself in the house."

Witten raised his eyebrows and asked with a smile: "But you still support his choice?"

"Yes, but I gave him a year," Deligne shrugged, this serious old man rarely used an uncertain tone, "After all, I dare not say that I will not I would be mistaken, because his performance in proving the twin prime number conjecture on the spot in the report meeting in Princeton really surprised me. There was even a moment when I had an illusion..."

Witten: "Illusion?"

Deligne was silent for a while, then slowly said: "I seem to see Grothendieck."

Hearing this sentence, Edward Witten was obviously taken aback.

Grothendieck!

The father of modern algebraic geometry, the pope of modern mathematics!

To describe the talent of a mathematical genius in a certain field, many people like the exaggeration of the successor of Faltings, or even the successor of Jean-Pierre Serre, but few people will A mathematical genius is compared with Grothendieck, even if this is just an exaggerated metaphor or expectation.

There must be no more than five new algebraists who can receive this honor.

After a while, Witten said in an unexpected tone.

"That's really... surprising."