Ultimate Scholar

Home of Andrew Wiles, England.

The phone rang suddenly, and Andrew Wiles was woken up, and of course his wife was also woken up.

At this time, it was midnight in the UK, and it was about three o'clock, which was the rest time.

Andrew Wiles picked up the phone with a troubled expression.

Who is calling him so late?

It turned out to be Simon Donaldson.

This old guy stays up so late, harassing him?

Don't know that sleep is very important for these elderly people?

When he got on the phone, he said angrily, "Simon, if you don't give me a reason that satisfies me, I will definitely remember the fact that you woke me up tonight."

"Hey, Andrew, don't worry, I was woken up by someone too." Simon Donaldson said, "Guess, what is your student who hasn't come here doing?"

Wilston was taken aback for a moment.

This is... Li Mu?

Calculating the time, it seems that it is indeed daytime in Huaguo.

"What happened again?" He asked suspiciously?

"Just now, my friend in the United States suddenly called and told me that there was news from Huaguo that Li Mu was proving the Polyignac conjecture and the Hardy-Littlewood conjecture."

Wiles: "???"

Question marks were written all over his face: "Are you sure? Is it true or not?"

"Why lie to you?" Simon Donaldson said, "I'm watching the live broadcast of his proof right now. He has already solved the Polignac conjecture, and now it's Hardy Littlewood's turn to conjecture. "

In an instant, Wiles was no longer sleepy.

Just kidding, how could he miss such a big event in the mathematics world?

"Give me the URL of the live broadcast, and I'll watch it right now."

"I have sent it to you. You have to translate for me later what Li Mu is talking about. After all, you have learned Chinese for so long."

"I can't guarantee this. I can fully translate it. You know that Chinese is difficult to learn."

While speaking, Wiles turned over and got up, and at the same time gave his wife a look, letting her continue to sleep by herself.

His wife had a helpless expression on her face.

Sometimes when a mathematician's wife is faced with such a thing, it seems commonplace.

Perhaps for most mathematicians, mathematics is more important than love.

Wiles came to the study, got a cup of coffee, and turned on the computer.

Entered the live broadcast room sent by Donaldson.

This is a Chinese website, so the text on the webpage is also in Chinese.

Although the webpage translation function can be used, Wiles still relied on his own Chinese ability to identify it carefully.

"Li Mu...proved...the Polignac conjecture and the Hardy-Littlewood conjecture!"

"It's actually true!"

He quickly clicked on the live broadcast, and saw Li Mu writing mathematical formulas on the blackboard.

"This is proving... the Hardy-Littlewood conjecture!"

With just a glance, Wiles could see what Li Mu was writing.

"This is a theory of divergence... It actually uses non-Archimedean absolute values... OMG, is this true?"

Simon Donaldson's voice came again on the phone.

"Of course it is true. Quickly translate for me and practice your simultaneous interpretation ability."

Wiles: "Don't worry, I haven't understood yet..."

However, Simon Donaldson still urged: "Translate for me quickly! Oh, karma, Li Mu's step is really critical. Judging from what he wrote on the blackboard, it seems that he has successfully found the pair of twin prime numbers and the prime number theorem." The superposition relationship between? Oh, what is he talking about?"

In this way, a Fields Medal winner and a Fields Special Award winner got up in the middle of the night and connected to the line, listening to a report by a young man from China.

In fact, there are many more like them.

A lot of well-known mathematicians in the world have entered this live broadcast room.

It doesn't matter what time zone these mathematicians are in, whether it's a break or not.

Even mathematicians from some countries such as Japan, Han, and Xin Apo, because their time zones are not much different from Hua, they are basically still working, but they are also attracted by this report.

As a result, the students of the mathematics department of these national universities received the news that the teacher asked for leave temporarily before the class. What's more, they were in the class, and then the teacher opened the live broadcast room and took them to watch it together. Li Mu's proof.

The euphemistic name is: Witnessing history.

It's really just what their teacher wants to see.

Of course, the result of this situation is that both the teacher and the students are confused.

Who made the content too esoteric. \b\b

Not only did they not understand Chinese, but they also did not understand what was being said.

For them, the only good thing is that the mathematical formula written by Li Mu on the blackboard can still make them associate, so as to figure out roughly how to prove it.

However, even if you want to do this, it is very difficult. Only those top mathematicians, and mathematicians who have a deep understanding of relevant knowledge can easily understand it. As for other abilities that are slightly less capable, or research Mathematicians in other fields can only be half-understood, or confused from beginning to end.

Can't understand, don't understand at all.

...

Beijing Auditorium.

Li Mu on the stage did not know that his report had attracted so many internationally renowned mathematicians to watch.

He continued to prove on stage wholeheartedly.

Whether it is divergence theory or non-Archimedean absolute value, they are all methods that he has thought of recently.

The source of these inspirations lies in the report of Professor Lin Yao that day.

The topic of Lin Yao's report that day [Non-Archimedean submorphic mapping of hypersurfaces in projective varieties], although not much related to the Hardy-Littlewood conjecture, is common to mathematics and mathematics. It is also common.

As long as the relationship is found, it can be used.

"...by Theorem 2.1 and Theorem 2.2, the algebraic extension of the finite field of characteristic p whose non-Archimedean absolute group is isomorphic to ^Zp in..."

【A(F)→H1(GF，T(A))...】

Wrote another formula on the blackboard.

Li Mu stood up straight with a slight smile on his face.

At the same time, the mathematicians who understood the field showed surprise again.

"Wait... is he turning the whole problem into a problem of algebraic geometry?"

Qiu Chengtong narrowed his eyes.

Through a series of transformations, Li Mu completely transformed the original Hardy-Littlewood conjecture into a problem in algebraic geometry.

"Does he want to use algebraic geometry to solve it?"

In Qiu Chengtong's mind, this idea has already arisen.

Use algebraic geometry to solve problems in number theory!

What a crazy thing.

One of the mathematicians who did this in the past was Gerd Faltings.

It is one of the top mathematicians in the world today, who used the method of algebraic geometry to prove the Model conjecture in number theory, and finally won the Fields Medal for it.

And now Li Mu also uses this method to complete the proof?

Zhang Yitang next to him also had the same expression.

He has seen many geniuses, and he himself is considered a genius, but he never thought that Li Mu would plan to do this.

At the same time, many mathematicians in the live broadcast room who were aware of Li Mu's intentions gasped for it.

"Can this really be done?"

In the UK, Andrew Wiles and Simon Donaldson have been on the phone all the time, exchanging information about Li Mu's report.

They are all top mathematicians, so they can also understand the meaning of what Li Mu wrote.

As for this question, they couldn't help but keep silent for a while.

till the end.

"I hope he can."

Even if Li Mu used other methods to prove this conjecture, it probably wouldn't make them so excited.

But if this problem is really solved using algebraic geometry methods, then this will have far-reaching significance for the mathematical community.

Because this will once again stimulate mathematicians' confidence in the realization of the Langlands Program and the unification of algebraic geometry and number theory.

This report will also become a classic report in the mathematics world.

...

on the rostrum. \b

Li Mu turned his head slightly and said with a smile, "I believe some friends have already seen my thoughts."

"Then here, we will officially enter the field of algebraic geometry—"

"And here, please let me briefly introduce a new theory to you."

"I call it k-module theory."

"For the time being, you can simply understand it as a combination of k-theory and modulus space."

His words once again shocked the mathematicians present.

Combining K-theory and modulus space?

K theory is closely related to algebraic geometry, algebraic number theory and other fields, and modulus space is the key research object of algebraic geometry.

It is not without precedent that the two have been used in combination in the past, but very rarely, because there has never been a systematic method that can perfectly combine these two methods.

And now Li Mu's intention... is to realize this?

Li Mu didn't explain much, turned his head, and began to write on the blackboard.

Everyone in the audience held their breath and focused, even if they couldn't understand, they knew that Li Mu was doing something important.

Following the list of formulas on a blackboard, Qiu Chengtong showed a dazed expression.

"So it turns out that each point in the module space is calculated according to the K0 functor, so as to generate the semigroup of the projective module isomorphism class... By the way, plus the incompleteness of the module space, after that, He is probably going to use this to estimate the distribution of pairs of twin primes..."

As a top mathematician, Qiu Chengtong's mathematical intuition is of course very strong.

Almost immediately, he saw Li Mu's purpose.

But even though he could see it, if he was asked to do it, he could only choose to give up.

It is too difficult technically to do this.

Especially the calculation link that needs to be carried out later will test the control of the whole method even more.

He might be able to give it a try when he was young, but now, he has to give up.

After that, Li Mu did indeed start a lot of calculations as he expected.

These calculations of his gave the other people on the scene a feeling of walking a tightrope. Once they made a mistake, it would be an absolute mistake.

However, Li Mu is like a humanoid computer, handling the entire complex calculation process perfectly, and his intuition in mathematics is even more vivid.

And such calculations also need enough blackboards.

So people saw the staff nearby dragging up a small blackboard from time to time, until all 20 small blackboards were dragged up——

[To sum up, π2(N) is approximately equal to ∫dt/(lnt)^2≈2Ct(N/(ln)^2N]

[where Ct is the twin prime constant. 】

[The certificate is completed. 】

On the last blackboard, on the last blank space, Li Mu wrote the last three lines.

"At this point, I think the Hardy-Littlewood conjecture is officially history."

"All the content of this report is over."

"Let me conclude with the honor and pride of presenting to you the Polignac-Lee theorem, and the Hardy-Littlewood-Lee theorem."

Li Mu smiled slightly, and then bowed to the audience.

There was thunderous applause.

He really did it, using the method of algebraic geometry to solve a number theory problem!