Ultimate Scholar

Before today's report started, Huaguo Mathematics Society and Li Mu did not announce to the public what the title of Li Mu's report would be.

So before the report started, people were also wondering why Li Mu had to make a report.

Let Fan Pairen go up and talk about it, and prove whether he understands it or not.

What can Li Mu say when he goes up?

Therefore, many mathematicians have asked the Huaguo Mathematical Society before.

The Huaguo Mathematical Society only responded with one sentence: a report related to the twin prime number conjecture.

Because they were afraid of saying the topic of the report in advance, they would scare Fan Pairen away.

The main character was not present, so the report would be a little less interesting.

After other scholars learn about the content of Li Mu's report, what else can they say? Although they don't know what else is worth reporting about the twin prime number conjecture, this is Li Mu's report after all, so maybe there will be something What about the more important content?

Ever since, these scholars came here like opening a blind box.

Otherwise, Fan Pairen alone is not worth so many of them coming, just go back and find out about the follow-up on the Internet. \b

But now it proved that their expectations for Li Mu had not been disappointed.

As soon as the topic of this report came out, the audience was stunned, and then there was an uproar.

Polignac conjectures!

The Hardy-Littlewood Conjecture!

Sure enough, it is related to the twin prime number conjecture, but, isn't this a bit too much...

Let’s forget about Polignac’s conjecture. After all, Li Mu said before that he already has a wonderful proof of this conjecture.

But what about the Hardy-Littlewood conjecture that popped up all of a sudden?

If the Polygnac conjecture and the twin prime conjecture still have some inheritance, then the Hardy-Littlewood conjecture is somewhat different to some extent.

Because the latter discusses progressive distribution, if you want to solve it, the methods are not necessarily similar.

It turned out that only about ten days had passed in a short period of time, and Li Mu was going to solve these two conjectures one after another?

Really killed the whole family of the twin prime conjecture?

For a while, these scholars were even a little hard to believe.

However, some scholars immediately picked up their mobile phones, contacted other scholars who had good relations but had left the capital, and told them the news.

Although there are still many scholars who come to see the report, some scholars have already left Shangjing.

After all, the leave they asked for was only for the few days when the meeting was held.

That is to say, it is still during the summer vacation, so so many scholars can be left behind.

And those who have already left the scholars, after receiving the news, they immediately beat their chests and stamped their feet, regretting endlessly.

Zhuo!

The last time they were able to witness the proof of the twin prime number conjecture, they were grateful for it, but now they missed the proof of the other two conjectures.

Of course, soon, these scholars suddenly remembered that there was a live broadcast of this report, so a group of people rushed into the live broadcast room.

Seeing the title on the PPT, apart from being shocked that Li Mu actually wanted to prove these two conjectures at the same time, he was also glad that he was not late.

Catch the live stream!

At the same time, some quick-response people suddenly remembered the intention of Li Mu's report.

This is to give Fan Pairen a hard time.

You, a Minke, came to Pengci to solve the twin prime number conjecture and other versions of the three major conjectures. In this huge comparison, even if Fan Pairen really understands a little, it seems weak.

Not to mention, he has been hammered by the fact that he pretends to understand.

For a while, there were many eyes in the audience, and they turned to the positions in the first row.

Today, Fan Pairen, as the invited speaker, is "honored" to be placed in the first row.

In the past, those who could sit in the first row were all leaders in the domestic and international mathematics circles.

So many mathematicians present ridiculed this, this time Fan Pairen can be regarded as a glorious ancestor.

And at this moment, even if Fan Pairen, who was sitting in the first row, didn't turn his head, he could still feel countless piercing gazes from behind.

Let him sit on pins and needles.

He never expected that not only would Li Mu report with him, but he would also have to prove the other two conjectures on the spot. \b

But looking at himself, he still doesn't even have a clue what to say in the report later.

Although Shi Lei asked him to speak useful content for ten minutes, at present, he might not even be able to speak for three minutes.

As for talking about life experience, talking about the tragic past, he understands the truth, but he can't talk about it, he doesn't have that eloquence.

Not everyone is a master of success.

Although he is a professor, every class in the school is 45 minutes a class, but the class in his private secondary school is very simple, 99% of the students do not attend the class, and almost all the teachers who can give serious lectures are extinct. Follow the script and you're done.

So he really can't do it, crap for forty minutes.

Thinking of this, his heart floated again, should he still slip away?

This idea that had appeared in him several days ago became more restless at this moment.

But now he is sitting in the first row, even leaving his seat would be too obvious, so he can only temporarily give up this idea.

However, in fact, he took it for granted, and not many people present cared too much about him.

Compared to Li Mu's report, he is no longer worthy of concern.

Even Yuan Xiang and others sitting in the first row listened to Li Mu's report seriously.

...

On the rostrum, Li Mu, who put on the previous suit again, opened the PPT, saw the surprised expression on the scene, and smiled slightly.

He had a panoramic view of everyone's expressions, including Fan Pairen.

He could imagine everyone's surprise before.

"As I said last time here, there is not enough blank space left on the blackboard and no time left to complete the proof of the Polignac conjecture."

He smiled and said: "But today, I will have a lot of time. The blackboard, I just saw it in the backstage lounge. The Huaguo Mathematical Society and Shangjing University have prepared 20 small blackboards. It seems that I have designated 20 small blackboards today. I can't run away."

The people present all smiled knowingly.

Yuan Xianghe and Zhengxing couldn't help laughing.

If you can still let your kid run away today, they will stop messing around in Huaguo's mathematics circle.

"Then we won't talk too much nonsense, let's start with the Polignac conjecture."

Li Mu nodded slightly towards the auditorium, then turned his head, and came to the first small blackboard.

There will be many small blackboards that need to be used today.

So even if he had twenty yuan, he had to save it.

God knows if the rostrum can be lined up after twenty small blackboards are pushed up.

"To save time, I will continue from where I discussed the Polignac conjecture at the end of my last report."

Afterwards, he wrote down on the blackboard the content deduced from the last half of the blackboard in the last report.

For him, even though it has been so long since these formulas, he still remembers them clearly.

"Last time I have deduced that when k belongs to 1 to 50, there are infinitely many pairs of prime numbers of the form (p, p+2k)."

"And next, how do we expand k to positive infinity?"

"Actually, the next step is very simple."

Li Mu said, and then began to write a line of formulas on the blackboard.

【H1(GK，Z/pZ)Z...】

The people present saw it, and those who understood suddenly showed expressions of surprise.

"The Kummer theory!"

"I probably thought of it, but how to do it?"

"Is it necessary to improve the Kummer theory again? The original Kummer theory alone should not be able to solve it."

While all the scholars were lost in thought, they also looked at Li Mu's proof more attentively.

In this way, as Li Mu's proof progressed step by step, everyone really discovered the difference with the original theory.

"Sure enough, he has improved!"

The eyes of those scholars who understood it brightened, and they couldn't help admiring it in their hearts.

But there are still the vast majority of people who are at a loss.

Is this also an easy step?

Is simplicity a concept that everyone can understand?

For a moment, they felt as if they had turned into Muggles.

Obviously, not all the scholars who come here are of extremely high mathematical quality.

The simplicity in Li Mu's mouth is completely another world to them.

Of course, Fan Pairen was also included among these people.

He looked at what Li Mu said in confusion.

In the last report, he could understand a little bit what Li Mu said at the beginning, even if it was only superficial, but this report, from the beginning to the present, he has not been confused.

He has studied the twin prime number conjecture for nearly 20 years, but it has not brought him much profound knowledge accumulation.

Because like the vast majority of civil science, he always hopes to use some relatively simple methods to prove.

As for why, it probably has something to do with their learning ability.

When they are completely unable to learn those difficult contents, they can only rely on the continuous arrangement and combination of simple methods to seek a breakthrough. \b

Even this "slightly" possibility is just a fantasy in their hearts.

And in the end, it became a joke. \b

At this moment, Fan Pairen's idea of ​​slipping away became more and more determined.

He realized more and more clearly that it was meaningless for him to stay any longer, except for embarrassment.

Anyway, even Peng Chuan couldn't get in touch.

As for the previously promised professor at Beijing University, I am afraid it has become even more extravagant.

Didn't you see that the dean of the School of Mathematics of Shangjing University is there?

Thinking of this, he looked around again.

However, his small actions did not attract the attention of others.

In other words, since Li Mu's report entered a more in-depth stage, no one cared about him anymore.

Even those who don't understand are taking notes seriously.

After all, Fan Pairen is just an insignificant person.

At most, it can only bring people a little fun.

...

As time passed, Li Mu's proof began to enter a critical stage. \b

The scholars present also became more attentive.

Even the scholars who were watching the live broadcast were taking notes while listening carefully to Li Mu's explanation.

"At this point, we have successfully substituted the k value into our original prime polynomial."

"Then we need to use one of our most classic proof methods, mathematical induction."

Li Mu changed his style of writing and started the well-known mathematical induction method.

At this time, all the scholars have also seen the results.

"Sure enough, it's mathematical induction, but I don't know how Li Mu will deal with this prime polynomial."

As a classic method in number theory, mathematical induction is often used to solve integer problems, and it is often used to prove that a certain propositional function P(n) holds for all positive integers.

And this problem has been written here, and most mathematicians can see that it is necessary to use mathematical induction.

It's just that this mathematical induction method is not so simple to use.

Because that complex prime polynomial can give them all a headache.

But then, Li Mu's proof process made them panic.

"When n=1, it becomes our twin prime number conjecture form, and it has been proved by me, so this case is true."

"Now we assume that P(n) is true, then P(n+1) =..."

"When it comes to the form of P(n+1), because the processing of this prime polynomial is more troublesome, we need to construct another formula to help us topple this domino."

When the mathematicians on the scene saw this step, they all fell into a state of concentration.

That's right, this step is the most troublesome point.

How would Li Mu construct another formula?

However, Li Mu just said: "Observe the original formula, then we can easily construct this new formula..."

Then, under the unbelievable gazes of everyone, he constructed a completely new polynomial that was fully established and could be integrated into the P(n+1) formula as if he could do it at his fingertips.

Once the two are substituted, in the last step of the mathematical induction method, the infinite polynomials of the two formulas are offset, just like dominoes being toppled.

Subsequently, P(n+1) is established.

Li Mu didn't even stop there, as if the new polynomial he constructed had nothing to say.

Everyday.

He went on to talk about the next step: "Therefore, we have successfully proved that for any positive integer k, there are infinitely many pairs of prime numbers of the form (p, p+2k)."

"So far, it is obvious that the Polignac conjecture is established."

Li Mu simply and neatly wrote the word [Zhengbi] on the blackboard, then turned gracefully and looked towards the audience.

At this moment, the auditorium has fallen into silence.

It was so quiet that I could hear the sound of a needle falling to the ground.

They were all numb.

…………

【4k words for this chapter】