Before the start of today's report, the Chinese Mathematical Society and Li Mu did not announce the title of the report Li Mu was going to give.
So before the report started, people were also confused as to why Li Mu also wanted to report.
Wouldn't it be enough to ask Fan Pairen to give a lecture and prove whether he understands it or not?
What could Li Mu say if he went up?
Therefore, many mathematics scholars have asked the Chinese Mathematical Society before.
To this, the Chinese Mathematical Society only responded with one sentence: a report related to the twin prime conjecture.
Because they were afraid that if they mentioned the topic of the report in advance, they would scare Fan Pairen away.
The protagonist was not present, so the report was a little less interesting.
After other scholars learned about the content of Li Mu's report, what else can they say? Although they don't know what else is worth reporting on the twin prime conjecture, this is Li Mu's report after all, and maybe there will be something. What about the more important content?
Ever since, these scholars came over like they were opening a blind box.
Otherwise, Fan Pairen alone is not worth so many of them, just go back and find out the follow-up on the Internet.
But now it has been proved that their high expectations for Li Mu have not been lived up to.
As soon as the topic of the report was revealed, the audience was stunned and there was an uproar.
Polignac conjecture!
Hardy-Littlewood Conjecture!
Sure enough, it is related to the twin prime conjecture, but isn't this a bit too much...
Forget it, Polignac conjectured. After all, Li Mu had said before that he already had a perfect proof for this conjecture.
But what about the Hardy-Littlewood conjecture that suddenly appeared?
If the Polignac conjecture and the twin prime conjecture still have a certain 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 turns out that only ten days have passed in just a short period of time. Li Mu has to solve these two conjectures in succession?
Did he really kill the whole family of twin prime numbers conjecture?
For a while, these scholars even found it hard to believe.
However, some scholars immediately began to pick up their mobile phones and contacted other scholars with good connections who had left Beijing to tell them the news.
Although there are still many scholars coming to see the report, some scholars have already left Beijing.
After all, the leave they asked for was only for the days when the meeting was held.
It is still during the summer vacation, so there are so many scholars left.
As for those scholars who had already left, they immediately beat their chests and regretted after receiving the news.
Blanch!
They were lucky to be able to witness the proof of the twin prime conjecture last time, but now they missed the proof of the other two conjectures in a single thought.
Of course, soon, these scholars suddenly remembered that this report was broadcast live, so a group of people rushed into the live broadcast room.
When I saw the title on the PPT, I was not only shocked that Li Mu actually wanted to prove these two conjectures at the same time, but I was also happy that I was not late.
Catch up on the live broadcast!
At the same time, some people who reacted quickly suddenly remembered the purpose of Li Mu's report.
This is going to give Fan Pairen a hard blow.
You are a civilian scientist who came over to Pengci to continuously solve the twin prime number conjecture and other versions of the three major conjectures. In this huge comparison, even if this Fan Pairen really understands a little bit, he seems weak.
Not to mention, it was proven that he didn't know how to pretend to understand.
For a time, many eyes in the audience were directed to the first row.
Today, Fan Pairen, as an invited speaker, is "honored" to be placed in the first row.
In the past, those who could sit in the front row were leading figures in the domestic and even international mathematics community.
Therefore, many mathematicians present joked about this. This time, Fan Pairen can be regarded as a glorious ancestor.
At this moment, Fan Pairen, who was sitting in the first row, could feel countless piercing glances coming from behind even if he didn't turn his head.
It made him sit on pins and needles.
He never expected that Li Mu would not only report with him, but also have two other major conjectures proven on the spot.
Looking back 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 experiences and the tragic past, he understands the truth, but he can't talk about it. He doesn't have the eloquence.
Not everyone is a success master.
Although he is a professor and every class at school is 45 minutes long, the classes at his second private school are very simple. 99% of the students don’t listen to the class, and there are almost no teachers who can teach seriously. Just follow the script and be done.
So he really couldn't do it, babbling for forty minutes.
Thinking of this, his heart began to wander again, should he just slip away?
This idea that had occurred to him several days ago became more and more agitated at this time.
But now he was sitting in the front row, and even leaving his seat would be too obvious, so he could only give up the idea for the time being.
However, in fact, he took it for granted, and not many people present cared too much about him.
Compared with 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 once again put on the same suit as before, opened the PPT, looked at the surprised expressions on the scene, and smiled slightly.
He had a panoramic view of everyone's expressions, including Fan Pairen.
He could have imagined everyone's surprise before.
"As I said last time here, there was not enough space left on the blackboard and not enough time left for me to complete the proof of the Polignac conjecture."
He smiled and said: "But today, I will have a lot of time. As for the blackboard, I just saw it in the backstage lounge. The Huaguo Mathematical Society and Beijing University have prepared 20 small blackboards. It seems that I have designated I can’t run away.”
Everyone present smiled knowingly.
Yuan Xiang and Lian Zhengxing couldn't help laughing.
If you can still let your kid run away today, they should stop hanging around in the Chinese mathematics community.
"Then let's not talk nonsense and let's start with the Polignac conjecture."
Li Mu nodded slightly toward the audience, then turned his head and came to the first small blackboard.
There will be a lot of small blackboards that need to be used today.
So even if he had twenty yuan, he had to use it sparingly.
God knows if the rostrum can be fully arranged after twenty small blackboards are pushed up.
"To save time, I'll pick up where I left off from my discussion of the Polignac conjecture at the end of my last report."
Then, he wrote on the blackboard what he had deduced from the last half of the blackboard in the last report.
For him, even if so long ago, he still remembered these gestures clearly.
"Last time I deduced that when k belongs to 1 to 50, there are infinite pairs of prime numbers of the form (p, p+2k)."
"And next, how do we extend k to positive infinity?"
"Actually, the next step is very simple."
Li Mu said, and then began to write a line of formula on the blackboard.
【H1(GK，Z/pZ)Z……】
When the people present saw it, those who understood it suddenly showed expressions of astonishment.
"Kummer theory!"
"I've probably thought of it, but what exactly should I do?"
"Do we need to improve the Kummer theory again? The original Kummer theory alone should not be able to solve the problem."
While all the scholars were lost in thought, they also looked at Li Mu's proof with more concentration.
In this way, as Li Mu continued his proof step by step, everyone discovered the differences with the original theory.
"Sure enough, he has improved!"
Those scholars who understood it all had their eyes lit up, and they couldn't help but admire it in their hearts.
But still, the vast majority of people look confused.
Can this be considered a simple step?
Is simplicity a concept that everyone can understand?
For a moment, they felt as if they had become Muggles.
Obviously, not all scholars who come here have extremely high mathematical qualities.
The simplicity in Li Mu's words is a completely different world to them.
Of course, these people also include Fan Pairen.
He looked at what Li Mu said in confusion.
In the last report, he could still understand a little bit of what Li Mu said at the beginning, even if it was only superficial, but in this report, he has been confused from the beginning to now.
He has studied the twin prime conjecture for nearly 20 years, but it has not brought him much profound knowledge accumulation.
Because like most civil sciences, 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 incapable of learning those difficult contents, they can naturally only rely on constant permutations and combinations of simple methods to seek the possibility of a breakthrough.
Even this "a glimmer" of possibility is just a fantasy in their hearts.
In the end, it became a joke.
At this moment, Fan Pairen's thoughts about slipping away became more and more determined.
He realized more and more clearly that if he stayed any longer, it would have no meaning other than being embarrassed.
Anyway, even Peng Chuan can no longer be contacted.
As for the previously promised professor at Beijing University, I am afraid it has become an extravagant hope.
Didn’t you see that the dean of the School of Mathematics at Shangjing University is there next to you?
Thinking of this, he observed his surroundings again.
However, his small actions did not attract the attention of others.
In other words, after Li Mu's report entered a more in-depth stage, no one cared about him anymore.
Even those who couldn't understand were taking notes carefully.
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.
The scholars present also became more attentive.
Even the scholars watching the live broadcast were taking notes and listening carefully to Li Mu's explanation.
"At this point, we have successfully substituted the k value into our original prime polynomial."
"Next we need to use one of our most classic proof methods, mathematical induction."
Li Mu's writing turned around and started the well-known mathematical induction method.
At this time, all scholars have seen the results.
"It's indeed mathematical induction. I just don't know how Li Mu is going to deal with this prime polynomial."
As a classic method in number theory, mathematical induction is often used to solve integer problems. It is often used to prove that a certain propositional function P(n) holds for all positive integers.
This problem has been written here, and most mathematicians can see that mathematical induction is needed.
It’s just that this mathematical induction method is not that simple to use.
Because that complex prime polynomial can give them all a headache.
But then, Li Mu's proof process was so impressive that they panicked.
"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 knock down this domino."
When the mathematicians on the scene saw this step, they all became concentrated.
Yes, this step is the most troublesome point.
How could Li Mu construct another formula?
However, Li Mu just said: "Observe the original formula, and then we can easily construct this new formula..."
Then, under everyone's disbelieving gazes, he seemed to have easily constructed a brand new polynomial that was completely established and could be integrated into the P(n+1) formula.
Once the two are substituted, in the final step of mathematical induction, the infinite terms of the two equations cancel out, just like a domino being toppled.
Subsequently, P(n+1) holds.
Li Mu didn't even pause, as if the new polynomial he constructed had nothing to say.
Commonplace.
He went on to talk about the next step: "Therefore, we have successfully proved that for the case where k belongs to any positive integer, there are infinite pairs of prime numbers of the form (p, p+2k)."
"At this point, it is obvious that the Polignac conjecture is established."
Li Mu simply wrote the word "certificate completed" on the blackboard, then turned around gracefully and looked at the audience seat.
At this moment, the audience has fallen into silence.
It was so quiet that you could hear a pin drop.
They were all shown off.
…………
[4k words in this chapter]
(End of chapter)
