The top student must be diligent

Chapter 155 Go to the Great Hall of the People to give a report!

"Goldbach's conjecture was proposed by the German mathematician Christian Goldbach in 1742. It states that every even number greater than 2 can be expressed as the sum of two prime numbers."

"This conjecture was first mentioned in a letter he wrote to the famous mathematician Euler. It has a history of nearly 300 years, but it has never been solved. At the same time, because its expression is very simple and quite profound The connotation makes it one of the most famous unsolved problems in the field of number theory, and is known as the crown jewel of number theory.”

"In the past, the best result on Goldbach's conjecture was the 1+2 form proved by Mr. Chen Jingrun, a famous Chinese mathematician in the last century, which is also called Chen's theorem in the mathematical community."

"Now, after several decades, Xiao Yi, a famous Chinese scholar and a top international mathematician, recently published a paper on proving Goldbach's conjecture. The proof process of his paper has been verified by the authority of the mathematics community and has been It is believed that Goldbach’s conjecture has been completely proved, and from now on, Goldbach’s conjecture will officially become a theorem.”

"This is a historic step for the history of mathematics, and it also symbolizes that our country has made great achievements in basic mathematics."

"Dean of the Huaguo Institute of Mathematics and Systems Science and academician of the Huaguo Academy of Sciences, Academician Xi Lan commented on this: Xiao Yi's results are a great progress for the entire mathematics community..."

"..."

In a house in Shangjing, on the TV, the announcer of CCTV News was telling the news about the proof of Goldbach's conjecture.

The legend of Goldbach's conjecture has a long history in China, and it is closely related to the achievements made by Chen Jingrun.

The birth of Chen's theorem was a shot in the arm for the Chinese scientific community at that time, letting the Chinese know that we could also make significant achievements in science.

And now that Goldbach's conjecture has been solved in the hands of the Chinese, how can the news media not write a big book about it?

The announcer's voice was impassioned and full of excitement.

On the sofa in front of the TV, there was an old woman listening to the sound on the TV. She was holding an old photo album from the last century in her hand. She was speechless but shed a thousand tears.

Until the news ended, she silently picked up the photo album in her hand, looked at the person in the photo, and said softly: "Jingrun, have you seen it? Goldbach's conjecture has been solved, and the person who solved it is our Hua Hua. China’s young genius, you don’t have to feel sorry.”

The person in the photo album is none other than Chen Jingrun, and this old woman is Chen Jingrun's wife, You Kun.

Chen Jingrun remained unmarried for the first half of his life until he was 45 years old, when he met You Kun in the hospital and fell in love at first sight. Finally, at the age of 47, he married this wife who was 18 years younger than him.

Unfortunately, sixteen years later, Mr. Chen became ill due to overwork and eventually died of illness at the age of 63.

But for Youkun, these sixteen years have also left a shadow in her heart.

The only sound left in the living room was the news broadcast on the TV, and the people on the sofa fell into deep reminiscence.

She seemed to recall the scene when her husband tried to explain to her what Goldbach's conjecture was and how he studied this problem.

However, for a person like her who knows everything about mathematics, she feels helpless after listening too much and often interrupts with other words.

And now, she regretted it, why couldn't she have listened to him more?

At that time, I just thought it was ordinary.

Until a moment later, there was a sudden sound of the door opening, and then a middle-aged man ran in and shouted: "Mom! Mom!"

After arriving in the living room, he saw the old woman on the sofa. His eyes lit up and he ran over immediately: "Mom, have you seen the news? Goldbach's conjecture has been proven!"

He said excitedly: "Dad, his lifelong dream has finally come true!"

The old woman raised her head at this time, glanced at her and her husband's only son, and said with a straight face: "How old are you to be so frizzy?"

"Aren't you excited for my dad!" The son cried out, and at this time he sharply noticed the twinkling light in the corner of his mother's eyes, and immediately said: "Look, aren't you crying? , you are still talking about me.”

"And here, you are still holding a photo of my dad!" The son chuckled: "You are so old, and you are still so sensational."

"You're still retorting, aren't you? Are you itchy?" The old woman wiped her eyes and glared at her son.

"Okay, okay, I won't argue with you." The son stopped arguing with his mother, and then said: "I just heard Uncle Xi say that Xiao Yi will be invited to come here to give a report on Goldbach's conjecture. Will you go and take a look then?”

The old woman looked at the old photo frame in her hand. After being silent for a long time, she finally smiled and said, "Go, of course, and by the way, take Dad with you."

…

With the announcement of the conclusion of Xiaoyi Goldbach's conjecture paper by the "Annals of Mathematics" review committee, the entire mathematics community once again entered into a carnival.

Likewise, the whole world has expressed great concern about this.

After all, the reputation of Goldbach's conjecture is a very big problem around the world, whether in China or other countries.

Who makes the description of this problem very simple? As long as you can understand odd and even numbers, as well as prime and composite numbers, you can understand the meaning of this conjecture.

All major media outlets published news with this as the headline.

"A mathematical genius from China once again proved the world's difficult problem: Goldbach's conjecture!"

"The Empire's fierce tiger won the crown jewel of number theory today!"

"Less than half a year later, Xiao Yi made another huge breakthrough: all even numbers greater than 2 can be expressed as the sum of two prime numbers! 》

...

Different titles, but the same content, are flooded on various news portals.

Similarly, on various online platforms, the heat of discussion is also rising.

Some people are discussing how difficult it is to prove the Goldbach conjecture - of course, those who discuss this are basically the onlookers; others are discussing what kind of impact the conclusion of the Goldbach conjecture will have on the mathematical community, but this is not to say that there is any impact, because neither the conclusion of the twin prime conjecture nor the conclusion of the Goldbach conjecture can help mathematicians solve other problems.

The most critical value of this kind of conjecture lies in the new theories or methods invented by mathematicians in the process of proving them. As for the value of the conclusion, it is not very high.

This is why problems like the Goldbach conjecture are well-known even outside the mathematical community, but are not included in the millennium mathematical problems like the Riemann conjecture.

Of course, this does not prevent the proof of the Goldbach conjecture from being very powerful.

In any case, this can be regarded as the practice of the purpose of pure mathematics that has absolutely no application value, right?

In addition to these two discussion groups, there is another group of folk mathematicians who strongly oppose it.

The twin prime conjecture and the Goldbach conjecture are the hardest hit areas for amateur scientists. Now that these two problems have been solved, how can those amateur scientists and mathematicians accept it?

So these people came out one after another and claimed that they were the real provers.

However, anyone with a discerning eye could see that this was their last struggle.

And these amateur mathematicians could not affect Xiao Yi at this time.

…

Unlike the enthusiasm of the entire mathematics community, even though the whole world is basically discussing him now, Xiao Yi has been quite leisurely during this period. He goes to class every day when he has nothing to do, and then spends the rest of his time studying theoretical physics.

With the twin prime conjecture and the Goldbach conjecture both solved by him, he has not yet decided what problem to study next, and has not yet found a problem that can interest him.

The Riemann hypothesis is a good option, but unfortunately, after a little research, he can be sure that it will take a lot of effort to solve this problem.

After all, the Riemann hypothesis is probably a problem that can be judged as a high-value problem by the [Ruthless Lianxue] BUFF, and there is still a lot to go to solve it.

In addition to these things, he also served as the "instructor" of the papers of three roommates.

As for the price...

"Godfather!"

"Godfather! I have a problem here, how do you think I can solve it?"

Song Ziyang handed the draft paper to Xiao Yi respectfully and asked.

"Well." Xiao Yi nodded with satisfaction at this title, took the draft paper, read it, and asked: "Tell me, what problem did you encounter."

Song Ziyang said: "I tried to use the mountain pass lemma to prove the existence of the solution, but encountered some difficulties in verifying the PS condition. Specifically... I am not sure how to prove the boundedness and convergence of the function sequence."

Xiao Yi nodded slightly, and at the same time turned the draft paper in his hand again, and continued to read.

The topic Song Ziyang is studying is [Research on the Existence of Solutions of Nonlinear Elliptic Equations Based on Critical Point Theory], which is mainly about functional analysis, involving variational methods, Sobolev space, critical point theory and other aspects.

It is a good topic, but the difficulty is at the level of graduate students.

After reading the content on the draft paper, he then stretched out his hand and said, "Pen."

"Oh!"

Song Ziyang quickly picked up the pen, looking humbly asking for advice.

After taking the pen, Xiao Yi wrote a formula on the draft paper: [Δu+V(x)u=f(x,u)].

"I will simply use this nonlinear elliptic equation to give you an example."

When guiding them, Xiao Yi never solves the problem directly, but abstracts the problem and then solves it with examples.

Whether they can figure out the method from it depends on themselves.

"First, let's review the application conditions of the Mountain Pass Lemma. In this problem, the functional we consider is I(u)=1/2∫Ω(|u|^2+V(x)u^2)dx∫ΩF(x,u)dx, where F(x,u) is the primitive function of f(x,u)."

"In order to apply the Mountain Pass Lemma, we need to verify two key points: one is that the functional I(u) satisfies the geometric conditions, and the other is that it satisfies the PS conditions."

"The first geometric condition, you try to verify it first."

Without giving a direct answer, Xiao Yi tested him a little.

Song Ziyang nodded, quickly took out another piece of draft paper and pen, and began to verify. Soon he came to the conclusion: "There exists p greater than 0 and e∈H01(Ω), so that when ||u||=p, I(u)\u003e0, and I(e) is less than 0."

Xiao Yi nodded, which shows that Song Ziyang's basic skills are quite good.

"Very good, then let's look at the PS condition, that is, if {un}H01(Ω) satisfies I(un) is bounded and I′(un)→0, then we need to prove that {un} has a strongly convergent subsequence in H01(Ω)."

"First, using I(un) is bounded, we know..."

As Xiao Yi began to guide, he also showed Song Ziyang step by step how to prove the boundedness and convergence of the function sequence.

Finally, Song Ziyang suddenly realized: "So that's it! I understand!"

"It's OK as long as you understand." Xiao Yi smiled and handed back the pen and draft paper, "Then continue to study your problem."

"Okay, godfather!" Song Ziyang agreed repeatedly.