Speaking of Jiang Shu, since he heard about the world's difficult problems in number theory, he became obsessed with the proof and stayed up all night. Because of this, he has been in a state of not thinking about food or tea for several days.

There are only a few well-known world-wide problems, all of which are conjectures in number theory. These problems seem to be very simple, but the proof is complicated, so they are widely circulated in the mouths of ordinary people. Problems in other branches of mathematics are difficult to understand because ordinary people cannot understand them.

There is no such treatment as number theory.

When Jiang Shu woke up this morning, he arrived in the classroom early and was still thinking about the twin prime conjectures, Goldbach's conjecture and Mersenne's prime conjecture.

There is a reason why he focuses on these three conjectures, because he does not understand what the Riemann Hypothesis is about.

If you want to understand the Riemann Hypothesis, you must first learn analytic number theory. This is something that only a master's degree can understand. Without a good foundation in mathematics, you will not be able to understand it.

Anyway, because Jiang Shu was curious and wanted to know what the Riemann Hypothesis meant, he read Analytic Number Theory, and then he was completely confused when he saw Bell's summation formula on the first few pages. Can you imagine a bunch of calculus summation formulas?

How wonderful is it that the formulas are so densely stacked together?

He just couldn't figure out how to derive it.

The difficulty of analyzing number theory blinded him.

When other students saw that Jiang Shu was still making these conjectures, they felt that Jiang Shu might have something wrong with his head.

"Are you crazy?"

"Maybe it can actually be proven?"

"impossible!"

However, Jiang Shu really got another proof of Goldbach's conjecture this morning. The whole class was once again shocked. He showed the proof to Li Xuan with great interest.

Li Xuan was very helpless. After reading Jiang Shu's proof, he found that his train of thought was as follows:

[Not for non-mathematics enthusiasts]

Suppose a large even number m and a prime number above 3 are n, then m=3+(m-3)=5+(m-5)=……=n+(m-n). To prove Goldbach’s conjecture, an even number greater than 2

Whether it is the sum of prime numbers, just prove that there must be one situation where m-n is a prime number.

Using proof by contradiction, assuming (m-n) is not a prime number, then m-n can be written down from 3+(m-3), 5+(m-5), taking infinite values. However, m-n
.

Goldbach's conjecture can be proved.

…

Li Xuan looked at it and shook his head: "Jiang Shu, your proof is wrong."

Jiang Shu was not convinced. He thought for a long time before he thought of using proof by contradiction: "Where is the mistake?"

Li Xuandao: "The logic is wrong. There is no proof process from the previous step to the next step. Mathematical arguments are very rigorous. You cannot take it for granted. For example, the key to your proof is that m-n cannot actually take infinite values.

, then your entire proof will be completely invalid."

Li Xuan was speechless.

This guy is simply obsessed. He is still reading elementary mathematics and has basically no idea about these difficult problems in the world.

Liang Zhihui also looked at the proof and sneered: "Jiang Shu, I have thought of your proof since I was in the fifth grade of elementary school. I was so proud that I thought I had proved Goldbach's conjecture, and then I was beaten by my father.

I knew I was wrong. Mathematics is rigorous, and the key point is that you must not skip steps. You think it is a simple test question, and if you prove that you can skip steps, the teacher will sometimes give you points."

Jiang Shu was hit again.

Li Xuan didn't want to read classmate Jiang Shu's certificate anymore. To be honest, it was a waste of time. He wanted to read more competition books and prepare for the Chaoyang Cup Winter Camp. The time to leave for Peking University to participate in the Chaoyang Cup Winter Camp was coming soon.

…

…

Then the news reached Lin Xuerui.

She knew from her classmates that Jiang Shu was a little obsessed with world problems. She walked up to the podium during class and specifically said this: "I heard that there are students in our class who want to prove world problems? It just so happens that the instructor has a weakened version of Goldbach's conjecture.

, Chen Jingrun’s proof paper, I hope it can inspire some ideas for students.”

There were four copies of the paper, which were immediately passed down. Any student who was interested could take a look at it.

Li Xuan was stunned for a moment. He had never seen the proof process of Chen's theorem. To be honest, he was quite curious. Then he took it and looked at the paper. Of course, it is impossible to have a sudden enlightenment.

Just looking at him made him feel a little dizzy.

There are various lemmas in the paper, terrifyingly long formulas, and incomprehensible symbols.

Li Xuan always felt that he had learned a lot these days. He changed a competition book every day and felt very good about himself. But here he found that he could not even understand the proof of Chen's theorem.

He's still a rookie...what can he say?

Lin Xuerui said lightly: "Chen Jingrun's proof of Goldbach's conjecture (1+2), "Expressing an even number as the sum of a prime number and the product of no more than two prime numbers", you can simply understand. He proved Goldbach's conjecture

It is a weakened version of Bach's conjecture, but it is a weakened version. It is actually completely different from Goldbach's conjecture. It is two levels of difficulty, very different."

The students glanced at the paper and remained silent.

Jiang Shu was dumbfounded after reading the paper. Compared with his proof, Chen's theorem was so complex that it was scary, no different from the Book of Heaven.

You can at least understand some of the meaning of the university textbooks, but only Chinese characters can be read in this kind of paper.

Seeing the different expressions of her classmates, Lin Xuerui smiled and said: "Which of you can understand this proof of Chen's theorem? Li Xuan, you are the best in the class, can you understand it?"

Li Xuan shook his head: "I don't understand."

Lin Xuerui was not surprised and continued:

"It's normal not to understand. In fact, only a master's degree in mathematics can understand this proof. If you understand it, you can almost graduate. This is the case."

"So, proving the world's difficult problems is not that simple. With your current level, one day God will trick you and teach you the proof process, and you won't be able to understand the proof."

"You have to know that mathematics is an edifice built by human thinking. Countless geniuses in history have repaired the foundation of this edifice extremely firmly. The mathematical knowledge you have learned in high school and all the things you can think of have been thought of by predecessors.

All the proven theorems have been proved by previous generations, so I won’t leave out any soup for you.”

When Li Xuan heard this, he couldn't help but think of Peng Serie's theorem, and he deeply realized that he actually thought of this theorem independently, but his predecessors had done all the work two hundred years ago.

At this time, Lin Xuerui glanced at Li Xuan and said with a smile:

"So, if you want to prove the twin prime number conjecture, you must improve your knowledge, absorb the wisdom of your predecessors, and stand on the shoulders of giants. The most basic thing is that you must first learn analytic number theory.

, algebraic number theory, geometric number theory, transcendental number theory, combinatorial number theory... Of course, there is also the most cutting-edge field now, arithmetic algebraic geometry. Students, you know that in order to prove Fermat's conjecture, Wiles solved almost all the most difficult problems in the world.

All theories have been put to use, and only then can algebraic geometry be used to prove number theory problems."

"Not to mention high school students, even when you are in college, do you think the twin prime number conjecture can be proven? Or take a step back and understand the proof? Suppose God gives you a trick one day and gives you the proof, then what do you think about college students?

Can you understand the proof? Sorry, I can only say that you can’t understand it 100%. You can’t even understand the proof, and you still want to prove it yourself?”

"The mathematics you learn in high school is just superficial, and college is the introduction to mathematics. For example, the twin prime number conjecture is a world problem. It weighs 100 kilograms. At the level of college students and high school students, they can lift up to 1 kilogram. There is no absolute level.

Can’t lift 100 kilograms.”

"Coach, I won the CMO gold medal in high school. I was among the top 60 people in the country in mathematics that year. I studied hard at Peking University for almost seven years, but I didn't come into contact with the most cutting-edge knowledge of mathematics. I can only say that I just understood what mathematicians think today.

What the research is doing.”

"To prove these difficult problems, you must understand the most cutting-edge work of mathematicians, such as the Langlands Program, contact number theory, algebraic geometry and reduction group representation theory, and know how to equivalently transform number theory problems, such as the twin prime conjecture, etc.

Valence transformation proves the universal formula of twin primes."

"So, don't waste your efforts to prove some world problems now. If you are interested in mathematics, you can study it in college. Then maybe someone among you will really prove this world problem... Now, your goal is to

The high school math league is done, don’t be too ambitious, just take a look at the college textbooks if you’re interested in calculus, don’t read too much about anything else right now, laying a solid foundation is the most important thing.”

At the end, Lin Xuerui saw the classmates below shaking their heads in despair and sighing. But surprisingly, only Li Xuan's eyes remained gleaming. To be more precise, they were unafraid.
Chapter completed!