Reshaping life starting from the Junior Class of HKUST

Chapter 216 Levels of Mathematical Conjectures

Wu Zhe and Zhang De discussed with them for a while, but they didn't have any clues for a while, and Wu Zhe left after chatting for a while.

Back in the dormitory, Wang Chao and the others were not there.It's normal to think about it, even if there is no class, the three of them are too busy to see anyone.

After turning on the computer, Wu Zhe played light music, closed his eyes and leaned back on the chair.He looked like he was resting with his eyes closed.But the mind never stopped for a moment.

Induction doesn't work, so try using reverse derivation.

Assume twin primes are finite pairs, and let the largest pair of twin primes be (Pn-1, Pn).It can be seen that the prime numbers within Pn are limited, and they are set as P1, P2Pn-1, and Pn.

Then construct a large prime number P=(P1P2P3**Pn)+1
显然P不能被从P1到Pn的所有素数整除，永远余1，所以P是素数。同理可证得，P-2=（P1P2P3**Pn）-1显然也是素数，被任何从P1到Pn的素数除永远差1。

Since P is a prime number and P-2 is also a prime number, the two form a pair of twin prime numbers.

Then the problem comes, the twin prime pair formed by P and P-2 is larger than the "largest prime pair" originally set, thus negating (Pn, Pn-1) as the largest twin prime pair.

Just like climbing a ladder, no matter how big (Pn-1, Pn) is, you can always find a pair of prime numbers larger than (Pn-1, Pn).

No, there is a mathematical loophole here, that is, you cannot prove that (Pn-1, Pn) is the largest prime number.
-
Wu Zhe came up with various formulas and methods in his mind, but all he got was a dead end.The front always seems to be covered with fog.

Sighing dejectedly, Wu Zhe also understood that there was no such flash of inspiration.Maybe there is really no way to take twin primes.Twin prime number conjecture can reach at least the third level.

There may be a distinction of academic value between mathematical conjectures and mathematical conjectures, but it is difficult to use a standard to measure the difficulty of a conjecture.

However, it is not impossible to classify mathematical conjectures and mathematical conjectures.

If we put aside all non-academic factors such as political significance, economic significance, and news rendering, and only talk about the academic value "to today's mathematics community", then thousands of mathematical conjectures can be roughly divided into several levels.

The first echelon is undoubtedly the millennium problems such as Riemann's conjecture, NP complete problem, Yang-Mills gauge field existence and mass interval hypothesis, the so-called seven major mathematical problems in the world, and Hilbert's 23 problems Some of the questions in and so on.

Once these conjectures are proved, it will not only promote the development of the mathematics field, but also have a profound impact on other disciplines.

The second level, of course, is the most well-known three major modern mathematical problems, Goldbach's conjecture, the four-color problem, and Fermat's last theorem.Two of them have been resolved.The four-color problem is still forcibly proved by a computer, and it is still not solved at the mathematical level.The remaining Mr. Chen has already achieved "1+2".In addition, some of the questions in the Langlands program and some of the questions in Hilbert's 23 questions can also be listed here.

The third echelon, the distinction between conjectures at this level and the second echelon is actually not obvious, and it involves subjective opinions, and there may be large differences.If it is typical, the Jacobi conjecture can be counted in this column.

As for the fourth echelon, the Sitapan conjecture proved by Wu Zhe before can be counted in this list, and all sub-problems of the first, second, and third echelon problems, or the "weak conjecture" of a certain conjecture can also be inserted.

There are even more in the fifth echelon. Some unpopular branches that no one cares about, conjectures proposed by an unknown mathematician, and all conjectures that do not reach the fourth echelon can be included in this echelon.

The twin prime number conjecture and the Polignac conjecture have properly entered the ranks of the third level.As for the problem of proving this level, the Fields Medal is not easy to get, but the possibility of getting it is basically [-]% to [-]%.Even if you can't get it, you can be regarded as a person who left a name in the history of mathematics.

Of course, the study of mathematical conjectures is only a part of theoretical mathematics research, but not all.Many people have never proved any major mathematical conjectures in their lives, but this does not prevent him from making contributions to the entire mathematical community.

For example, Mr. Grothendieck, who laid the foundation of modern algebraic geometry and completely changed the face of the subject of functional analysis, these two contributions alone are probably unmatched by any mathematical conjecture.After all, many mathematical conjectures today are based on his "prototype theory".

And there are not so many lunatics in the mathematics world to study mathematical conjectures, most of them are still engaged in various types of basic research and applied mathematics research.

This is why Zhang Detong was shocked when he heard that Wu Zhe was going to play math guessing again.If mathematicians are all guessing, it is estimated that there will be many more people in mental hospitals than there are now.

When Wang Chao and the others went back to the dormitory, what they saw was that Wu Zhe looked a bit like a dead dog.The music is on, and the eyes are blank.He kept rubbing his temples with his hands.

Seeing Wu Zhe like this, the three of them hurriedly put down the things in their hands and asked, "What are you doing now? Seeing you like this is the last time you insisted on solving the four-color problem?"

Wu Zhe muttered: "It's okay, I'm paying attention? It's just a little sleepy. I encountered some difficulties."

When Wang Chao heard that Wu Zhe had a problem, he immediately became interested and said, "It's simple! Brothers are all here, let me tell you the details."

Wu Zhe glanced at Wang Chao and said, "As for the problem you mentioned last time, the twin prime number conjecture. If you give me some advice, I'm about to get a headache." After speaking, he also glanced at the boss and Shen Zhiwen.

After hearing Wu Zhe's words, Wang Chao and the others were dumbfounded.After a few people glanced at each other, they said at the same time: "I'm sorry to bother you, please leave."

Let's talk about helping you out of life and emotional problems.That may be okay, but if you want us to give you Wu Zhe's opinion on the mathematical conjecture, you are really thinking too much.Except for you pervert, have you ever heard of any freshman playing math guessing?
Wu Zhe made them make up their minds mostly as a joke.

"I'm not joking, I've been really studying number theory recently, and I've really taken twin prime numbers as my future research direction. By the way, your exempted exams have started! How are you doing?"

Wang Chao and the others looked at each other and smiled, Huang Minghai said: "It's all okay, there's no big problem. The test paper we did is not as abnormal as yours. It's much simpler."

Wang Chao also smiled and said: "We prepared according to the difficulty of your exam. We were determined to die, but when the test papers were issued, we found that the test was easy. This is the correct way to open a university. Ah Zhe, your test is not normal."

Shen Zhiwen also said softly beside him: "Azhe, when will you be normal?"

MMP, Wu Zhe always felt like he was scolding Shen Zhiwen when he heard what he said, but he couldn't find any evidence.

Seeing Wu Zhen's suspicious expression, Wang Chao immediately smiled and said: "Don't doubt it, I'm just scolding you. The whole class has suffered a lot from you. The homework is caused by you. Everyone wanted to be exempted from the exam. You can do less. You have blocked this road again. If the three of us hadn’t tried it this time, in the next semester, you will see how many people will scold you.”

(End of this chapter)