my scientific age

Chapter 211 The Prime Number Theorem!

The charm of mathematics lies in the fact that the difficulty of learning various theories of knowledge will not change due to the passage of time.

pain.

A mathematical theory is there.

Quiet, neither sad nor happy, every mathematical theory contains information entropy that ordinary people cannot comprehend and absorb in a lifetime.

The abyss of mathematics is composed of these profound and extremely difficult to understand mathematical theories.

This is a test that every wise man must go through on the way forward. There is no way to avoid it. There is no shortcut. Opportunity and overtaking in corners are meaningless in front of it.

As for the question of whether there is a 'bottom' in the mathematical abyss, based on the existing knowledge system and cognition, the answer is naturally - no.

Analytic number theory, a frontier branch in the field of basic mathematics, is a school of number theory that uses mathematical analysis as a research tool to study the properties of integers with mathematical analysis and prove them. The study of problems is one of the contents of advanced number theory.

In the cognition of the vast majority of ordinary people, the cognition of the subject of analytic number theory basically comes from the well-known Goldbach conjecture.

Of course, even Goldbach's conjecture, many people can't really understand it, and more than half of them understand it as - to prove '1+1=2'.

Analytic number theory mainly studies the distribution law of prime numbers, and prime numbers are called prime numbers. At this time, a conventional question arises - why study prime numbers?

Because it's fun.

Well, this is bullshit.

Because prime numbers with unique properties play a great role in the study of number theory, all positive integers greater than 1 can be expressed as a combination of prime numbers. In a sense, the status of prime numbers in number theory is similar to that of physics. If we can grasp the mystery of the distribution of prime numbers, we may be able to grasp the mystery of the universe.

You must know that the definition of prime numbers is so simple that even elementary school students understand, but the distribution of prime numbers is extremely mysterious and bizarre.

Finding one prime number is easy, finding ten prime numbers is easy, and finding the distribution law of all prime numbers is extremely difficult.

From Euler to Gauss, Gauss to Riemann, the law of distribution of prime numbers has not been fully grasped.

When it comes to analytic number theory, we have to mention that the founder of the entire analytic number theory school comes from the god-level math apostle and grandfather-Bornhard Riemann.

On the basis of the mathematics emperor Euler and his mentor Gauss, the ancestor Riemann pioneered the establishment of analytic number theory, which opened a new ceiling for the research of number theory at that time, and also provided an iron job for the current Yu Hua.

If nothing else, at least relying on the research on analytic number theory, it is not a problem to go to any university in the country as a teaching assistant or lecturer.

Thank you grandpa for the meal.

Yu Hua, who was studying the whole book, read the wonderful points and sighed silently in his heart.

In terms of seniority, Riemann is his grandfather.

In terms of achievements, the ancestors are completely in the god-level echelon composed of Euler, Newton and Gauss.

In terms of mathematical contributions, Riemann almost single-handedly established the system of modern mathematics. He is not only the father of analytic number theory, but also the father of complex function theory and Riemann geometry. He is also pioneering in combinatorial topology and algebraic geometry. sexual contribution.

On talent...

Today, he seems to be on a par with the patriarch, at least, he can see the back of the patriarch.

He used to be, sorry to bother you...

Analytic number theory is mainly studied through Euler's constant, complex variable function, circle method, sieve method, exponential sum method, characteristic and method, density and other methods.

This introduction to number theory in my hand mainly records Master Hua Luogeng's research on number theory. According to the catalogue, the contents of the notes are composed of elementary number theory and advanced number theory. , an overview of the distribution of prime numbers, and the classic Waring problem and Goldbach conjecture.

It has to be said that Master Hua Luogeng’s research on Goldbach’s conjecture can be called No.1 in China. Although there is no proof of ‘5+5’ in it, the contents of the notes have fully proved the brand-new research of Italian Professor Lacey on Goldbach’s conjecture this year. results.

证明‘5+5’非常难，而完整证明现有的‘5+7’，‘4+9’等成果，很难。

The whole proof process has benefited Yu Hua a lot, and the part of the notes about Goldbach's conjecture, in addition to the latest results of Professor Lacey this year, there are also previous achievements such as '6+6', '7+7' and so on. complete proof.

Among them, the sieve method of analytic number theory plays an irreplaceable role.

Regarding the famous Hualin problem, Yu Hua only saw the content of the problem and some basic deductions, but did not see the famous Fahrenheit theorem and Fahrenheit inequality in history.

However, this is normal. First, Fahrenheit's theorem was published in 1940, and now in 1937, there are still more than two years. Second, such an important mathematical achievement, even if there is, it will not be placed on it.

This is the mathematical result of a mathematician's painstaking efforts, and it is extremely important.

For this, Yu Hua said that he can understand, and there is no careful thought.

There are many scientific achievements that can maintain the genius design. Yu Hua doesn't need to think about Fahrenheit's theorem, and he can't do anything to steal the master's results.

Some scientific achievements, just take it.

Some scientific achievements cannot be obtained.

'Some' depend on nationality, status, contribution to the country, importance of the outcome, mood, and many more.

"The basic concepts of analytic number theory have been understood. It turns out that the study of prime numbers is so interesting. No wonder so many mathematicians never stop pursuing prime numbers..." Yu Hua, who stayed in the master bedroom, carefully studied the complete introduction to number theory. With a comprehensive and systematic understanding of number theory and various number theory issues, the level of knowledge has been improved again. Close your eyes, ponder and understand the information entropy contained in each mathematical formula and method.

understand, digest.

It's like eating.

Since the end of the interview for Tsinghua's recommended entrance examination, Yu Hua has been working on Yu's Seven Pagodas while studying the Introduction to Number Theory. However, the mathematical knowledge contained in it is extremely difficult, which makes Yu Hua's learning progress not fast.

Although, these things basically belong to the 'basic' of advanced number theory.

After so many days, I finally finished digesting the whole book.

After reading Master Hua Luogeng's book, Yu Hua can basically be regarded as an introduction to analytic number theory, and his two feet have truly stepped into the road of no return to study prime numbers.

interesting.

Really interesting.

Although Yu Hua has always regarded mathematics as a tool, this in no way prevents the fun of studying prime numbers.

"With my current academic level and strength, I can only say that I have touched some thresholds, which is not enough to prove '5+5'. Also, I may need to add some academic achievements as a transition. After all, I am just a prospective college student, only A result that is not considered a result, the number is set at two."

After consuming all the knowledge content, Yu Hua opened his eyes, and changed from the academic research state to the normal thinking state: "Asymmetric cryptography can be used as a transitional achievement, and the second transitional result should be closely related to the study of prime numbers, and has The important influence is enough to raise my identity and academic status to a higher level..."

After thinking carefully in his mind, a pair of eyes inadvertently looked at the table of contents of the desktop notes - the prime number theorem.

(End of this chapter)