What is Riemann conjecture?
In short, what does Riemann conjecture say? It is a method to find prime numbers.
What is a prime number? We should have learned in junior high school, that is, those numbers that can only be divisible by 1 and ourselves, such as 2, 3, 5, 7, 1 1 and so on. The study of prime numbers belongs to the category of number theory.
As early as in ancient Greece, there was a study of prime numbers in Euclid's Elements of Geometry. Euclid proved that there are infinitely many prime numbers by absurd methods, but what is the distribution law of prime numbers? Euclid didn't find it.
Since then, mathematicians have been trying to find the distribution law of prime numbers. 1859, Riemann published a paper on the number of prime numbers less than the known number, exploring the mystery of the distribution of prime numbers. This eight-page paper is Riemann conjecture? Birthplace? .
Paper manuscript
Riemann discovered the frequency law of prime numbers through research and put forward the Riemann zeta function, which is the sum of an infinite series.
Zeta function
Riemann proved that analytic extended Zeta function has two kinds of zeros. One of them is the periodic zero of trigonometric sine function, which is called trivial zero; The other is the zero point of Zeta function itself, which is called nontrivial zero point. For nontrivial zero, Riemann put forward three propositions.
In the first proposition, Riemann pointed out the number of nontrivial zeros, and was quite sure that they were distributed in a banded region whose real part was greater than 0 but less than 1.
In the second proposition, Riemann proposed that almost all nontrivial zeros lie on a straight line whose real part is equal to 1/2.
And the third proposition is the bright spot: it is very likely that all nontrivial zeros are located on a straight line whose real part is equal to 1/2.
Riemann said that the first proposition was too simple to prove at all, but it was not until 86 years later that the first proposition was completely proved by the German mathematician Mon Goldt.
As for the second proposition, Riemann claimed that he had already proved it, but the proof process needed to be simplified. However, because of suffering from illness, Riemann died young at the age of 39. After his death, his manuscript was set on fire by the housekeeper, and since then, Riemann's proof process has completely disappeared from the world.
1932. German mathematician Siegel sorted out the manuscripts left by Riemann, which made Riemann's formula for calculating zero point resurface. This formula is named Riemann-Siegel formula.
With this formula, mathematicians push the second proposition to? At least 40% of nontrivial zeros are on the critical line? , and then there is no new progress.
The third proposition is Riemann conjecture, which is called critical line from now on. As for the third proposition, even Riemann himself is not sure. No one can give an answer even now. If the Riemann conjecture is proved to be true, then all nontrivial zeros of the function, that is, the intersection of two images, will appear on a straight line.
Complete expression of Riemann conjecture
There is a mathematics institute called Clay Institute. In 2000, they gave seven unsolved mathematical puzzles a prize of $ 654.38+0 million, one of which was to prove Riemann's conjecture. Now 18 years have passed, and only 7 problems have been solved 1. Riemann conjecture has not been conquered.
Riemann conjecture? What followed was an epic disaster.
Since19th century, more and more mathematical theoretical achievements have been dispersed, and many branches that were considered useless in the early days have already become the most powerful tools of modern science and technology, which have contributed to the development of modern science and technology.
Newton's calculus became the torch of the first industrial revolution. Linear algebra, matrix analysis, statistics, group theory and so on have brought us information civilization. Non-Euclidean geometry (especially Riemannian geometry) and tensor analysis make it possible to sail on land and sea, and binary makes human beings enter the computer age.
Prime number has become the key to the Internet, protecting all privacy on the Internet for human beings, and encrypting and signing the private key. .....
Mathematicians apply prime numbers to cryptography precisely because humans have not discovered the law of prime numbers. If we use it as a key to encrypt, even if we use supercomputing, it will lose the meaning of cracking because it takes too long to solve the prime number.
RSA public key encryption algorithm, which is widely used by major banks, is based on a very simple prime fact: multiply two large prime numbers, but it is extremely difficult to factorize their products.
Because when factorizing the product of two big prime numbers, there are only two big prime numbers except 1 and itself (these two are not in the decomposition range), but we don't know them when factorizing, so we should try to divide them step by step from the smallest prime number 2 until the smaller one of the two big prime numbers.
This is why all the major banks in the world regard quality as their own security password system.
Once the secret of prime numbers is solved, there is no need for quantum computers. According to its principle, it can even crack the security password system of modern banks and make them bankrupt.
Not only banks, but now almost all Internet encryption methods will no longer be secure, and the Internet will become a naked world solution.
So mathematicians call the way to attack Riemann's conjecture interesting: The governors are shivering in front of the bank safe, and many hackers are lurking on the keyboard? .
The danger brought by Riemann conjecture will not only affect banks, but also the Internet, and may even shake the mathematical community.
In these hundreds of years, countless mathematicians have devoted their efforts to Riemann conjecture, and there are more than 1000 mathematical propositions in mathematical literature based on Riemann conjecture.
If Riemann conjecture is proved, those mathematical propositions can be promoted to theorems; On the other hand, if Riemann's conjecture is falsified, at least some of those mathematical propositions will become funerary objects and be swept into the dust heap of history.
Those inferences based on Riemann conjecture can be said to be waiting for the final judgment in fear. No matter what the result is, it will definitely affect the math building.
A mathematical conjecture is closely related to so many mathematical propositions, which is extremely rare in the world. Perhaps it is because of this relationship that the reputation and aura of Riemann conjecture become more remarkable and fascinating.
So give up the solution of Riemann conjecture?
However, solving Riemann conjecture is more like being reborn in Noah's ark than disaster. Hilbert, known as the uncrowned king of mathematics, once said: Every mathematical problem is a goose that lays golden eggs.
Just like the proof of Fermat's last theorem, expand? Infinite descent method? And the application of imaginary numbers; Gave birth to Kumar? Ideal number theory? ; He contributed to the proof of Mo Deer conjecture and Gushan-Zhicun conjecture. Expand the application of group theory; Deepen the study of elliptic equation; The growing point of differential geometry in number theory is found. Did you find Ilawakin? The combination of Fleche's method and Eva Shawa's theory; It has promoted the all-round development and research of mathematics. At the same time, it also gave birth to a group of heavyweight mathematicians.
Wiles cracked Fermat's last theorem.
If human beings can really solve Riemann conjecture, then new mathematical methods, new mathematical laws and new mathematical tools will emerge as the times require, bringing human beings to a new civilization.
Hilbert once said: There is nothing unknowable for us, and in my opinion, there is nothing unknowable for natural science. Get rid of this stupid unknowability and let's make up our minds to do the opposite. We must know, and we will know. ?
The reason why human beings can continue to develop is precisely because we are constantly uncovering all the mysteries contained in nature.