Pang Xuelin officially began the research on the ABC conjecture.

The abc conjecture is difficult, and the conceptual expression of this conjecture alone is enough to make ordinary people confused.

Generally speaking, conjectures in the field of number theory are more accurate and intuitive to express.

For example, the Fermat's theorem, which has been proved by Andrew Wiles, can be directly expressed as: when the integer n is greater than 2, there is no positive integer solution for the equation x, y, z.

For example, the famous Goldbach conjecture can be understood in one sentence: any even number greater than 2 can be written as the sum of two prime numbers.

But the abc conjecture is an exception.

It is very abstract to understand.

Simply put, there are 3 numbers: a, b and =a+b. If these three numbers are coeliminated and there is no common factor greater than 1, then d obtained by multiplying the non-repetitive prime factors of these three numbers seems to be larger than that.

For example: a=2,b=7,=a+b=9=3*3.

These three numbers are mutually equitable, so if the unrepeatable factors are multiplied, d=2*7*3=42 is greater than =9.

You can also experiment with several sets of numbers, such as: 3+7=10, 4+11=15, which also meets this seemingly correct rule.

However, this is just a rule that seems correct, and there are actually counterexamples!

The abc@he website operated by the Institute of Mathematics of Leiden University in the Netherlands is using a distributed computing platform based on boinc to find counterexamples of the abc conjecture. One of the counterexamples is 3+125=128: where 125=5^3, 128=2^7, then the non-repeating mass factor multiplication is 3*5*2=30, and 128 is larger than 30.

In fact, computers can find endless counterexamples of this.

So we can express the abc conjecture in this way, d is not usually much smaller than "increased".

How is it usually not much smaller?

If we enlarge d a little bit and zoom into d (to the power of 1+e), then although it is still not guaranteed to be too large, it is enough to make the counterexample from infinite to limited.

This is the expression of the abc conjecture.

The abc conjecture not only involves addition (the sum of two numbers), but also includes multiplication (main factor multiplication), and then there is a vague multiplication (1+e power). The most deceptive thing is that there are counterexamples.

Therefore, the difficulty of this conjecture can be imagined.

In fact, except for the unsolved conjectures involving multiple mathematical branches, other conjectures in number theory, such as the Goldbach conjecture, twin prime conjecture, and the already solved Fermat's theorem, basically none of the abc conjecture is important.

Why is this?

First of all, the abc conjecture is counterintuitive for number theory researchers.

There are countless counterintuitive theories in history that have been verified as correct.

Once the counterintuitive theory is proven to be correct, it basically changes the process of scientific development.

To give a simple example: Newtonian law of inertia, if an object is not subjected to external forces, it will maintain its current state of motion. This was undoubtedly a heavyweight thought bomb in the 17th century.

The object will of course change from motion to stop when it is not under force. This is a normal idea derived by ordinary people at that time based on their daily experience.

In fact, this idea will seem too naive to anyone who has studied junior high school physics in the 20th century and knows that there is a kind of force called friction.

But for people at that time, the inertia theorem was indeed quite contrary to human common sense!

The abc conjecture is to the current number theory researchers, just like Newton's law of inertia to ordinary people in the seventeenth century, which violates common sense in mathematics.

This common sense is: "The prudent factors of a and b should have no connection with the prudent factors of their sum."

One of the reasons is that allowing addition and multiplication to interact algebraically will create infinite possibilities and insolvencies. For example, the Hilbert tenth question on the unified methodology of Diopantu equations has long been proven impossible.

If the abc conjecture is proven to be correct, then there must be a mysterious relationship between addition, multiplication and prime numbers that has never been touched by human known mathematical theories.

Furthermore, the abc conjecture has a significant relationship with many other unsolved problems in number theory.

For example, the problem of Diopan's equation mentioned just now, the generalization conjecture of Fermat's final theorem, the mordell conjecture, the erds-woods conjecture, etc.

Moreover, the abc conjecture can indirectly deduce many proven important results, such as Fermat's final theorem.

From this perspective, the abc conjecture is a powerful detector of the unknown universe with prime structure, second only to the Riemann conjecture.

Once the abc conjecture is proven, its impact on number theory is tantamount to the theory of relativity and quantum physics in modern physics.

It is precisely because of this that in 2012, Shinichi Masahiro claimed that he had proved the ABC conjecture that caused such a big sensation in the mathematics community.

Shinichi Moritsuki was born on March 29, 1969 in Tokyo, Japan. He entered Princeton University in the United States at the age of 16 and entered graduate school three years later. He studied under the famous German mathematician and 1986 Fields Prize winner Faltings, and received his Ph.D. in mathematics at the age of 23 (i.e. 1992).

Even in the eyes of Faltings, who has always been strict and sarcastic, Shinichi Hoshi was one of his favorite students.

In 1992, because of his introverted and weird personality and was not adapted to American culture, Shinichi Mori returned to Japan and served as a researcher at the Institute of Number Analysis of Kyoto University.

During this period, Shinichi Wangyue made outstanding contributions in the field of "Far Abel Geometry" and was invited to deliver a 45-minute speech at the Berlin International Mathematician Conference in 1998.

After 1998, Wangyue Shinichi began to devote all his energy to the proof of the abc conjecture and almost disappeared in the mathematics community.

It was not until 2012 that Shinichi Wangyue published a 512-page ABC conjecture proof paper that once again attracted large-scale attention from the mathematics community.

To a certain extent, Shinichi Moon is somewhat similar to Perelman, but Perelman successfully proved the Poincaré conjecture, while Shinichi Moon's ABC conjecture proof has not been recognized by the mathematics community.

Wangyue Xinyi's theoretical tool for studying the ABC conjecture is Far Abel Geometry.

Therefore, before studying the paper on the ABC conjecture of Wangyue Xinyi, Pang Xuelin also asked Tian Mu to find the relevant works of Wangyue Xinyi on the geometry of far Abel.

Far Abel Geometry was founded by Pope Grothendieck in the 1980s and is a very young discipline in the mathematics community.

The subject of this discipline is the structural similarity of basic groups of algebraic clusters on different geometric objects.

Barnach, the father of modern analytics, said: "Mathematicians can find similarities between theorems, excellent mathematicians can see similarities between proofs, and excellent mathematicians can detect similarities between branches of mathematics. Finally, the sophisticated mathematicians can overlook the similarities between these similarities."

Grotendyk can be called a true mathematician, and Far Abel Geometry is a branch of mathematics that studies "similarity and similarity".

From the discovery of the root-finding formula of the monocyte-clums equation in the 16th century (i.e. the Cardano equation) of Italian mathematicians Ferro and Tartalia, to the discovery of the group structure of solutions to special higher order equations in the 19th century.

Algebraic clusters in algebraic geometry are common solutions to a large class of equations.

The basic group of algebraic clusters is another synthesis of algebraic cluster theory that has already integrated a large category of theories, and is concerned with what structure is independent of the representation of algebraic clusters of geometric objects.

Therefore, for mathematicians, another problem in checking whether there are any errors in the proof of Shinichi of the Moon is: to thoroughly understand the proof of the 512-page ABC conjecture of Shinichi of the Moon, you need to first understand Shinichi's 750-page work on far Abel geometry!

There are only about 50 mathematicians in the world who have enough background knowledge in this regard to read the far Abelian geometry book of Wangyue Xinyi, not to mention the "generalized Tehimeer Theory established by Wangyue in proof conjecture.

So far, only Shinichi Moon himself can understand this theory.

Pang Xuelin did not expect that he could thoroughly study the ABC conjecture in just a few years. He just wanted to use his years on Mars to understand the relevant ideas of Wangyue Xinyi's research on the ABC conjecture and find out the mistakes and omissions in the paper.
Chapter completed!