What Are the Different Mathematician Jobs?

The world's three major mathematical conjectures are the Fermat conjecture, the four-color conjecture, and the Goldbach conjecture.

The world's three major mathematical conjectures

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When the integer n> 2, the indefinite equation x ^ n + y ^ n = z ^ n for x, y, z has no positive integer solution.

Introduction

Content and submission

The content of the four-color problem is: "Any flat map can use four colors to make countries with common borders different colors." Expressed in mathematical language, that is, "arbitrarily subdivide the plane into non-overlapping Area, each area can always be marked with one of the four numbers 1,2,3,4, without causing two adjacent areas to get the same number. "

The adjacent area referred to here means that a whole section of the boundary is common. If two districts

guess

Of the mathematical conjectures related to prime numbers in history, the most famous is of course the "Goldbach conjecture".

On June 7, 1742, German mathematician Goldbach put forward a bold conjecture in a letter to the famous mathematician Euler:

Any odd number not less than 3 can be the sum of three prime numbers (for example: 7 = 2 + 2 + 3, when 1 was still a prime number).

In the same year, on June 30, Euler wrote another version of Goldbach's conjecture in a reply:

Any even number can be the sum of two prime numbers (for example: 4 = 2 + 2. 1 was still a prime number at the time).

This is the famous Goldbach conjecture in the history of mathematics. Obviously, the former is a consequence of the latter. Therefore, just prove the latter to prove the former. So the former is called the weak Goldbach conjecture (which has been proven), and the latter is the strong Goldbach conjecture. Since 1 is no longer a prime number, these two conjectures become

Any odd number not less than 7 can be written as the sum of three prime numbers;

Any even number not less than 4 can be written as the sum of two prime numbers.

Brief description

Conjecture manuscript

In his reply to Goldbach, Euler clearly stated that he was convinced that both conjectures were correct theorems, but Euler could not prove it at the time. Since Euler was the greatest mathematician in Europe at that time, his confidence in Goldbach's conjecture affected the mathematical community in Europe and the world. Since then, many mathematicians have been eager to try, and even devoted their lives to proving the Goldbach conjecture. But until the end of the 19th century, the proof of Goldbach's conjecture did not make any progress. The difficulty of proving Goldbach's conjecture is far beyond people's imagination. Some mathematicians liken Goldbach's conjecture to "the pearl on the crown of mathematics".

We can see Goth from the specific examples of 6 = 3 + 3, 8 = 3 + 5, 10 = 5 + 5, ..., 100 = 3 + 97 = 11 + 89 = 17 + 83, ... Bach's conjecture is true. Some people even verified all the even numbers within 33 million one by one, and none of them did not meet Goldbach's conjecture. In the 20th century, with the development of computer technology, mathematicians discovered that Goldbach's conjecture still holds for larger numbers. But natural numbers are infinite. Who knows if a counterexample to Goldbach's conjecture will suddenly appear on a certain sufficiently large even number? So people gradually changed the way they explored problems.

In 1900, Hilbert, the greatest mathematician of the 20th century, listed the "Goldbach Conjecture" as one of the 23 mathematical problems at the International Mathematical Conference. Since then, mathematicians in the 20th century "jointly" attacked the "Goldbach Conjecture" fortress around the world and finally achieved brilliant results.

Proof process

The main methods used by mathematicians in the 20th century to study Goldbach's conjecture were advanced mathematical methods such as the sieve method, the circle method, the density method, and the triangle sum method. The idea of solving this conjecture is like "narrowing the enclosing circle" and gradually approaching the final result.

In 1920, the Norwegian mathematician Brown proved the theorem "9 + 9", thereby delineating the "big encirclement" that attacked the "Goldbach conjecture". What is going on with "9 + 9"? The so-called "9 + 9" is translated into a mathematical language: "Any sufficiently large even number can be expressed as the sum of the other two numbers, and each of these two numbers is the number of 9 odd prime numbers Product. "Starting from this" 9 + 9 ", mathematicians around the world concentrated their efforts on" narrowing the perimeter ", of course, the final goal was" 1 + 1 ".

In 1924, German mathematician Redmacher proved the theorem "7 + 7". Soon, "6 + 6", "5 + 5", "4 + 4" and "3 + 3" were captured one by one. In 1957, Chinese mathematician Wang Yuan proved "2 + 3". In 1962, Chinese mathematician Pan Chengdong proved "1 + 5", and in the same year, he and Wang Yuan proved "1 + 4". In 1965, Soviet mathematicians proved "1 + 3".

In 1966, the famous Chinese mathematician Chen Jingrun conquered "1 + 2", that is: "Any even large number can be expressed as the sum of two numbers. One is the product of two odd prime numbers. "This theorem is called" Chen's Theorem "in the world's mathematical community.

Thanks to Chen Jingrun's contribution, humans are only one step away from the final result of Goldbach's conjecture "1 + 1". But in order to achieve this last step, it may take a long exploration process. Many mathematicians believe that in order to prove "1 + 1", new mathematical methods must be created, and the past may not be possible.