Fermat's last theorem: the second of the three major mathematical problems in the modern world.

Goldbach conjecture, the third of the three major mathematical problems in the modern world.

Four-color theorem (one of the three major mathematical problems in the modern world), also known as four-color conjecture and four-color problem, is one of the three major mathematical conjectures in the world. The essence of the four-color theorem is the inherent property of a two-dimensional plane, that is, two straight lines in the plane that cannot intersect and have no common points. Many people have proved that it is impossible to construct five or more connected regions on the two-dimensional plane, but it does not rise to the level of logical relationship and two-dimensional inherent attributes, which leads to many wrong counterexamples. But these are precisely the textual research and development promotion of the rigor of graph theory. The computer proves that although we have made tens of billions of judgments, we have only succeeded in a huge number of advantages, which does not conform to the strict logic system of mathematics, and there are still countless math enthusiasts involved.

Fermat's Last Theorem, also known as Fermat's Last Theorem, was put forward by French mathematician Pierre de Fermat in the 7th century. It asserts that when the integer n>2, the equation X N+Y N = Z N about X, Y and Z has no positive integer solution. Wolfsk of Germany once announced that he would award 65,438+ten thousand marks to the first person who proved the theorem within 100 years after his death, which attracted many people to try and submit their "proofs". After it was put forward, it was proved by British mathematician andrew wiles in 1995 after more than 300 years of history.

Goldbach put forward the following conjecture in his letter 1742 to Euler: any even number greater than 2 can be written as the sum of two prime numbers. But Goldbach himself could not prove it, so he wrote to the famous mathematician Euler and asked him to help him prove it, but until his death, Euler could not prove it. Because the convention that "1 is also a prime number" is no longer used in mathematics, the modern statement of the original conjecture is that any integer greater than 5 can be written as the sum of three prime numbers. Euler also put forward another equivalent version in his defense, that is, any even number greater than 2 can be written as the sum of two prime numbers. Today's popular conjecture is said to be Euler's version. Any sufficiently large even number can be expressed as the sum of a number with no more than one prime factor and a number with no more than b prime factors, and the proposition is called "a+b". 1966 Chen Jingrun proved that "1+2" holds, that is, "any sufficiently large even number can be expressed as the sum of two prime numbers, or the sum of a prime number and a semi-prime number". The common conjecture today is the Euler version, that is, any even number greater than 2 can be written as the sum of two prime numbers, which is also called "strong Goldbach conjecture" or "Goldbach conjecture about even numbers". From Goldbach's conjecture about even numbers, it can be inferred that any odd number greater than 7 can be written as the conjecture of the sum of three prime numbers. The latter is called "weak Goldbach conjecture" or "Goldbach conjecture on odd numbers". If the Goldbach conjecture about even numbers is right, then the Goldbach conjecture about odd numbers will also be right. The weak Goldbach conjecture has not been completely solved, but in 1937, vinogradov, a mathematician of the former Soviet Union, proved that an odd prime number large enough can be written as the sum of three prime numbers, which is also called Goldbach -V Noguera Dov theorem or triple prime number theorem.