First, Goldbach conjecture (first, any even number not less than 6 is the sum of two odd prime numbers; 2. Any odd number not less than 9 is the sum of three odd prime numbers. 2. Four-color problem (the content of the four-color problem is: "Any map with only four colors can make countries with the same border have different colors." Expressed in mathematical language, it means "divide the plane into non-overlapping areas at will, and each area can always be marked with one of the four numbers 1, 2, 3 and 4, without making two adjacent areas get the same number." Third, Fermat's conjecture (any cube of a number cannot be decomposed into the sum of two cubes, and any quartic party with voting rights cannot be decomposed into the sum of two quartic powers; More generally, except for the quadratic power, the sum of any power of two numbers cannot be equal to the number of the third person with the same power. ) Fourth, the twin prime conjecture (1849, Polinak put forward the twin prime conjecture, that is, guessing that there are infinite pairs of twin prime numbers. 5. Calabi conjecture (Is it possible to have a gravitational field without material distribution in a closed space? )