1. Goldbach conjecture: 1 even number can be divided into two prime numbers plus "unsolved problem" (this problem is known as the jewel in the crown of mathematics, and Chen Jingrun proved that 1 even number can be divided into 1 prime number plus two prime numbers, commonly known as 1+2).

2. Fermat's conjecture: any natural number abc, when n is greater than 2, the n power of A plus the n power of B will not be equal to the n power of C. "This problem has been solved, and the bonus has been paid." (Fermat, a law major, said after writing this conjecture: I thought of a wonderful solution to this problem, but the page was too short to write .. Later, mathematicians were furious, tried to solve it, and finally.

3. Four-color conjecture: any map can distinguish all countries with only four colors (1976, American mathematicians Appel and Harken used two computers for more than 50 days, and1000 billion logical judgments, it is said that it is only because no one can prove the process wrong at first).

4. Tree planting: Plant 20 trees, 4 trees 1 row. How many lines can be planted at most (16th century16th line,19th century18th line, 20 lines at the end of 20th century)?

5. Euclid's fifth postulate: ... Equivalent expression ... There are only 1 parallel lines beyond 1 points of a straight line. "There is no solution to this problem" (Euclid deduced Euclidean geometry through this assumption, also called plane geometry; The tenacious and unfortunate Lobachevsky introduced non-Euclidean geometry, also known as Riemannian geometry, which laid the foundation of general relativity through the opposite of this hypothesis ...)

6. Riemann conjecture: All the solutions of Riemann zeta function at 0 are on the same straight line "This problem has no solution" (this problem is very mysterious, and it is said that it involves number theory functions and even economic and social aspects. Nash, the originator of game theory, spent n years solving this problem, but he was crazy ...)

7. Corner and valley conjecture: 1 natural number, if it is even, divide by 2, if it is odd, multiply by 3, and add 1, and the final result will always be 1.

8. Monochrome triangle: There are 6 points, and every 2 points are connected by black or red. Is it necessary to have a 1 monochromatic triangle? "This problem is not solved" (another expression: 6 people together, there must be 3 people who know or don't know)