"Mathematical Problems" is an anthology of Hilbert's speech "Mathematical Problems" at the International Congress of Mathematicians in Paris from 65438 to 0900. The 23 mathematical problems he raised in his speech stimulated the imagination of the whole mathematical field and promoted the development of mathematics in the 20th century. In this speech, Hilbert also expounded his incisive views on the essence of mathematics, the source of mathematical knowledge, the importance of mathematical problems and research methods. # The main idea of progress shows that the first problem, continuum hypothesis, is partially solved. 1963, American mathematician paul cohen proved that ZFC could not deduce the continuum hypothesis. In other words, whether the continuum hypothesis is established cannot be decided by ZFC. The compatibility of arithmetic axioms has been solved. Kurt G?del proved Godel's incomplete theorem in 1930. The third problem, the proof that the volumes of two tetrahedrons are equal, has been solved. Hilbert's student Max Dean proved the impossibility by counterexample. The fourth problem is to establish all metric spaces so that geodesics of all line segments are too vague. Hilbert's definition of this problem is too vague. The fifth question, whether all continuous groups are differentiable, has been solved. 1953, Japanese mathematician Hidehiko Yamabe got a completely positive result. Question 6 Axiomatic Physics Non-mathematics Many people question whether physics can be axiomatized as a whole. Question 7: If B is an irrational number and A is an algebraic number that is not zero 1, then whether ab is a transcendental number has been independently solved by Gelfand and Schneider in 1934 and 1935 respectively. The eighth question Riemann conjecture, Goldbach conjecture and twin prime conjecture are unsolved. Zhang proved the weak twin prime conjecture at 20 13. Question 9: Partial solution of general reciprocal law in arbitrary algebraic number field. 192 1 Japan's Masako Takagi and 1927's Emile E. Adin in Germany each have partial solutions. The tenth problem, the solvability of indefinite equations, has been solved. 1970 the Soviet mathematician Marty Sevik proved that in general, the answer is no, and the second form of algebraic coefficient in question 11 has been solved. The rational part is solved by Hasse in 1923, and the real part is solved by Higl in 1930. The twelfth problem, the extension of algebraic numbers, has been solved. 1920, Takagi Sadako founded Abel's domain theory. Problem 13: It has been solved to solve any seventh order equation with binary function. André Andrey Kolmogorov and Vladimir Arnold proved that this is impossible. The problem 14 proves that the finiteness of a complete function system has been solved. 1962, Japanese Masayoshi Nagata put forward a counterexample. Question 15 Schubert enumerated the strict basic parts of calculus (Schubert's enumerated calculus), and some of them were strictly proved by van der Waals in 1938. Problem 16: The topological structure of algebraic curves and surfaces has not been solved. Question 17: Writing rational function as sum of squares fraction has solved the real closed domain of Emil Artin in 1927. Question 18: can the non-regular polyhedron lay the space tightly to solve the problem of the closest arrangement of spheres? Bieber Bach proposed in 19 10 that "n-dimensional space is embedded by finite groups". Question 19: Are all solutions of Lagrangian system solved analytically by Russian mathematician Bernstein in 1904? Solve. Question 20: Have all the variational problems with boundary conditions been solved? Question 2 1: Prove the existence of a linear differential equation of a given singular group. Question 22: Use automorphic function to unify the analyzable relation to solve it. 1904 was solved by Kobe and Poincare. The long-term development of variational method has not been solved.