Reprinted] Twenty-three mathematics issues of Hilbert
Sending station: Nanjing University Small Lily Station (Fri May 30 01:01:29 2003)
In 1900, the German mathematician D. Hilbert was titled "Mathematics issue at the 2nd International Mathematician Conference of Paris.
"The famous lecture, which expressed the meaning of all kinds of mathematical problems, the source and research methods published a brilliant insight.
The core part of the lecture is 23 issues raised by Hilbert in accordance with the results of the results of mathematics research in the 19th century.
1 Continuous assumptions in 1963, P.j. Cohen proved that the authenticity of continuous hypothesis is not possible to judge in the Cecumell-Frenkul system.
2 Compatibility of arithmetic axioms in 1931, K. Gotel's "incomplete theorem" pointed out that the "metamorphia" proves that arithmetic axiom compatibility with Hilbert. Mathematical compatibility issues have not been resolved.
3 Two-class high-end four-faceted volumes of the squares of M.W. De En has given affirmation of this issue.
4 The straight line is the shortest distance problem of two points, and there are many progress in construction and exploration of various special metrics, but the problem is not resolved.
5 Do not define the micro-hypothetical Li Qun concept of the group's function A.M. Glyn, d. Montgomery and L. Qi Ping is equal to the final affirmation of this issue in 1952.
6 The general significance of physical axioms' mathematical physics physics still needs to be discussed. As for the probability theory of the ribbon mentioned in Hilbert issues, it has been established by а.н. Kurmoolov (1933).
7 Some numbers are unreasonable and transcendence in 1934, AO Gair Frengde and T. Schneid have independently solved the second half of the problem, that is, for any algebra □ □ 0, 1, and any algebra □ Prove the transcendence of □□.
The number of prime numbers includes Liman's conjecture, Gotbach guess and twin pixe problems. Treatment of Liman's conjecture is still resolved. Gothic results are the best results in Chen Jingrun (1966), but there is still a distance from the final resolution.
⑨ The most common mutual anti-law in any number of fields has been resolved by Gao Ma □ (1921) and E. E. Antine (1927).
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The 11 factor is a secondary H. Hasse (1929) and C.L. Siegel (1936, 1951), is an important result on this issue.
12 The Cromonic theorem on the Abel field is unresolved to any algebra.
13 It is impossible to use a function of only two variables to solve the consecutive function scenarios in 1957 by в. и. Arnold. The analysis of the function is not resolved.
14 Proof of a complete function of a complete function system In 1958, Yongtian Ya is given a negative solution.
15 Shubert count calculations The rigorous base algebraic geometry foundation has been established by B.L. Van De Valden (1938 ~ 1940) and A. Wei (1950), the rationality of Schubert is still resolved.
The top half of the 16-generation curve and the surface of the surface, и.г. Petrovski has declared the number of □ = 2 pole limit ring, but this conclusion is wrong, has been Chinese mathematicians raised an antique example (1979).
17 The square representation of the positive form has been resolved by E.Artan in 1926.
18 Solved by a full multifaceted structure spatial part.
19 Regular variational problems will be analyzed in 1904, с.н. Burnstein proves that a variation of a variation of nonlinear elliptic equation has a solution. This result is also extended to multi-variable and elliptical groups.
20 The study of the biamatic partial side value problem of the general boundary value problem is booming.
21 The existence of a linear differential equation with a given single value group has been resolved by the Hilbert himself (1905) and H. Rar (1957).
22 Single value of the parsing relationship has been resolved by P. Club (1907).
23. Further development of variational method.
These 23 issues involve most of the important fields of modern mathematics, driving the development of mathematics in the 20th century, said in the history of mathematics
Mathematics in Hilbert.
