ヒルベルト啼玛

# ヒルベルト啼玛

ひるべるともんだい

1900钳妈2搀パリ柜狠眶池荚柴的(ICM)でその办婶が绩されたヒルベルトによる眶池の踏豺疯啼玛礁。呵姜弄に23の啼玛よりなる。

### リスト

1. a. Is there a transfinite number between that of a denumerable set and the numbers of the continuum?
1. b. Can the continuum of numbers be considered a well ordered set?
2. Can it be proven that the axioms of logic are consistent?
3. Give two tetrahedra which cannot be decomposed into congruent tetrahedra directly or by adjoining congruent tetrahedra.
4. Find geometries whose axioms are closest to those of Euclidean geometry if the ordering and incidence axioms are retained, the congruence axioms weakened, and the equivalent of the parallel postulate omitted.
5. Can the assumption of differentiability for functions defining a continuous transformation group be avoided? (This is a generalization of the Cauchy functional equation.)
6. Can physics be axiomized?
7. Let be algebraic and irrational. Is then transcendental?
8. Prove the Riemann hypothesis.
9. Construct generalizations of the reciprocity theorem of number theory.
10. Does there exist a universal algorithm for solving Diophantine equations?
11. Extend the results obtained for quadratic fields to arbitrary integer algebraic fields.
12. Extend a theorem of Kronecker to arbitrary algebraic fields by explicitly constructing Hilbert class fields using special values.
13. Show the impossibility of solving the general seventh degree equation by functions of two variables.
14. []Show the finiteness of systems of relatively integral functions.
15. Justify Schubert's enumerative geometry
16. Develop a topology of real algebraic curves and surfaces.
17. Find a representation of definite form by squares.
18. Build spaces with congruent polyhedra.
19. Analyze the analytic character of solutions to variational problems.
20. Solve general boundary value problems.
21. Solve differential equations given a monodromy group. More technically, prove that there always exists a Fuchsian system with given singularities and a given monodromy group.
22. Uniformization.
23. Extend the methods of calculus of variations.
1. 息鲁挛啼玛
2. 换窖の给妄の痰谭解
3. 撵烫姥と光さの霹しい煌烫挛の挛姥が霹しいことを圭票年妄だけでは沮汤できないこと
4. 木俐が呵没调违を涂える傣部池の寥骏弄甫垫
5. 疤陵凡Lie凡になるための掘凤
6. 湿妄池の称婶嚏の给妄弄胺い
7. 硷硷の眶の亩臂拉の沮汤
8. 燎眶尸邵の啼玛
9. 办忍陵高恕搂
10. 稍年数镍及の铜妄腊眶豺の赂哼するか容かを铜嘎豺の缄檬で冉年すること
11. 办忍の洛眶弄眶挛における2肌妨及侠
12. 梧挛?の菇喇啼玛
13. 办忍の7肌洛眶数镍及は2恃眶の息鲁簇眶の圭喇によっては豺けないこと
14. 涂えられた驴灌及铜妄簇眶のなす茨が铜嘎改の驴灌及として栏喇されるか
15. 洛眶傣部池の答撩づけ
16. 洛眶妒俐?および妒烫の疤陵の甫垫
17. 悸眶挛惧の年射规の铜妄簇眶を士数下として山すこと
18. いくつかの驴烫挛と圭票な驴烫挛によって鄂粗をうめつくすこと
19. 赖搂恃尸啼玛?の豺は撅に豺老簇眶?であるか
20. 办忍董肠猛啼玛
21. 涂えられたモノドロミ〖凡?をもつ俐妨腮尸数镍及は赂哼するか
22. 瘦妨簇眶?による豺老簇眶の办罢步
23. 恃尸池の数恕の甫垫の鸥倡

*リスト¨リスト::眶池簇息