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- Hilbert's_thirteenth_problem abstract "Hilbert's thirteenth problem is one of the 23 Hilbert problems set out in a celebrated list compiled in 1900 by David Hilbert. It entails proving whether or not a solution exists for all 7th-degree equations using algebraic (variant: continuous) functions of two arguments. It was first presented in the context of nomography, and in particular "nomographic construction" — a process whereby a function of several variables is constructed using functions of two variables. Hilbert considered the general seventh-degree equationand asked whether its solution, x, a function of the three variables a, b and c, can be expressed using a finite number of two-variable functions.Hilbert originally posed his problem for algebraic functions (Hilbert 1927, "...existenz von algebraischen Funktionen...", i.e., "...existence of algebraic functions..."). However, Hilbert also asked in a later version of this problem whether there is a solution in the class of continuous functions. A more general question in the second ("continuous") variant of the problem is: can every continuous function of three variables be expressed as a composition of finitely many continuous functions of two variables? The affirmative answer to this general question was given in 1957 by Vladimir Arnold, then only nineteen years old and a student of Andrey Kolmogorov. Kolmogorov had shown in the previous year that any function of several variables can be constructed with a finite number of three-variable functions. Arnold then expanded on this work to show that only two-variable functions were in fact required, thus answering Hilbert's question.Arnold later returned to the question, jointly with Goro Shimura (V. I. Arnold and G. Shimura, Superposition of algebraic functions (1976), in Mathematical Developments Arising From Hilbert's Problems).".
- Hilbert's_thirteenth_problem wikiPageExternalLink smf_sem-cong_2_1-11.pdf.
- Hilbert's_thirteenth_problem wikiPageExternalLink RMS_59_1_R03.pdf?request-id=ef17fbdb-1a1c-4250-ae5f-0e1885b837fa.
- Hilbert's_thirteenth_problem wikiPageID "2336190".
- Hilbert's_thirteenth_problem wikiPageRevisionID "606678625".
- Hilbert's_thirteenth_problem hasPhotoCollection Hilbert's_thirteenth_problem.
- Hilbert's_thirteenth_problem subject Category:Disproved_conjectures.
- Hilbert's_thirteenth_problem subject Category:Hilbert's_problems.
- Hilbert's_thirteenth_problem subject Category:Polynomials.
- Hilbert's_thirteenth_problem type Abstraction100002137.
- Hilbert's_thirteenth_problem type Attribute100024264.
- Hilbert's_thirteenth_problem type Condition113920835.
- Hilbert's_thirteenth_problem type Difficulty114408086.
- Hilbert's_thirteenth_problem type Function113783816.
- Hilbert's_thirteenth_problem type Hilbert'sProblems.
- Hilbert's_thirteenth_problem type MathematicalRelation113783581.
- Hilbert's_thirteenth_problem type Polynomial105861855.
- Hilbert's_thirteenth_problem type Polynomials.
- Hilbert's_thirteenth_problem type Problem114410605.
- Hilbert's_thirteenth_problem type Relation100031921.
- Hilbert's_thirteenth_problem type State100024720.
- Hilbert's_thirteenth_problem comment "Hilbert's thirteenth problem is one of the 23 Hilbert problems set out in a celebrated list compiled in 1900 by David Hilbert. It entails proving whether or not a solution exists for all 7th-degree equations using algebraic (variant: continuous) functions of two arguments. It was first presented in the context of nomography, and in particular "nomographic construction" — a process whereby a function of several variables is constructed using functions of two variables.".
- Hilbert's_thirteenth_problem label "Décimo-terceiro problema de Hilbert".
- Hilbert's_thirteenth_problem label "Hilbert's thirteenth problem".
- Hilbert's_thirteenth_problem label "Treizième problème de Hilbert".
- Hilbert's_thirteenth_problem label "Тринадцатая проблема Гильберта".
- Hilbert's_thirteenth_problem label "معضلة هيلبرت الثالثة عشر".
- Hilbert's_thirteenth_problem label "希爾伯特第十三問題".
- Hilbert's_thirteenth_problem sameAs Treizième_problème_de_Hilbert.
- Hilbert's_thirteenth_problem sameAs Décimo-terceiro_problema_de_Hilbert.
- Hilbert's_thirteenth_problem sameAs m.074nl0.
- Hilbert's_thirteenth_problem sameAs Q838094.
- Hilbert's_thirteenth_problem sameAs Q838094.
- Hilbert's_thirteenth_problem sameAs Hilbert's_thirteenth_problem.
- Hilbert's_thirteenth_problem wasDerivedFrom Hilbert's_thirteenth_problem?oldid=606678625.
- Hilbert's_thirteenth_problem isPrimaryTopicOf Hilbert's_thirteenth_problem.