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Hilbert's thirteenth problem : ウィキペディア英語版 | Hilbert's thirteenth problem 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 conjecture, that it is not always possible to find such a solution, was disproven in 1957. ==Introduction== Hilbert considered the seventh-degree equation : and asked whether its solution, ''x'', considered as a function of the three variables ''a'', ''b'' and ''c'', can be expressed as the composition of a finite number of two-variable functions.
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