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Hilbert's seventh problem is one of David Hilbert's list of open mathematical problems posed in 1900. It concerns the irrationality and transcendence of certain numbers ( Irrationalität und Transzendenz bestimmter Zahlen ).
Hilbert's problems ranged greatly in topic and precision. Some of them, like the 3rd problem, which was the first to be solved, or the 8th problem (the Riemann hypothesis), which still remains unresolved, were presented precisely enough to enable a clear affirmative or negative answer.
Part of the seventh of Hilbert's twenty-three problems posed in 1900 was to prove, or find a counterexample to, the claim that a b is always transcendental for algebraic a ≠ 0, 1 and irrational algebraic b. In the address he gave two explicit examples, one of them being the Gelfond–Schneider constant 2 √ 2.
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 a solution exists for all 7th-degree equations using algebraic (variant: continuous ) functions of two arguments .
Pages in category "Hilbert's problems" The following 35 pages are in this category, out of 35 total. ... Hilbert's seventh problem; Hilbert's eighth problem;
In 1900 David Hilbert posed a question about transcendental numbers, Hilbert's seventh problem: If a is an algebraic number that is not 0 or 1, and b is an irrational algebraic number, is a b necessarily transcendental? The affirmative answer was provided in 1934 by the Gelfond–Schneider theorem.
In mathematics, particularly in dynamical systems, the Hilbert–Arnold problem is an unsolved problem concerning the estimation of limit cycles.It asks whether in a generic finite-parameter family of smooth vector fields on a sphere with a compact parameter base, the number of limit cycles is uniformly bounded across all parameter values.
Hilbert's 13th problem was the conjecture this was not possible in the general case for seventh-degree equations. Vladimir Arnold solved this in 1957, demonstrating that this was always possible. [ 2 ]