Search results
Results from the WOW.Com Content Network
In an isosceles triangle, if the ratio of the base angle to the angle at the vertex is algebraic but not rational, is then the ratio between base and side always transcendental? Is a b {\displaystyle a^{b}} always transcendental , for algebraic a ∉ { 0 , 1 } {\displaystyle a\not \in \{0,1\}} and irrational algebraic b {\displaystyle b} ?
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.
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;
Many mathematical problems have been stated but not yet solved. These problems come from many areas of mathematics, such as theoretical physics, computer science, algebra, analysis, combinatorics, algebraic, differential, discrete and Euclidean geometries, graph theory, group theory, model theory, number theory, set theory, Ramsey theory, dynamical systems, and partial differential equations.
Kip Thorne concludes, in remarks based on Hilbert's 1924 paper, that Hilbert regarded the general theory of relativity as Einstein's: "Quite naturally, and in accord with Hilbert's view of things, the resulting law of warpage was quickly given the name the Einstein field equation rather than being named after Hilbert.
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 [disambiguation needed] 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 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 .
In mathematics, Hilbert's fourth problem in the 1900 list of Hilbert's problems is a foundational question in geometry.In one statement derived from the original, it was to find — up to an isomorphism — all geometries that have an axiomatic system of the classical geometry (Euclidean, hyperbolic and elliptic), with those axioms of congruence that involve the concept of the angle dropped ...