In mathematics, the ' (, German for 'decision problem') is a challenge posed by David Hilbert in 1928. The asks for an algorithm that will take as input a description of a formal language and a mathematical statement in the language and produce as output either "True" or "False" according to whether the statement is true or false. The algorithm need not justify its answer, nor provide a proof, so long as it is always correct. Such an algorithm would be able to decide, for example, whether statements such as Goldbach's conjecture or the Riemann hypothesis are true, even though no proof or d...