Entscheidungsproblem
In 1936 and 1937, Alonzo Church and Alan Turing showed independently, that there can be no answer to the Entscheidungsproblem. They showed that it is impossible for an algorithm to decide whether statements in arithmetic are true or false. For this reason, there can be no solution for the Entscheidungsproblem. This was proven by Alan Turings "Turing Machine" which was created in the 1930s.