The problem asks for an algorithm that considers, as input, a statement and answers "yes" or "no" according to whether the statement is universally valid, i.e., valid in every structure. By the completeness theorem of first-order logic, a statement is universally valid if and only if it can be deduced using logical rules and axioms. The problem was posed in 1928 by David Hilbert and Wilhelm Ackermann. It was answered in the negative by Alonzo Church and Alan Turing in independent papers in 1936.