In computability theory, the halting problem is the decision problem of, given an arbitrary computer program and an input, determining whether said program will eventually finish running and halt, or will continue to run forever. Alan Turing proved in 1937 that the halting problem is undecidable, meaning that no general algorithm exists that can correctly solve the problem for all possible program–input pairs. The problem comes up often in discussions of computability since it demonstrates that some functions are mathematically definable but not computable.