#computing # [[Epistemic status]] #shower-thought # Entscheidungsproblem #to-digest Are all problems solvable? Yes using a [[Turing machine]]. Except one, the [[Halting problem]]. A [[Turing machine]] can be programmed to execute an algorithm that solve any mathematical problem. >One thing to bear in mind about a Turing 'machine' will be that it is a piece of"abstract mathematics' and not a physical object. The concept was introduced by the English mathematician, code- breaker extraordinary and seminal computer scientist Alan Turing in 1935--6 (Turing 1937), in order to tackle a very broad-ranging problem, known as the Entscheidungsproblem, partially posed by the great German mathematician David Hilbert in 1900, at the Paris International Congress of Mathematicians ("Hubert's tenth problem'), and more completely, at the Bologna International Congress in 1928. Hilbert had asked for no less than a general algorithmic procedure for resolving mathematical questions- or, rather, for an answer to the question of whether or not such a procedure might in principle exist. >~ [[Roger Penrose]]