 As explained in  Sec. 1.1,  Turing machines were originally intended to formalize the notion of computability in order to tackle a fundamental problem of mathematics. Independently of Turing, Alonzo Church gave a different but logically equivalent formulation (see  Sec. 4).  Today, most computer scientists agree that Turing’s, or any other logically equivalent, formal notion captures all computable problems, viz. for any computable problem, there is a Turing machine which computes it. This is known as the Church-Turing thesis, Turing’s thesis (when the reference is only to Turing’s work) or Church’s thesis (when the reference is only to Church’s work).