 To their surprise, all such notions turned out to be extensionally equivalent: any function computable within any of these formalisms is computable within any of the others. They took this as evidence that their quest for a precise definition of “algorithm” or “effectively computable function” had been successful. The resulting view—that TMs and other equivalent formalisms capture the informal notion of algorithm—is now known as the Church-Turing thesis (more on this in Section 4). The study of computable functions, made possible by the work of Turing et al., is part of the mathematical theory of computation.