Church-Turing Thesis
Church's Thesis or the Church-Turing Thesis is the proposal that the informal notion of "a function that can be computed by an algorithm" (or computed "mechanically") can be identified with the the set of functions computable by a Turing Machine. Roughly, this says that we won't be able to come up with any formalism, F, that captures our intuitive notion of an algorithm that will be more powerful than a Turing Machine where more powerful means that there are functions that can be computed by F that are not computable by a Turing Machine but not the converse.