The history of the Church—Turing thesis "thesis" involves the history of the development of the study of the nature of functions whose values are effectively calculable; or, in more modern terms, functions whose values are algorithmically computable. It is an important topic in modern mathematical theory and computer science, particularly associated with the work of Alonzo Church and Alan Turing. The debate and discovery of the meaning of "computation" and "recursion" has been long and contentious. This article provides detail of that debate and discovery from Peano's axioms in through recent discussion of the meaning of " axiom ". In , Giuseppe Peano presented his The principles of arithmetic, presented by a new method , based on the work of Dedekind.

## Turing machine

## Alan Turing ( - ) - Biography - MacTutor History of Mathematics

Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It only takes a minute to sign up. Connect and share knowledge within a single location that is structured and easy to search. My understanding is that the thesis is essentially a definition of the term "computable" to mean something that is computable on a Turing Machine. Is this really all there is to it? If so, what makes this definition so important?

### Alan Mathison Turing

Connect and share knowledge within a single location that is structured and easy to search. For questions about the interpretation, extension and validity of the Church-Turing thesis, the hypothesis that states that a function is effectively calculable by a human if and only if the function is computable on a Turing machine. Stack Overflow for Teams — Collaborate and share knowledge with a private group.

The Church-Turing thesis is not the usual place to start an introduction to computational theory, but it is a useful place because it gives a feel for the way that CS theory approaches questions. Let us consider the matter of computation, which is the ability to transform some input information into some output information. An example computation might be estimating the life expectancy of a minmi given a variety of fossil evidences. Is there a language in which we can describe every task that can be performed? Is there a set of techniques we can combine to do absolutely everything?

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