The Church–Turing thesis is a fundamental concept in computer science and mathematics that proposes a formal definition of what it means for a function to be computable. Formulated independently by mathematicians Alonzo Church and Alan Turing in the 1930s, the thesis asserts that any function that can be effectively computed by a human using a set of clear, finite instructions (an algorithm) can also be computed by a Turing machine.
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The Church–Turing thesis asserts that every effectively calculable function is computable by a formal model equivalent to a Turing machine. It identifies an informal notion of effective procedure with a mathematical class rather than stating a theorem within one formal system.