In mathematical logic, a Godel numbering is a function that assigns to each symbol and well-formed formula of some formal language a unique natural number, called its Godel number. The concept was first used by Kurt Godel for the proof of his incompleteness theorem. A Godel numbering can be interpreted as an encoding in which a number is assigned to each symbol of a mathematical notation, after which a sequence of natural numbers can then represent a sequence of strings. These sequences of natural numbers can again be represented by single natural numbers, facilitating their manipulation in formal theories of arithmetic. Since Godel's paper was published in 1931, the term "Godel numbering" has been used to refer to more general assignments of natural numbers to mathematical objects.

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