Alonzo Church

Alonzo Church (1903–1995) was an American mathematician and logician who developed lambda calculus and helped establish computability theory and mathematical logic.

Lambda calculus: A formal system of function abstraction and application that can express general computation. Church developed it as a foundation for defining functions and formalizing computation.
Church encoding: A method of representing data and operations using only functions in lambda calculus. It demonstrates how arithmetic and logical structures can be built within Church’s calculus.
Alan Turing: A British mathematician and computer scientist who defined an abstract model of computation. Turing independently established a model equivalent in computational power to Church’s lambda calculus.
Princeton University: A private research university in Princeton, New Jersey, founded in 1746. Church spent most of his academic career there and built a major center for mathematical logic.
Computability theory: The study of which problems can be solved by algorithms and which functions can be computed. Church’s work helped establish this field by giving a formal account of effective computation.
Church–Turing thesis: The thesis that effectively calculable functions are exactly those computable by a Turing machine. Church and Alan Turing independently identified the same boundary of effective computation.
Beta reduction: The operation of applying a lambda abstraction to an argument by substitution. It is the central computation step in the lambda calculus Church developed.
Kurt Gödel: An Austrian-born logician whose incompleteness theorems transformed mathematical logic. Gödel’s results and correspondence helped shape Church’s approach to formal systems and computability.
Principia Mathematica: A three-volume work by Alfred North Whitehead and Bertrand Russell seeking to derive mathematics from logic. Its logicist ambitions formed part of the foundational debate Church’s work addressed.
Undecidable problem: A decision problem for which no algorithm gives the correct answer on every possible input. Church’s theorem demonstrated a fundamental undecidable problem in mathematical logic.

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