[2] He is best known for the lambda calculus, the Church–Turing thesis, proving the unsolvability of the Entscheidungsproblem ("decision problem"), the Frege–Church ontology, and the Church–Rosser theorem.

Alongside his doctoral student Alan Turing, Church is considered one of the founders of computer science.

[20] Church is known for the following accomplishments: The lambda calculus emerged in his 1936 paper showing the unsolvability of the Entscheidungsproblem.

[24] The lambda calculus influenced the design of Lisp and functional programming languages in general.

[27] Church’s elaboration of a methodology involving the logistic method, his philosophical criticisms of nominalism and his defense of realism, his argumentation leading to conclusions about the theory of meaning, and the detailed construction of the Fregean and Russellian intensional logics, are more than sufficient to place him high up among the most important philosophers of this century.

He is credited with formulating the Slingshot Argument, which suggests that sentential references must be truth-values, rather than propositions.

[11] Many of them have led distinguished careers in mathematics, computer science, and other academic subjects, including Peter B. Andrews, George A. Barnard, David Berlinski, William W. Boone, Martin Davis, Alfred L. Foster, Leon Henkin, John G. Kemeny, Stephen C. Kleene, Simon B. Kochen, Maurice L'Abbé, Gary R. Mar, Michael O. Rabin, Nicholas Rescher, Hartley Rogers, Jr., J. Barkley Rosser, Dana Scott, Raymond Smullyan and Alan Turing.

[29] In addition to those he directly supervised, Church also had a large influence on other mathematicians and computer scientists.