**Alonzo Church** made important contributions to mathematical logic and theoretical computer science.

- Church spent two years as a National Research Fellow, one year at Harvard University then a year at Göttingen and Amsterdam.
- There was Church together with his students Rosser and Kleene.
- Alan Turing, who had been thinking about the notion of effective calculability, came as a visiting graduate student in 1936 and stayed to complete his Ph.D. under Church.
- It is effectively a rewritten and polished version of lectures Church gave in Princeton in 1936 on the λ-calculus.
- Church is probably best remembered for 'Church's Theorem' and 'Church's Thesis' both of which first appeared in print in 1936.
- Church's Theorem, showing the undecidability of first order logic, appeared in A note on the Entscheidungsproblem published in the first issue of the Journal of Symbolic Logic.
- Church's Theorem extends the incompleteness proof given of Gödel in 1931.
- Church's Thesis appears in An unsolvable problem in elementary number theory published in the American Journal of Mathematics 58 (1936), 345-363.
- Church was a founder of the Journal of Symbolic Logic in 1936 and was an editor of the reviews section from its beginning until 1979.
- The aim of comprehensive coverage, which in 1936 had seemed quite practical, became less so as the years went by and by 1975 the rapid expansion in symbolic logic publications forced Church to give up this aspect and begin to provide only selective coverage.
- We mentioned above that Church retired from Princeton in 1967 and went to the University of California at Los Angeles.
- Church wrote the classic book Introduction to Mathematical Logic in 1956.
- This was a revised and very much enlarged edition of Introduction to mathematical logic which Church published twelve years earlier in 1944.
- Another area of interest to Church was axiomatic set theory.
- Church bases his form of the theory of types on his λ-calculus.
- Other work by Church in this area includes Set theory with a universal set published in 1971 which examines a variant of ZF-type axiomatic set theory and Comparison of Russell's resolution of the semantical antinomies with that of Tarski published in 1976.
- Church considered this topic for about 40 years during the latter part of his career, beginning with his paper A formulation of the logic of sense and denotation in 1951.
- Although most of Church's contributions are directed towards mathematical logic, he did write a few mathematical papers of other topics.
- The first examines ideas and results in the elementary theory of ordinary and partial differential equations which Church feels may encourage further investigation of the topic.
- Church had 31 doctoral students including Foster, Turing, Kleene, Kemeny, Boone, and Smullyan.

Born 14 June 1903, Washington, D.C., USA. Died 11 August 1995, Hudson, Ohio, USA.

View full biography at MacTutor

Algebra, Group Theory, Origin Usa

**O’Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive