His work is of major importance in mathematical logic, recursion theory and in theoretical computer science. He created the lambda calculus in the 1930's which today is an invaluable tool for computer scientists.
He is best remembered for Church's Theorem (1936), which shows there is no decision procedure for arithmetic. It appears in An unsolvable problem in elementary number theory published in the American Journal of Mathematics 58 (1936), 345-363. His work extended that of Gödel.
Church founded the Journal of Symbolic Logic in 1936 and remained an editor until 1979. He wrote the book Introduction to Mathematical Logic in 1956.
He had 31 doctoral students including Turing, Kleene, Kemeny and Smullyan.
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