# Search - List of Books by Alonzo Church

*"I was an undergraduate at Princeton, and I was pressed by the math department to go on to graduate school. Actually they gave me fellowships that paid my way, otherwise I would not have been able to continue." -- Alonzo Church*

**Alonzo Church** (June 14, 1903 — August 11, 1995) was an American mathematician and logician who made major contributions to mathematical logic and the foundations of theoretical computer science. He is best known for the lambda calculus, Church—Turing thesis, Frege—Church ontology, and the Church—Rosser theorem.

*"I tried reading Hilbert. Only his papers published in mathematical periodicals were available at the time. Anybody who has tried those knows they are very hard reading."**"Never had any mathematical conversations with anybody, because there was nobody else in my field."**"The only thing that might have annoyed some mathematicians was the presumption of assuming that maybe the axiom of choice could fail, and that we should look into contrary assumptions."**"Well it was not exactly a dissertation in logic, at least not the kind of logic you would find in Whitehead and Russell's Principia Mathematica for instance. It looked more like mathematics; no formalized language was used."*

Alonzo Church was born on June 14, 1903 in Washington, D.C. where his father, Samuel Robbins Church, was the Justice of the Municipal Court for the District of Columbia. The family later moved to Virginia after his father lost this position because of failing eyesight. With help from his uncle, also named Alonzo Church, he was able to attend the Ridgefield School for Boys in Ridgefield, Connecticut. After graduating from Ridgefield in 1920, Church attended Princeton University where he was an exceptional student, publishing his first paper, on Lorentz transformation, and graduating in 1924 with a degree in mathematics. He stayed on at Princeton, earning a Ph.D. in mathematics in three years under Oswald Veblen.

He married Mary Julia Kuczinski in 1925 and the couple had three children, Alonzo Church, Jr. (1929), Mary Ann (1933) and Mildred (1938).

After receiving his Ph.D. he taught briefly as an instructor at the University of Chicago and then received a two-year National Research Fellowship. This allowed him to attend Harvard University in 1927—1928 and then both University of Göttingen and University of Amsterdam the following year. He taught at Princeton, 1929—1967, and at the University of California, Los Angeles, 1967—1990. In 1990, he received the Doctor Honoris Causa from the State University of New York at Buffalo in connection with an international symposium in his honor organized by John Corcoran. He had previously received honorary doctorates from Case Western Reserve University (1969) and Princeton University (1985).

He died in 1995 and was buried in Princeton Cemetery.

Church is best known for the following accomplishments:

- His proof that Peano arithmetic and first-order logic are undecidable. The latter result is known as Church's theorem.
- His articulation of what has come to be known as Church—Turing thesis.
- He was the founding editor of the
*Journal of Symbolic Logic*, editing its reviews section until 1979.
- His creation of the lambda calculus.

The lambda calculus emerged in his famous 1936 paper showing the existence of an "undecidable problem". This result preceded Alan Turing's famous work on the halting problem, which also demonstrated the existence of a problem unsolvable by mechanical means. Church and Turing then showed that the lambda calculus and the Turing machine used in Turing's halting problem were equivalent in capabilities, and subsequently demonstrated a variety of alternative "mechanical processes for computation." This resulted in the Church—Turing thesis.

The lambda calculus influenced the design of the LISP programming language and functional programming languages in general. The Church encoding is named in his honor.

Many of Church's doctoral students have led distinguished careers, including C. Anthony Anderson, Peter B. Andrews, George A. Barnard, William W. Boone, Martin Davis, Alfred L. Foster, Leon Henkin, John G. Kemeny, Stephen C. Kleene, Simon B. Kochen, Maurice L'Abbé, Isaac Malitz, Gary Mar, Michael O. Rabin, Nicholas Rescher, Hartley Rogers, Jr., J. Barkley Rosser, Dana Scott, Raymond Smullyan, and Alan Turing. A more complete list of Church's students is available via Mathematics Genealogy Project.

- Alonzo Church,
*Introduction to Mathematical Logic* (ISBN 978-0-691-02906-1)
- Alonzo Church,
*The Calculi of Lambda-Conversion* (ISBN 978-0-691-08394-0)
- Alonzo Church,
*A Bibliography of Symbolic Logic, 1666—1935* (ISBN 978-0-8218-0084-3)
- C. Anthony Anderson and Michael Zelëny, editors,
*Logic, Meaning and Computation: Essays in Memory of Alonzo Church* (ISBN 978-1-4020-0141-3)

- Enderton, Herbert B., Alonzo Church: Life and Work. Introduction to the
*Collected Works of Alonzo Church*, MIT Press, not yet published.
- Enderton, Herbert B., In memoriam: Alonzo Church,
*The Bulletin of Symbolic Logic*, vol. 1, no. 4 (Dec. 1995), pp. 486—488.
- Wade, Nicholas, Alonzo Church, 92, Theorist of the Limits of Mathematics (obituary),
*The New York Times*, September 5, 1995, p. B6.
- Hodges, Wilfred, Obituary: Alonzo Church,
*The Independent (London)*, September 14, 1995.
- Alonzo Church interviewed by William Aspray on 17 May 1984.
*The Princeton Mathematics Community in the 1930s: An Oral-History Project*, transcript number 5.
- Rota, Gian-Carlo, Fine Hall in its golden age: Remembrances of Princeton in the early fifties. In
*A Century of Mathematics in America, Part II*, edited by Peter Duren, AMS History of Mathematics, vol 2, American Mathematical Society, 1989, pp. 223—226. Also available here.

**Total Books:** 7