Alonzo Church

Alonzo Church
Alonzo Church (1903–1995)
Born	June 14, 1903 Washington, D.C., US
Died	August 11, 1995 (aged 92) Hudson, Ohio, US
Residence	United States
Nationality	American
Fields	Mathematics, Logic
Institutions	Princeton University (1929–67) UCLA (1967–95)
Alma mater	Princeton University
Thesis	Alternatives to Zermelo's Assumption (1927)
Doctoral advisor	Oswald Veblen
Doctoral students	C. Anthony Anderson Peter Andrews George Alfred Barnard Martin Davis Alfred Foster Leon Henkin David Kaplan John George Kemeny Stephen Kleene Gary R. Mar Michael O. Rabin Hartley Rogers, Jr J. Barkley Rosser Dana Scott Raymond Smullyan Alan Turing
Known for	Lambda calculus Church–Turing thesis Frege–Church ontology Church–Rosser theorem

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, proving the undecidability of the Entscheidungsproblem, Frege–Church ontology, and the Church–Rosser theorem.

Life

Alonzo Church was born on June 14, 1903, in Washington, D.C., where his father, Samuel Robbins Church, was the judge 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.^[1] After graduating from Ridgefield in 1920, Church attended Princeton University where he was an exceptional student, publishing his first paper, on Lorentz transformations, and graduating in 1924 with a degree in mathematics. He stayed 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 philosophy and mathematics at Princeton, 1929–1967, and at the University of California, Los Angeles, 1967–1990. He was a Plenary Speaker at the ICM in 1962 in Stockholm.^[2] He received honorary Doctor of Science degrees from Case Western Reserve University in 1969,^[3] Princeton University in 1985,^[4] and the University at Buffalo, The State University of New York in 1990 in connection with an international symposium in his honor organized by John Corcoran.^[5]

A deeply religious person, he was a lifelong member of the Presbyterian church.^[6]

He died in 1995 and was buried in Princeton Cemetery.

Mathematical work

Church is known for the following accomplishments:

• His proof that the Entscheidungsproblem, which asks for a decision procedure to determine the truth of arbitrary propositions in a mathematical theory, is undecidable. This is known as Church's theorem.
• His proof that Peano arithmetic is undecidable.
• His articulation of what has come to be known as the 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 1936 paper showing the unsolvability of the Entscheidungsproblem. This result preceded Alan Turing's 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.

Students

Many of Church's doctoral students have led distinguished careers, including C. Anthony Anderson, 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, Isaac Malitz, Gary R. Mar, Michael O. Rabin, Nicholas Rescher, Hartley Rogers, Jr., J. Barkley Rosser, Dana Scott, Raymond Smullyan, and Alan Turing.^[7] A more complete list of Church's students is available via Mathematics Genealogy Project.

Books

• Alonzo Church, Introduction to Mathematical Logic (ISBN 978-0-691-02906-1)^[8]
• Alonzo Church, The Calculi of Lambda-Conversion (ISBN 978-0-691-08394-0)^[9]
• Alonzo Church, A Bibliography of Symbolic Logic, 1666–1935 (ISBN 978-0-8218-0084-3)
• C. Anthony Anderson and Michael Zelëny, (eds.), Logic, Meaning and Computation: Essays in Memory of Alonzo Church (ISBN 978-1-4020-0141-3)

See also

• Church–Turing–Deutsch principle
• Higher-order logic
• Universal set

Notes

1. The Ridgefield School for Boys, also known as the Ridgefield School, was a private school that existed from 1907 to 1938. See The Ridgefield School.
2. Church, Alonzo. "Logic, arithmetic and automata." In Proceedings of the International Congress of Mathematicians, pp. 23–35. 1962.
3. Honorary degrees awarded by Case Western Reserve University
4. Honorary degrees awarded by Princeton University
5. Finding Aid for The Honorary Degree Conferral of Doctor of Science to Alonzo Church, 1990
6. "Introduction Alonzo Church: Life and Work" (PDF). p. 4. Retrieved 6 June 2012. A deeply religious person, he was a lifelong member of the Presbyterian church.
7. "Mathematics Genealogy Project". Archived from the original on 4 August 2010. Retrieved 12 August 2010.
8. Henkin, Leon (1957). "Review: Introduction to Mathematical Logic by Alonzo Church" (PDF). Bull. Amer. Math. Soc. 63 (5): 320–323. doi:10.1090/s0002-9904-1957-10129-3.
9. Frink Jr., Orrin (1944). "Review: The Calculi of Lambda-Conversion by Alonzo Church" (PDF). Bull. Amer. Math. Soc. 50 (3): 169–172. doi:10.1090/s0002-9904-1944-08090-7.

References

• 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.

External links

• O'Connor, John J.; Robertson, Edmund F., "Alonzo Church", MacTutor History of Mathematics archive, University of St Andrews.
• Alonzo Church at the Mathematics Genealogy Project
• Princeton University Library, Manuscripts Division, The Alonzo Church Papers, 1924–1995: finding aid.
• A bibliography of Church's reviews for The Journal of Symbolic Logic, with a link to each