Alonzo Church

Alonzo Church (June 14, 1903 – August 11, 1995) was an American mathematician, logician, computer scientist, and philosopher. His work reshaped mathematical logic and the foundations of theoretical computer science. He is most famous for creating the lambda calculus, formulating the Church–Turing thesis, proving that the Entscheidungsproblem (decision problem) has no solution, developing the Frege–Church ontology, and establishing the Church–Rosser theorem. Along with his doctoral student Alan Turing, Church is regarded as a founder of computer science.

Church was born in Washington, D.C. His father, Samuel Robbins Church, served as a justice of the peace and a municipal court judge. His grandfather, Alonzo Webster Church, was the Librarian of the United States Senate, and his great-grandfather, also named Alonzo Church, was a professor of mathematics and astronomy who became the sixth president of the University of Georgia. As a child, Church lost partial vision in an accident with an air gun. After his father lost his university position due to failing eyesight, the family moved to Virginia. With help from an uncle (also named Alonzo Church), he attended the private Ridgefield School for Boys in Connecticut. Graduating in 1920, he entered Princeton University, where he excelled. He published his first paper, on Lorentz transformations, in 1924 and earned a bachelor’s degree in mathematics that same year. He remained at Princeton for graduate studies, completing a Ph.D. in mathematics under Oswald Veblen in just three years.

In 1925, he married Mary Julia Kuczinski. They had three children: Alonzo Jr. (1929), Mary Ann (1933), and Mildred (1938). After his doctorate, Church briefly taught as an instructor at the University of Chicago. A two-year National Research Fellowship allowed him to study at Harvard University (1927–1928), then at the University of Göttingen and the University of Amsterdam the following year. He spent nearly four decades at Princeton, teaching philosophy and mathematics from 1929 to 1967. He then held the Flint Professorship of Philosophy and Mathematics at the University of California, Los Angeles, from 1967 to 1990. He was a plenary speaker at the 1962 International Congress of Mathematicians in Stockholm.

Church received honorary Doctor of Science degrees from Case Western Reserve University (1969), Princeton University (1985), and the University at Buffalo (1990), the last in connection with a symposium organized in his honor by John Corcoran. He was elected a Corresponding Fellow of the British Academy in 1966, a member of the American Academy of Arts and Sciences in 1967, and a member of the National Academy of Sciences in 1978. A lifelong Presbyterian, Church died on August 11, 1995, at age 92, and is buried in Princeton Cemetery.

Church’s mathematical contributions include proving that the Entscheidungsproblem—the question of whether a decision procedure can determine the truth of any proposition in a first-order mathematical theory—is undecidable, a result now called Church’s theorem. He invented the lambda calculus and used it to show that Peano arithmetic is undecidable. He articulated what became known as the Church–Turing thesis. He was a founding editor of the *Journal of Symbolic Logic*, overseeing its reviews section for 43 years (1936–1979). He wrote the influential textbook *Introduction to Mathematical Logic*. The Church–Rosser theorem is another key result. The lambda calculus first appeared in his 1936 paper on the unsolvability of the Entscheidungsproblem, which preceded Alan Turing’s work on the halting problem. After learning of Church’s results, Turing came to Princeton later that year to study under Church for a Ph.D. Together, they showed that the lambda calculus and the Turing machine were equivalent in power, and they demonstrated various alternative mechanical computation processes, leading to the Church–Turing thesis. Church’s ideas also underpin efforts to automatically generate controller implementations from specifications. The lambda calculus influenced the design of Lisp and functional programming languages generally; the Church encoding is named for him. In 2015, the Alonzo Church Award for Outstanding Contributions to Logic and Computation was established by ACM SIGLOG, EATCS, EACSL, and the Kurt Gödel Society, recognizing a major contribution published within the previous 25 years that has not already won a Turing Award, Paris Kanellakis Award, or Gödel Prize. Church also worked on the theory of random sequences.

Philosophically, Church developed a methodology based on the logistic method, criticized nominalism, defended realism, and argued for conclusions about the theory of meaning. He constructed detailed intensional logics based on the work of Gottlob Frege and Bertrand Russell. He created the Frege–Church ontology, drawing on Frege’s ideas, and formulated the Slingshot Argument, which contends that sentential references must be truth-values rather than propositions. Over his career, Church supervised 31 doctoral students.