Haskell Curry

The focus of Curry's work were attempts to show that combinatory logic could provide a foundation for mathematics. Towards the end of 1933, he learned of the Kleene–Rosser paradox from correspondence with John Rosser. The paradox, developed by Rosser and Stephen Kleene, had proved the inconsistency of a number of related formal systems, including one proposed by Alonzo Church (a system that had the lambda calculus as a consistent subsystem) and Curry's own system. However, unlike Church, Kleene, and Rosser, Curry did not give up on the foundational approach, saying that he did not want to "run away from paradoxes."

By working in the area of combinatory logic for his entire career, Curry essentially became the founder and biggest name in the field. Combinatory logic is the foundation for one style of functional programming language. The power and scope of combinatory logic are quite similar to that of the lambda calculus of Church, and the latter formalism has tended to predominate in recent decades.

During World War II, Curry worked at the Frankford Arsenal,

where he developed a steepest descent algorithm, based on work by Cauchy.

This became a foundational example of modern gradient descent methods.

In 1947 Curry also described one of the first high-level programming languages and provided the first description of a procedure to convert a general arithmetic expression into a code for one-address computers.

He taught at Harvard, Princeton, and from 1929 to 1966, at the Pennsylvania State University. In 1942, he published Curry's paradox. In 1966 he became professor of logic and its history and philosophy of exact sciences at the University of Amsterdam, the successor of Evert Willem Beth.

Curry also wrote and taught mathematical logic more generally; his teaching in this area culminated in his 1963 Foundations of Mathematical Logic. His preferred philosophy of mathematics was formalism (cf. his 1951 book), following his mentor Hilbert, but his writings betray substantial philosophical curiosity and a very open mind about intuitionistic logic.