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The focus of Curry's work were attempts to show that combinatory logic could provide a foundation for mathematics. (edit: accidentally stripped the part here mentioned that was in 1933 ie. very pre-computer) [...]. 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 which had the lambda calculus as a consistent subsystem) and Curry's own system. [...]
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.
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And I think there's more but it's hardly my field. Prolog is grown out of predicate calculus which has its roots in propositional calculus, which goes back to the ancient greeks.
The mathematical foundations of things can be surprisingly old. I saw a 3D wireframe of a goblet with perspective, and that was from the 1500's. It could have been done on a 1980's home computer by appearance.
