This talk will be about the early days of lambda-calculus. But the rival
system of function-abstraction, combinatory logic, was invented some years
before lambda-calculus. In fact December 7 is the 80th anniversary of Moses
Schoenfinkel's first talk on combinators at Goettingen. This talk will
therefore deal with combinators as well as lambda. Both techniques achieved
very satisfying successes in their early years before 1940, which were not
surpassed until their application to computer science in the 1970's. (This
talk will be based on an article being written with Felice Cardone for a
forthcoming history of mathematical logic edited by D. van Dalen and J.
Dawson.)