# Lambda Calculus as a branch of set theory

This answer to a question about whether C is the mother of all languages contained an interesting tidbit that I am curious about:

The functional paradigm, for example, was developed mathematically (by Alonzo Church) as a branch of set theory long before any programming language ever existed.

Is this true? What is the link between these topics that is so fundamental as to make lambda Calculus an outgrowth of set theory? The best I can come up with is that standard mathematical functions possess domains and codomains.

It's false. The $$\lambda$$-calculus arose through efforts to understand foundations of mathematics. Nowadays some people mistakenly equate foundations with set theory. The Stanford Encyclopaedia of Philosophy has a very good writeup on the $$\lambda$$-calculus, as well as its history, I recommend it.