Lambda calculus is a model of computation. A pretty lightweight model that can still do everything that other programming languages can. Combinators are an even simpler model of computation that is still equally powerful. That simplicity / power ratio is what makes them cool.

A while back I built all the way up to FizzBuzz from just S and K combinators. Took days of doing all the math by hand, lol.

Here's my write up of doing that. I did it in JavaScript because most combinator articles online were prohibitively academic for my layman mind. https://joshmoody.org/blog/programming-with-less-than-nothin...