To be clear: the Y combinator is just one way to define a fixed-point combinator in the untyped lambda calculus. You can define fixed-point combinators differen

To be clear: the Y combinator is just one way to define a fixed-point combinator in the untyped lambda calculus. You can define fixed-point combinators differently and achieve the same effect. I do agree that the realization that it's possible to build recursive functions in the lambda calculus is mind-blowing (and far from obvious!)