Does learning about the Lambda calculus have any take-aways for programming in modern languages, or is it more of a cool toy/mostly of interest for language designers and academics?
For example, C++ templates were not meant to be Turing-complete, but they work by rewriting terms [1], so you can encode lambda calculus in it, and run arbitrary programs at compile time.
Philip Wadler does a better job than me at getting excited by lambda calculus. He calls it "the omniversal programming language", and claims that aliens will probably have discovered it [2].
[1]: http://matt.might.net/articles/c++-template-meta-programming... [2]: https://www.youtube.com/watch?v=IOiZatlZtGU
It's also a great way to get a deeper understanding of computation and how it relates to logic. The lambda calculus is special for being an incredibly minimal model of computation that's still expressive enough to write programs (albeit a little awkwardly). Expressing something you care about in lambda calculus is way easier than using a Turing machine directly or even programming in assembly!
You only the ability to define and call functions. Functions can only recombine their input. And somehow it is still as powerful as, say, python!
Don't need some built in math , invent numbers using function definitions. Don't need built in recursion, just implement it using functions as the y-combinator!
There are also some practical usages of the whole implement-data-as-functions idea. There are some libraries in haskell that do this, for instance, which means that the compiler can optimize dsl's.