Functional Programming – Is It Strongly Related to Mathematics?

Functional programming languages do much more compile time optimization. One of the reasons is purity - concurrency is trivial because there is no state. So the compiler can take two branches and concurrencize them easily without changing the behavior of the program.

At the same time, anything that can be calculated without state (ie anything non-monadic in haskell) can be calculated ahead-of-time by the compiler, but such calculations could be expensive and thus are probably only done partially.

Additionally, anything that isn't needed computationally can be completely optimzied out of the program.

They use math because Functional Programming is very good at modelling mathematical constructs and is very tied into mathematical concepts, particularly Lambda Calculus. Also since I/O is typically a fairly thorny and advanced subject in a lot of languages of the functional paradigm mathematics via the REPLs of the various languages becomes a good way of teaching the language at first.

Because Functional Programming treats Functions as first class constructs within the programming language, function generation becomes very important. Therefore higher math becomes fairly important particularly graph theory.

Imperative Languages are just as mathy but it's all arithmetical at base since they are closer to the machine which can only add anyway. Functional languages with their higher abstraction tend more toward mathematics. The general use in academia doesn't help either as they get used and thus taught by people who know a lot of math and are teaching people who are expect to learn a lot of math. So it's possible to "dumb it down" so to speak but it is unlikely given these factors.

http://learnyouahaskell.com/ - Is probably one of the gentlest introductions to Functional Programming, I double checked and there's nothing beyond basic algebra and graph theory in there.