Brainfuck is to Turing machines what Lisp is to Lambda calculus or Prolog is to predicate logic. There's enough syntactic sugar to make it a practical programming language that is based on a mathematical theory. Learning it will, arguably, make you a better programmer.
This seems to be like a conveniently sized practice project, a little I/O with the real world with a simple computational task that's fun to write.
It would be really cool to make some slightly more usable programming language that compiles to Brainfuck so that mortals could write non-trivial programs in it and impress their friends.
It's not impressive, though. It's not surprising that someone is able to create a program using a Turing-complete language. It's just surprising that they decided to waste their time with an unreadable one. It's far more impressive to do basically anything else related to programming.
I had an idea once to make a brainfuck web framework as an April fool's day joke along the lines of Cobol on Cogs.
The trick, I figured, would be to make a simple basic-like language, and actually write the framework in that, and then make a compiler that translated it to brainfuck.
This `netfuck' code is well documented, though. I'm not even sure which questions I'd want to ask first about the author's relationship with programming.
Jesus christ. O.o;; This is the first I've seen the language... I think if I wrote stuff at work in brainfuck they would think I was just wasting time. XD