I'm not sure what to think about this answer. The first paragraph doesn't seem to address anything i said. The linked article seems to agree with my understanding, from the preamble, but contains too much Haskell syntax for me to ne able to understand what he's explaining, so i can't say for sure. And i know even less about the mathematical aspect.
However, still, thanks for letting me know that i might be moving in the right direction.
"It it seems like monads get created when a pain point of a language is so often, and so consistently worked around in the same fashion"
Well, pretty much. Here is a post about that: http://blog.sigfpe.com/2006/08/you-could-have-invented-monad...
Then there is the mathematical aspect to them, that can point to unexpected connections and new possibilities for abstraction.