Why is math so adept at describing the world?

Except for some mathematical concepts which were developed explicitly for the purpose of describing the physical world, many mathematical concepts were developed without any forethought to their application.

Can you be more explicit. A blanket statement saying that "many" were developed without any forethought is really wrong sounding. As "many" were developed for real-world application. Having relationships to more advanced formulas is no coincidence. You should go read up on the history of math.

Why should the universe speak a language invented by us?

It speaks a language that any intelligent race could conceive. I would not consider math to be invented by humans. It was more like discovery through our interpretation using symbols and signs.