Speaking of mathematics in the context of “general intellectual activity” brings to mind Raymond Wilder’s take on “mathematics as a cultural system”.
I would like to keep that in mind, if on a back burner, and focus on a more directed species of intellectual activity that goes under the name of inquiry, the flower of which species we know as scientific method, however much method or madcap various lights may see in it. Whatever the case, that brings us to the task of placing mathematical inquiry within the sphere of inquiry in general.
Here I can do no better than recommend C.S. Peirce’s theory of inquiry as one of the best tacks we can take for approaching this task.