The term black box theory is used in philosophy in mathematics (to mean what???)

The term is important in philosophical contexts, because various philosophers have proposed black box theories for various fields. Probably the most prominent such theory is the so called black box theory of consciousness, which states that the mind is fully understood once the inputs and outputs are well defined, and generally couples this with a radical skepticism about the possibility of ever describing what goes on inside the mind.

See also: Black box