work out vs mathematics

work out is not a noun while mathematics is a noun.

Word	Noun	Adjective	Verb	Adverb
work out	No	No	Yes	No
mathematics	Yes	No	No	No

work out (noun)	mathematics (noun)
	a science (or group of related sciences) dealing with the logic of quantity and shape and arrangement

work out (verb)	mathematics (verb)
do physical exercise
give a workout to
come up with
work out in detail
find the solution to (a problem or question) or understand the meaning of
make a mathematical calculation or computation
be calculated
happen in a certain way, leading to, producing, or resulting in a certain outcome, often well