mathematics vs work out

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

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

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

mathematics (verb)	work out (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