mathematics vs prove

mathematics is a noun but prove is not a noun.

Word	Noun	Adjective	Verb	Adverb
mathematics	Yes	No	No	No
prove	No	No	Yes	No

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

mathematics (verb)	prove (verb)
	establish the validity of something, as by an example, explanation or experiment
	obtain probate of
	prove formally; demonstrate by a mathematical, formal proof
	provide evidence for
	take a trial impression of
	cause to puff up with a leaven
	increase in volume
	put to the test, as for its quality, or give experimental use to
	be shown or be found to be