mathematics vs differentiate

mathematics is a noun but differentiate is not a noun.

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

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

mathematics (verb)	differentiate (verb)
	become distinct and acquire a different character
	become different during development
	evolve so as to lead to a new species or develop in a way most suited to the environment
	calculate a derivative; take the derivative
	mark as different
	be a distinctive feature, attribute, or trait; sometimes in a very positive sense