mathematical vs mathematics

mathematical is not a noun while mathematics is a noun.

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

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

mathematical (adjective)	mathematics (adjective)
relating to or having ability to think in or work with numbers
of or pertaining to or of the nature of mathematics
characterized by the exactness or precision of mathematics
statistically possible though highly improbable
beyond question