mathematics vs mathematical

mathematics is a noun but mathematical is not a noun.

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

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

mathematics (adjective)	mathematical (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