mathematics vs closed

mathematics is a noun but closed is not a noun.

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

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

mathematics (adjective)	closed (adjective)
	not open or affording passage or access
	(set theory) of an interval that contains both its endpoints
	used especially of mouth or eyes
	not open
	blocked against entry
	not open to the general public
	with shutters closed
	requiring union membership
	not having an open mind