closed vs mathematics

closed is not a noun while mathematics is a noun.

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

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

closed (adjective)	mathematics (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