mathematics vs irrational

mathematics and irrational both are nouns.

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

mathematics (noun)	irrational (noun)
a science (or group of related sciences) dealing with the logic of quantity and shape and arrangement	a real number that cannot be expressed as a rational number

mathematics (adjective)	irrational (adjective)
	not consistent with or using reason
	real but not expressible as the quotient of two integers