mathematics vs science

mathematics and science both are nouns.

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

As nouns, science is a hypernym of mathematics; that is, science is a word with a broader meaning than mathematics:

mathematics: a science (or group of related sciences) dealing with the logic of quantity and shape and arrangement
science: a particular branch of scientific knowledge

Other hypernyms of mathematics include scientific discipline.

mathematics (noun)	science (noun)
a science (or group of related sciences) dealing with the logic of quantity and shape and arrangement	a particular branch of scientific knowledge
	ability to produce solutions in some problem domain