mathematician vs scientist

mathematician and scientist both are nouns.

Word	Noun	Adjective	Verb	Adverb
mathematician	Yes	No	No	No
scientist	Yes	No	No	No

As nouns, scientist is a hypernym of mathematician; that is, scientist is a word with a broader meaning than mathematician:

mathematician (noun)	scientist (noun)
a person skilled in mathematics	a person with advanced knowledge of one or more sciences