algebraist vs mathematician

algebraist and mathematician both are nouns.

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

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

algebraist (noun)	mathematician (noun)
a mathematician whose specialty is algebra	a person skilled in mathematics