arithmetician vs mathematician

arithmetician and mathematician both are nouns.

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

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

arithmetician (noun)	mathematician (noun)
someone who specializes in arithmetic	a person skilled in mathematics