The adjective pedantic means someone is overly concerned with formal rules and unimportant details mostly related to academic subjects.
Synonyms are hairsplitting, particular, precise or stilted.
The words origin is not certain but some sources from Latin paedagogans meaning “to teach” or from Greek paedagogein meaning “to instruct children”.
I see him as very pedantic, always concerned with traditional rules.
She was pedantic in her duties and cruel with her employees by micromanaging them.
The students saw him as a pedantic professor who was not able to recognise the creativity of his class.