Erudite could be used to describe this woman.
An example of erudite is a professor of literature.
Origin of eruditeMiddle English erudit ; from Classical Latin eruditus, past participle of erudire, to instruct, literally , free from roughness ; from e-, out + rudis, rude
Origin of eruditeMiddle English erudit, from Latin &emacron;rud&imacron;tus, past participle of &emacron;rud&imacron;re, to instruct : &emacron;-, ex-, ex- + rudis, rough, untaught; see rude.
(comparative more erudite, superlative most erudite)
From Latin ērudītus, participle of ērudiō (“educate, train”), from e- (“out of”) + rudis (“rude, unskilled”).