This is the 14044th most frequent German word.
gelehrt
Learned; scholarly.
Here, 'gelehrt' is the past participle form of the verb 'lehren' (to teach), used in the present perfect tense to indicate a completed action of him teaching philosophy.
Er hat Philosophie gelehrt.
He taught philosophy.
In this sentence, 'gelehrte' is an adjective form meaning 'learned' or 'erudite', describing the woman as knowledgeable.
Die gelehrte Frau erklärte die Theorie verständlich.
The learned woman explained the theory clearly.
Here, 'Gelehrtheit' (derived from 'gelehrt') is a noun form referring to the intellectual qualities or erudition of an individual.