Who discovered comets?

Comets have been seen by earth's people since the beginning of time so no known individual person is credited with their discovery.

There may be no record of the individual who first discovered comets. But there's a record as to where the word in English comes from. Its origins go back to the classical Latin word 'cometes', which is from the even earlier, ancient Greek. The original word 'kome' is classical Greek for 'hair of the head'. From that word, its pioneer use in the form 'kometes', as 'stars with hair', is credited to Aristotle [384 B.C.E. - 322 B.C.E.].