theorem n.

1590s, "conception, mental scheme," from Late Latin theoria (Jerome), from Greek theōria "contemplation, speculation; a looking at, viewing; a sight, show, spectacle, things looked at," from theōrein "to consider, speculate, look at," from theōros "spectator," from thea "a view" (see theater) + horan "to see," which is possibly from PIE root *wer- (3) "to perceive." Philosophy credits sense evolution in the Greek word to Pythagoras.

Earlier in this sense was theorical (n.), late 15c. Sense of "principles or methods of a science or art" (rather than its practice) is first recorded 1610s (as in music theory, which is the science of musical composition, apart from practice or performance). Sense of "an intelligible explanation based on observation and reasoning" is from 1630s.