idea vs theorem

idea and theorem both are nouns.

Word	Noun	Adjective	Verb	Adverb
idea	Yes	No	No	No
theorem	Yes	No	No	No

As nouns, theorem is a hyponym of idea; that is, theorem is a word with a more specific, narrower meaning than idea:

idea (noun)	theorem (noun)
the content of cognition; the main thing you are thinking about	an idea accepted as a demonstrable truth
your intention; what you intend to do	a proposition deducible from basic postulates
an approximate calculation of quantity or degree or worth
a personal view
(music) melodic subject of a musical composition