theorem vs idea

theorem and idea both are nouns.

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

As nouns, idea is a hypernym of theorem; that is, idea is a word with a broader meaning than theorem:

Other hypernyms of theorem include thought.

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