Theorem
Part of speech: noun
Definition: A mathematical statement of some importance that has been proven to be true. Minor theorems are often called propositions. Theorems which are not very interesting in themselves but are an essential part of a bigger theorem's proof are called lemmas A mathematical statement that is expected to be true; as, Fermat's Last Theorem (as which it was known long before it was proved in the 1990s.)
Example sentence: I realized that anything to do with Fermat's Last Theorem generates too much interest.
Theory
Part of speech: noun
Definition: An unproven conjecture.An expectation of what should happen, barring unforeseen circumstances.A coherent statement or set of statements that attempts to explain observed phenomena.A logical structure that enables one to deduce the possible results of every experiment that falls within its purview.A field of study attempting to exhaustively describe a particular class of constructs.A set of axioms together with all statements derivable from them.