A theorem is a mathematical statement that has been proved — shown, step by careful step, to follow from things already accepted as true. The proof is what makes it a theorem. Before the proof, the same statement is only a 'conjecture' (a good guess); after the proof, it is settled forever, and no later discovery can undo it. That is very different from a scientific theory, which fits the evidence we have so far and can be overturned. Famous ones carry their prover's name: Pythagoras' theorem, Fermat's Last Theorem. The word lives in mathematics, logic, physics and computer science, and it is quite formal. Outside those subjects people sometimes reach for it playfully to mean 'a rule I am confident about' ('my theorem is that the shortest queue always slows down') — that is a joke borrowing the authority of mathematics, and it works because everyone knows a real theorem is airtight. Countable: a theorem, several theorems. English also has a rare verb 'theorem', meaning to state or treat something as a theorem, but you will almost never meet it, and using the noun is always the safer choice.