a proposition deducible from basic postulates
"The Pythagorean theorem is a classic example of a mathematical proposition that can be strictly deduced from basic geometric postulates."
an idea accepted as a demonstrable truth
"The ancient Greeks developed many mathematical theorems that are still used today."
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.
"The Pythagorean theorem is a famous mathematical statement asserting that the square of the hypotenuse equals the sum of the squares of the other two sides, and it has been rigorously proven to be true."
In plain English: A theorem is a mathematical statement that has been proven to be true based on other known facts and rules.
"The teacher explained that every theorem must be proven before it can be used to solve other problems."
Usage: Use this word for any significant, proven mathematical statement rather than an unproven guess or observation. Remember that minor results within a proof are typically labeled as propositions instead of theorems.
To formulate into a theorem.
"The mathematician worked hard to prove and formulate his conjecture into a rigorous theorem."
In plain English: There is no verb form of theorem because it is only used as a noun to describe an important mathematical statement that has been proven true.
"The mathematician proved that no finite group satisfies all three conditions in his new theorem."
The word theorem comes from Ancient Greek, where it originally meant a "speculation" or "proposition to be proved." It entered English via Middle French and Late Latin, carrying the sense of a mathematical statement that requires demonstration.