Theorem May 2026

The distinction between a conjecture and a theorem is the existence of a proof. For example, the —which states that every even integer greater than 2 is the sum of two primes—has been tested for trillions of numbers and appears true, but because it lacks a formal proof, it remains a conjecture rather than a theorem. The Evolution of Proof

: A statement that follows almost immediately from a proven theorem with little or no additional proof required. Famous Examples of Theorems theorem

: A "helper" result. Lemmas are smaller theorems used as stepping stones to prove a larger, more significant result. The distinction between a conjecture and a theorem

: The logical argument that demonstrates why a theorem must be true. Modern proofs must follow strict rules of inference to be accepted by the mathematical community. Famous Examples of Theorems : A "helper" result