Theorem

: The "given" or foundational statements that are accepted as true without proof. All proofs eventually trace back to these.

Proves that in any consistent mathematical system, there are statements that are true but cannot be proven. Theorems vs. Conjectures theorem

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 : The "given" or foundational statements that are