A theorem (the term is derived from the Greek theoreo, which means I look at) denotes either a proposition yet to be proven, or a proposition proven correct on the basis of accepted results from some area of mathematics. Since the time of the ancient Greeks, proven theorems have represented the foundation of mathematics. Perhaps the most famous of all theorems is the Pythagorean theorem.

Mathematicians develop new theorems by suggesting a proposition based on experience and observation which seems to be true. These original statements are only given the status of a theorem when they are proven correct by logical deduction. Consequently, many propositions exist which are believed to be correct, but are not theorems because they can not be proven using deductive reasoning alone.

Historical background

The concept of a theorem was first used by the ancient Greeks. To derive new theorems, Greek mathematicians used logical...