Theorem

The concept of a theorem was first used by the ancient Greeks. To derive new theorems, Greek mathematicians used logical deduction from premises they believed to be self-evident truths. Since theorems were a direct result of deductive reasoning, which yields unquestionably true conclusions, they believed their theorems were undoubtedly true. The early mathematician and philosopher Thales (640-546 B.C.) suggested many early theorems, and is typically credited with beginning the tradition of a rigorous, logical proof before the general acceptance of a theorem. The first major collection of mathematical theorems was developed by Euclid around 300 B.C. in a book called The Elements.

The absolute truth of theorems was readily accepted up until the eighteenth century. At this time mathematicians, such as Karl Friedrich Gauss (1777-1855), began to realize that all of the theorems suggested by Euclid could be derived by using a set of different premises, and that a consistent non-Euclidean structure of theorems could be derived from Euclidean premises. It then became obvious that the starting premises used to develop theorems were not self-evident truths. They were in fact, conclusions based on experience and observation, and not necessarily true. In light of this evidence, theorems are no longer thought of as absolutely true. They are only described as correct or incorrect based on the initial assumptions.