# Theorem - Historical Background, Characteristics Of A Theorem

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proven theorems proposition correct

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.

## Additional Topics

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 initial premises on which all theorems are based are called axioms. An axiom, or postulate, is a basic fact which is not subject to formal proof. For example, the statement that there is an infinite number of even integers is a simple axiom. Another is that two points can be joined to form a line. When developing a theorem, mathematicians choose axioms, which seem most reliable based on their …

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