Concepts
Theorem
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A theorem is a statement that has been proven true within a mathematical system: a well formed statement of the theory shown, by a logical argument using the system's inference rules, to follow necessarily from its axioms and from theorems already established. A theorem is distinct from a conjecture, an unproved statement believed to be true but not yet demonstrated; a conjecture becomes a theorem only once it receives a genuine proof, which is why a long unproved claim such as Fermat's Last Theorem could carry the name theorem for centuries while still awaiting the proof that finally justified it.
Cross-Tradition Connections
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Euclid (MacTutor)
MacTutor History of Mathematics, University of St AndrewsBiography sectionQuote, Biography section
The Elements begins with definitions and five postulates; ... these postulates also implicitly assume the existence of points, lines and circles, and that there is a unique line joining any two points.
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