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.
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Kurt Godel, Scientists Godel's incompleteness theorems (1931) are the discipline's landmark example of a theorem with proof, showing formal systems powerful enough for arithmetic contain true statements they cannot prove.
Proof, Concepts A theorem is a statement established as true by a mathematical proof
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Source Theorem (Wikipedia)
Source Theorem (Wikipedia)
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Source Euclid (MacTutor)
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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.
Theorem (Wikipedia)
Belongs To: Mathematics, Lead sentence
In mathematics and formal logic, a theorem is a statement that has been proven, or can be proven.
Belongs To: Logic, Lead sentence
In mathematics and formal logic, a theorem is a statement that has been proven, or can be proven.
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