Mathematical statements that have been proven to be true based on previously established statements such as axioms, definitions, and other theorems. They represent fundamental truths or relationships in mathematical systems.
From Greek 'theorema' meaning 'spectacle, contemplation, speculation,' derived from 'theorein' (to look at, observe). The term evolved from general philosophical observation to specifically denote proven mathematical propositions in ancient Greek mathematics.
Famous theorems like the Pythagorean theorem have shaped human understanding for millennia, yet new theorems are still being discovered today. What's fascinating is that a theorem, once proven, becomes an eternal truth - the Pythagorean theorem will be just as valid a million years from now as it was 2,500 years ago.
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