Theorem
THEER-um
/ˈθɪərəm/
A proposition, especially in mathematics, that can be proven from accepted premises or axioms.
A theorem is a statement that has been rigorously proven true within a specific mathematical system. It's not just a guess or an observation, but a logical consequence of other established truths.
The story behind the word. The word 'theorem' comes from the Greek 'theorema,' meaning 'a sight,' 'a spectacle,' or 'a principle.' It's related to 'theorein,' meaning 'to look at,' 'to contemplate,' or 'to speculate.' In ancient Greek mathematics, a 'theorema' was something observed or contemplated that could then be demonstrated or proven. It wasn't just a random thought, but an insight that could be rigorously established.
Word relationships
- proposition: A proposition is a statement that can be true or false; a theorem is a proposition that has been proven true.
- postulate: A postulate (or axiom) is a statement assumed to be true without proof, serving as a basis for theorems.
Commonly confused with
- Hypothesis: A theorem is a proven statement in mathematics, while a hypothesis is a proposed explanation or idea that needs to be tested through observation or experimentation.
Word family
- theoretic (adjective): Relating to theory rather than practice.
- theoretical (adjective): Concerned with theory; hypothetical.
Collocations
- mathematical theorem
- prove a theorem
- fundamental theorem
- central limit theorem
Example sentences
- "The Pythagorean theorem states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides." Referring to a famous mathematical truth.
- "To prove the theorem, the mathematician had to construct a series of logical steps from known axioms." Discussing its role in proofs.
- "Fermat's Last Theorem remained unproven for over 350 years, captivating generations of mathematicians." Highlighting its importance.
Memory hook
A 'THEOR-em' is a 'THEORY' that has been 'PROVEN' true. Proven-theory
When not to use
Do not use 'theorem' interchangeably with 'hypothesis' or 'theory.' A theorem is proven; a hypothesis is proposed for testing; a theory is a well-substantiated explanation.
Fun facts
- Many theorems are named after the mathematicians who first proved them, like 'Euclid's Theorem' or 'Gödel's Incompleteness Theorems.'
- The concept of a 'proof' in mathematics, which leads to a theorem, is one of the most rigorous forms of logical reasoning.
Related words
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