What is the difference between...?

Question

theory and theorem

Ichigo - what about in mathematics? I'm pretty sure the Pythagorean theorem is not an idea.

Answer 1

In mathematics, a theorem is a statement, often stated in natural language, that can be proved on the basis of explicitly stated or previously agreed assumptions. In logic, a theorem is a statement in a formal language that can be derived by applying rules and axioms from a deductive system.

http://en.wikipedia.org/wiki/Theorem

In common usage, people often use the word theory to signify a conjecture, an opinion, or a speculation. In this usage, a theory is not necessarily based on facts; in other words, it is not required to be consistent with true descriptions of reality. True descriptions of reality are more reflectively understood as statements which would be true independently of what people think about them. In this usage, the word is synonymous with hypothesis. This common usage of theory leads to the common but misguided statement "It's not a fact, it's only a theory."

In science, a theory is a mathematical or logical explanation, or a testable model of the manner of interaction of a set of natural phenomena, capable of predicting future occurrences or observations of the same kind, and capable of being tested through experiment or otherwise falsified through empirical observation.

http://en.wikipedia.org/wiki/Theory

Answer 2

theory is a particular conception or view of something to be done or of the method of doing it; a system of rules or principles.

theorem is an idea, belief, method, or statement generally accepted as true or worthwhile without proof.

in short, a theory is an idea that has been proven by many people and a theorem is an idea without proof.

Answer 3

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Answer 4

Theory:

contemplation or speculation.
guess or conjecture.

Theorem:

an idea, belief, method, or statement generally accepted as true or worthwhile without proof.

Answer 5

a theory is something that's been proven.

a theorem is something that somebody believes to be true