Theory vs Theorem: Understand the Difference

[Physics is Phun]

What's the difference?

 

[Tide]

"Theory" usually refers to the physical world and "theorem" refers to the mathematical world.

 

[CrankFan]

A theorem is a mathematically provable statement.

A theory in mathematics is usually thought to be a non-trivial collection of related theorems and definitions like, the theory of calculus, theory of groups, etc.

 

[T@P]

this is sort of related, but why are some theorems in physics called laws? why arent there "laws" in math too?

 

[matt grime]

There are. Law of excluded middle, for instance. Law of large numbers. They are also called principles. There is no immutable naming law, or principle or theorem. One man's lemma is another mans theorem. For instance's Schur's Lemma is a vital theorem, but Mackey's Theorem is just a lemma... (though things starting if...then... ought to be called propositions).