Theory vs Theorem: Understand the Difference

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The discussion clarifies the distinction between "theory" and "theorem," noting that theories pertain to the physical world while theorems are mathematically provable statements. A mathematical theory comprises a collection of related theorems and definitions, such as calculus or group theory. The conversation also addresses the terminology used in physics, where some theorems are referred to as laws, while similar concepts in mathematics are often called laws or principles, like the law of excluded middle or the law of large numbers. The naming conventions in mathematics are not fixed, leading to varying classifications of results, such as the difference between a lemma and a theorem. Ultimately, the discussion highlights the fluidity of terminology in both mathematics and physics.
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What's the difference?
 
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"Theory" usually refers to the physical world and "theorem" refers to the mathematical world.
 
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.
 
this is sort of related, but why are some theorems in physics called laws? why arent there "laws" in math too?
 
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).
 

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