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For me, intuitively, a mathematical principle is simply an influential theorem.

Still, I am not clear on how and who decides (or decided) if a theorem/statement is a mathematical principle.

Can you clarify this to me?

NOTE: Wikipedia lists around 40 mathematical principles, in various fields, and of various significance. For example:

VividD
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    Zorn's lemma, the well-ordering principle, the axiom of choice. Naming of things is historically contingent, there's no logic to it. – user4894 Dec 31 '14 at 20:26
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    I recommend reading http://en.wikipedia.org/wiki/Theorem#Terminology It mentions common uses of the terms lemma, axiom, principle, theorem, corollary, etc and as user4894 mentioned above me the differences between the terms is largely arbitrary with little to no difference between the uses. – JMoravitz Dec 31 '14 at 21:48

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