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I remember reading once that it was found that two math theorems were essentially equivalent to each other, how often does this occur? ex. In two dimensions the divergence theorem is said to be equivalent to Green's theorem.

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    It might be of interest if some example(s) were mentioned where this has happened. I guess what you might mean is two theorems already known were later shown to imply each other... – coffeemath Jun 03 '16 at 04:18
  • All theorems (i.e statements provable in a given formal system) are logically equivalent to each other, in the sense that if $A$ is provable then so is $B \implies A$, and if $B$ is provable then so is $A \implies B$. I know this is not what you mean, but it's not clear how to precisely define what you do mean. – Robert Israel Jun 03 '16 at 04:49
  • I cannot seem to find any exact examples at the moment, but the one I listed in the OP as well as what @coffeemath stated is exactly what I mean. –  Jun 03 '16 at 05:00

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