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I want to know whether or not a journal that published a proof $P$ of an important theorem $T$ is still open to accept another proof $P'$ of $T$ such that $P'$ is greatly simpler than $P$, assuming, of course, that $P'$ is correct.

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    $\begingroup$ Sure, why not? It would depend on how important $T$ was and how much better or how illuminating the new proof was. I don't see why it would matter whether the old proof was published in the same journal or some other journal. $\endgroup$ – bof Aug 21 '14 at 8:11
  • $\begingroup$ Do you have a simple proof of Fermat's Last Theorem? $\endgroup$ – bof Aug 21 '14 at 8:13
  • $\begingroup$ @bof: Thanks for your attention. I am just being wary and discreet about choosing a journal. I have a simple proof of another of Fermat's theorem. We will see! $\endgroup$ – Megadeth Aug 21 '14 at 8:13
  • $\begingroup$ It's less about $T$ than about $P'$, you might say: A substantially new proof may use different (new?) methods, from which we can possibly learn more than from $T$ itself. Also, $P'$ may be so differnt that it may suggest different generalizations of $T$. You might even publish a new(!) proof of Pythagoras, adding to an already long collection. $\endgroup$ – Hagen von Eitzen Aug 21 '14 at 8:20
  • $\begingroup$ @bof: So did you imply that if $T$ is a conjecture then situation is different? $\endgroup$ – Megadeth Aug 21 '14 at 8:21
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I guess it depends on many things. First of all, what is the relevance of $T$ in its field? And secondly: what is the relevance of the new proof of $T$?

In my field of research, nonlinear PDEs, it frequently happens that a researcher can solve a PDE by a "new" approach. However, this approach might be confined to that particular equation, and a referee may decide that the publication of a paper with a new proof that applies to a single problem is not worth.

But it also happens that a researcher introduces a new method that can be used to prove (hopefully in an easier way) some known result. If this method is fairly general and can be applied to other problems, then a referee will probably accept the manuscript for publication.

Finally, more and more journals recommend to their referees that manuscripts should be original. A different proof of theorem $T$ will then be rejected almost immediately is the manuscript is written only to show that you found another proof.

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