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Me and my coauthors have recently submitted a paper to conference X. By talking to colleagues I discovered that another set of authors have had a very similar result, and submitted their paper to conference X.

Basically, the result is a theorem that solves an open problem stated in a paper which appeared at conference X in the previous year. The new theorem is essentially the same in both papers, but the proofs are very different.

What happens in this case?

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    I am not clear what you want to ask. Anything could happen. Yours could be wrong. Theirs could be wrong. Both could be wrong. Of course, it's very likely both are right. As long as the two teams did not copy each other, both of the teams would be fine. What are you really asking? – scaaahu Sep 15 '16 at 12:56
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    I'd be happy to see that "the proofs are very different" yet give the same result. Much less chance for mistake. And both at one conference seems like a great opportunity to compare notes, methods etc. Do you have a specific concerns? – Mołot Sep 15 '16 at 13:11
  • I assume by 'submitted' you also mean 'neither has yet been accepted'? If so, then it's possible the conference organizers will only select one of these papers based on whatever criteria they use - they could select both (or a unknown third one). I'm not sure how it works in mathematics, but could you contact the other academics and propose a panel if there's room for discussion? – Deleuze Sep 15 '16 at 14:14
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This sounds like a straight-forward case of multiple discovery.

In the case that both papers are well-written and have correct proofs, the typical and appropriate thing would be for both of them to be accepted. If one or both are not sufficient for the standards of the conference in their presentation or technical approach, however, then it would be reasonable for one or both to be rejected, however, even if they have identical results.

Given that there is often a great degree of variability in reviewing, however, it would likely be a good thing to get in contact with the conference organizers and let them know about the situation, so that they can ensure fair treatment of the two papers (e.g., via meta-review or by assigning the same reviewers to both).

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There have been instances where in such a case the authors of both papers have been asked by the program committee to merge their papers into one.

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