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I have a similar situation as in this question. I can prove a big conjecture by combining results from literature.

However, the difference is I want to maximize my credit. I tried to come up with a different proof. I have come up with a slightly different proof, but the proof is longer and it seems it has no new insight or new techniques. If I want to maximize my credit, should I just publish the easy proof, or the longer proof, or both on the same manuscript?

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    Could you clarify what precisely you mean by 'maximiz[ing] [your] credit'? Commented Mar 17, 2023 at 18:50
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    "I can prove a big conjecture by combining results from literature." Are you sure that both your overarching argument and all referenced results are correct and fit together? Often one finds such proofs only to figure out a day (or year) later that he missed some subtleties that ruin the argument completely. So I would start with checking everything. As to "maximizing credit", just "take it easy" and "memento mori". People are quite often not idiots and can see what exactly has been done no matter in what form you choose to present it. So maximize the clarity instead. :-)
    – fedja
    Commented Mar 17, 2023 at 19:17
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    This is not the first time you have made claims to have solved open problems, and I would advise you to follow @fedja's advice about being your own sceptic. Correctness is more important than fame, if you are trying to get started as a researcher.
    – Yemon Choi
    Commented Mar 17, 2023 at 21:58
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    "I want to maximize my credit." Or equivalently, you want to minimize the credit of the other researchers whose work you are relying on. If you put it that way, it doesn't sound so great, does it? And if people get wise to this, it won't exactly leave a good impression. Commented Mar 17, 2023 at 23:29

2 Answers 2

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If your "longer" proof has value for application to other problems then it may have value in itself, never mind maximizing credit. In math it is fairly frequently the case that a proof is more valuable than the theorem it proves if it gives wider insight.

There is also value in short proofs for important conjectures, especially if they have been around for a while. I'd love to see a short proof of the Four Color Theorem that doesn't rely on computers.

If reviewers would consider both proofs, then that might be best. If you can stay within page limits then a first submission might include both and then look at what the reviewers say, but be sure to explain why you have both proofs.

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This is not an answer to the post itself, but a commentary on the title of the question, "Maximize the credit vs. easy proof for big conjecture":

There are no "easy proofs for big conjectures". If there were such an easy proof, someone would have written it a long time ago. "Big conjectures" are, by definition, the ones a lot of people care about and many good people will have considered the question. They will have thought deeply about coming up with proofs, and will have brought their decades of experience to the task. Experience in the mathematical community shows that, typically, when someone claims that they have a "simple proof", they are usually wrong about their claim. As a consequence, I would suggest that before wondering how you can maximize your credit, you spend a good amount of time convincing yourself that you are the exception to the "usually wrong" rule.

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