21

Suppose a researcher comes up with a mathematical theorem, which can be obtained trivially from discovered theorems, but with an approach, that was never used before to describe or prove the theorem.

Then do the journals accept the paper because of the new approach or reject the paper because of no novelty?

  • See also the potential duplicate: academia.stackexchange.com/questions/111704/… – zibadawa timmy Aug 27 '18 at 10:33
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    What if Alan Turing didn't publish his paper because of the (previously published) Church's Lambda calculus paper for the Entscheidungsproblem? :) – Evariste Aug 27 '18 at 13:00
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    @Evariste Utopia! Everybody would be using functional languages instead of imperative ones. ... ...maybe. – leftaroundabout Aug 27 '18 at 13:18
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There is more to mathematics than theorems. Sometimes the best part is the methodology of the proof, especially if it can be used to also solve important problems in the field. If everybody has been thinking in a certain way about a class of problems for a hundred years and you give them a new way to think about it, you have made an important contribution.

So yes, a journal would publish that. But your paper needs to be clear about the novelty and importance of your approach.

My own dissertation had interesting theorems, but was noted for the proof of one of them that was something entirely new and unexpected.

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    I largely agree, but, not every proof methodology is interesting. How can the OP determine whether their methodology is interesting? – user2768 Aug 27 '18 at 9:51
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    @user2768 Why isn't that for the journals rather than the OP to determine? – BCLC Aug 27 '18 at 10:46
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    @user2768 wait what? I'm not familiar with publishing actually. How will journals know if something is publishable or not if they don't decide if it's publishable or not? – BCLC Aug 27 '18 at 12:09
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    @BCLC Journals use reviewers to advise the editors on which papers are worth publishing. So it comes back to Buffy's "People with a lot of experience" - i.e. the reviewers. – alephzero Aug 27 '18 at 12:25
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    @user2768, wait what?? Pursuing knowledge without knowing whether someone else will agree it should be published is a waste of time?? And scientific love of inquiry and knowledge just goes out the window into the garbage dump, does it? What a sad commentary on the state of academia. – Wildcard Aug 27 '18 at 19:56
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Edward Witten not only published a paper of this kind (entitled 'A New Proof of the Positive Energy Theorem'), but the paper strongly contributed to getting him a Fields Medal, the highest award in mathematics. Both proofs in the paper had already been proved by Schoen and Yau using different methods: the key is that he was using new methods to carry out the proof.

2

In my area, proving Schur positivity is a big thing. One can do that using RSK, bijections, involutions, crystals, dual equivalence, or representation theory.

Some proofs give more insight than others, so there are several different proofs of the same statement, as the different techniques have different pros and cons.

  • This doesn't answer the question, which was about what journals will accept. – Max Barraclough Aug 28 '18 at 9:49
  • Journals accept this - today I saw 'prominent researcher' put a new preprint on arxiv, reproving a theorem related to positivity using crystals, rather than dual equivalence. I have a (published) conjecture on how to prove the same thing using RSK. – Per Alexandersson Aug 28 '18 at 11:17

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