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A few months ago I came up with a proof for an old theorem. After being excited for a moment, I then tried to find my proof in the literature. Since I did not find it, then I started to wonder if it was worth publishing it.

I asked a few people about journals that could publish something like this, and they gave me two recommendations:

(1) The Mathematical Gazette, http://www.m-a.org.uk/the-mathematical-gazette

(2)The Plus Magazine, https://plus.maths.org/content/about-plus

First I submitted to the Mathematical Gazette, and my article was rejected because according to the reviewer I was trying to prove something very simple using something much more complex (although I just used undergraduate level math).

Then I submitted to Plus, and it was also rejected by the editors (it probably doesn't fit well with their magazine).

Do you have any suggestions? Thanks.

Qfwfq
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M.Lopes
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    All else failing, you could always post it on arXiv (and indeed you might do this even if you do publish it somewhere else); obviously this isn't really a "publication," but it does make your work public. – Noah Schweber Feb 10 '17 at 16:35
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    One thing that is probably asking yourself: are there any advantages to the new proof over the previously existing proofs? (e.g. does it rely on basic complex analysis rather than the nuclear theory of Banach algebras). If the new proof is longer than the old one, then this is likely to be a problem. – Anthony Quas Feb 10 '17 at 16:37
  • "Where to publish a new demonstration of an old theorem?" -- in a scientific magazine which ceased to exist before WWI, preferably before the original first published proof was conceived. – Włodzimierz Holsztyński Feb 10 '17 at 20:34
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    It all depends on what your "old theorem" is, and how your new proof of it looks like -- for example, if you have a 5-pages proof that all finite simple groups are either cyclic or 2-generated which does not use CFSG, I'd suggest you to submit to the Annals ... . – Stefan Kohl Feb 10 '17 at 21:02
  • @NoahSchweber, thank you for your suggestion. I think I will consider that option after a few more attempts. – M.Lopes Feb 10 '17 at 22:19
  • @AnthonyQuas, no, no advantages whatsoever. It's just interesting because it is more simple and quick than the standard demonstration, although it relies on more advanced math. – M.Lopes Feb 10 '17 at 22:20
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    @WłodzimierzHolsztyński, unfortunately my time machine has not been working lately. – M.Lopes Feb 10 '17 at 22:20
  • @StefanKohl, I don't want to go into many details, otherwise you'd prove it yourself. :) – M.Lopes Feb 10 '17 at 22:20
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    If your proof is of pedagogical interest and/or can be integrated in a review of the subject, you could try L'Enseignement mathématique. – Gro-Tsen Feb 10 '17 at 23:25

4 Answers4

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This question, as stated cannot be answered. Everything depends on the theorem and on the proof, and this information you did not state.

For example, at least one Fields medal was awarded for a "new proof of an old theorem" (Selberg, 1950). A new proof can be published in principle in any mainstream journal, if the theorem is important and the proof gives an important new insight.

Alexandre Eremenko
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    +1 for the prime number theorem example. As I was reading over the question and the other answers, I had this vague memory of an alternate proof of something that wound up being very famous, and then I realized what it was when I saw your answer. – Dave L Renfro Feb 10 '17 at 20:19
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    Thank you, Alexandre Eremenko. No, it doesn't give any new insight, that's why I wondered in the first place if it was worth publishing it. Then, I thought: why not? It's still interesting at least as a curiosity. – M.Lopes Feb 10 '17 at 22:27
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    It's not quite correct to describe Selberg's Fields Medal in this way. There was also at that time his substantial work on zeros of zeta and L-functions, and his development of sieve methods. – Lucia Feb 10 '17 at 23:08
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    @Lucia: There is no doubt that Selberg had other important results. But I suspect that the elementary proof of the Prime number theorem played a crucial role in this award. – Alexandre Eremenko Feb 11 '17 at 07:58
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    I think that's just not correct. I think Bohr who gave the citation (which I can't find) would not have thought of it this way. – Lucia Feb 11 '17 at 15:07
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    You can look at Bohr's citation here http://www.mathunion.org/ICM/ICM1950.1/ICM1950.1.ocr.pdf . It mentions prominently the work on sieves, the work on zeros of zeta, and of course also the elementary proof of the prime number theorem. There is no doubt that the elementary proof was rated highly --- my point is just that saying Selberg got the Fields medal for the elementary proof is going too far. – Lucia Feb 11 '17 at 21:57
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    There is also Gowers getting the Fields Medal for a new proof of Szemeredi's Theorem. Furstenberg got the Abel Prize in large part due to his proof of Szemerdi's theorem using ergodic methods. Szemerdi himself, of course, got the Abel Prize for his theorem (which by then was long overdue) – Stanley Yao Xiao Feb 16 '21 at 20:22
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If the old theorem is something commonly seen in an undergraduate math class (with the old demonstration), then this might be appropriate as a "Note" in the American Mathematical Monthly.

What could happen if you submit it? They may publish it. The referee may give you a reference for it. They may respond in the same way as the Gazette.

What if the old theorem is not commonly seen in an undergraduate math course? When you write a textbook on that area of math, you can include your new proof. But if you think it unlikely you will write a textbook on this, then probably there is little prospect for publishing this. Maybe if you make it known to the experts* then some day one of them may include it in their new textbook.

*Perhaps by posting somewhere on-line...

Gerald Edgar
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  • thank you!

    I'll submit to the American Mathematical Monthly as you suggest, and let's see how it goes.

    (The theorem is very common, and I won't certainly write any book on the subject.)

     – M.Lopes Feb 10 '17 at 22:23
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    Note that the Monthly has a very high standard of exposition; so you would want to make sure that you're not just writing a research article—not even a very well-written research article—but an engaging and clear expository article that happens to contain original research. – Greg Martin Feb 11 '17 at 02:08
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Alternately, when you write a paper on a related topic (ie, which already develops the necessary machinery), you could perhaps include it somewhere in that paper? I've seen this done numerous times.

Karl Schwede
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    Thank you, Karl Schwede.

    I won't write anything related, because my research field is very far from this. I just came up with this demonstration while "playing" with some different problems on a Sunday. :)

     – M.Lopes Feb 10 '17 at 22:29
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A new proof of an old theorem, especially using modern machinery, could well be within the scope of the Graduate Journal of Mathematics, which seeks to publish work either by graduate students or that would be of interest to graduate students. From their website:

The Graduate Journal of Mathematics is an electronic journal that publishes original work as well as expository work of general mathematical interest which add to the literature, have pedagogical value and help make more widely accessible significant mathematical ideas, constructions or theorems...One main aim of our journal is to help researchers in mathematics in general, and graduate students in particular, gain access to important ideas and communicate interesting mathematics.

Full disclosure: I am on the editorial board. And I'd be happy to receive a submission with a new proof of an old theorem.

David White
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    Please also add that we need not pay any money to access the articles. – Praphulla Koushik Feb 16 '21 at 16:45
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    Yes, it's all free and open access! – David White Feb 16 '21 at 17:54
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    Just saw this comment, I am glad I saw this comment! Right now I have "a new proof of an old theorem" (which is short in length: 7 pages in total, counting/including a one-page reference list). Since I am still a graduate student right now, I will consider submit it to The Graduate Journal of Mathematics – Fei Cao Apr 20 '21 at 22:46
  • @FeiCao perfect! We would welcome the submission. Short papers are great! – David White Apr 21 '21 at 13:36