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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.

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    $\begingroup$ 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. $\endgroup$
    – Noah Schweber
    Commented Feb 10, 2017 at 16:35
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    $\begingroup$ 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. $\endgroup$
    – Anthony Quas
    Commented Feb 10, 2017 at 16:37
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    $\begingroup$ 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 ... . $\endgroup$
    – Stefan Kohl ♦
    Commented Feb 10, 2017 at 21:02
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    $\begingroup$ @WłodzimierzHolsztyński, unfortunately my time machine has not been working lately. $\endgroup$
    – M.Lopes
    Commented Feb 10, 2017 at 22:20
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    $\begingroup$ If your proof is of pedagogical interest and/or can be integrated in a review of the subject, you could try L'Enseignement mathématique. $\endgroup$
    – Gro-Tsen
    Commented Feb 10, 2017 at 23:25

4 Answers 4

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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...

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  • $\begingroup$ 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.) $\endgroup$
    – M.Lopes
    Commented Feb 10, 2017 at 22:23
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    $\begingroup$ 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. $\endgroup$
    – Greg Martin
    Commented Feb 11, 2017 at 2:08
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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.

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    $\begingroup$ +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. $\endgroup$
    – Dave L Renfro
    Commented Feb 10, 2017 at 20:19
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    $\begingroup$ 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. $\endgroup$
    – M.Lopes
    Commented Feb 10, 2017 at 22:27
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    $\begingroup$ 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. $\endgroup$
    – Lucia
    Commented Feb 10, 2017 at 23:08
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    $\begingroup$ @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. $\endgroup$
    – Alexandre Eremenko
    Commented Feb 11, 2017 at 7:58
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    $\begingroup$ You can look at Bohr's citation here 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. $\endgroup$
    – Lucia
    Commented Feb 11, 2017 at 21:57
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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.

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    $\begingroup$ 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. :) $\endgroup$
    – M.Lopes
    Commented Feb 10, 2017 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.

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    $\begingroup$ Please also add that we need not pay any money to access the articles. $\endgroup$
    – Praphulla Koushik
    Commented Feb 16, 2021 at 16:45
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    $\begingroup$ Yes, it's all free and open access! $\endgroup$
    – David White
    Commented Feb 16, 2021 at 17:54
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    $\begingroup$ 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 $\endgroup$
    – Fei Cao
    Commented Apr 20, 2021 at 22:46
  • $\begingroup$ @FeiCao perfect! We would welcome the submission. Short papers are great! $\endgroup$
    – David White
    Commented Apr 21, 2021 at 13:36

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