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My preprint is on a topic that is based on high-school math and yet contains a fundamental discovery, but it is getting desk rejected from journal to journal because it does not fit the mould of articles that they usually recieve - mine is just 2 pages of which 50% is figures because I rely on a geometric proof.

P.S. I have tried Nature, Linear Algebra and its Applications, Applied Mathematical Letters, and Information Sciences so far.

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    Are you an undergraduate or a high school student? If so, submitting to an undergraduate journal may be an option. (For example, involve msp.org/involve/about/journal/about.html)
    – Darren Ong
    Apr 22 at 8:06
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    I assume you've done due diligence to know it's a fundamental discovery, meaning you're deeply aware of the theory behind the area you're working in, and also aware of the research being done? Is this a problem that's been identified as important and unsolved?
    – bob
    Apr 22 at 16:11
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    It might of course be that your discovery is not, in fact, "fundamental", but simply something every working mathematician in the field knows how to do.
    – Wolfgang Bangerth
    Apr 22 at 18:06
  • We do not recommend journals. You might be able to rephrase this question as "how to find journals that...." But, I suspect what you really want to know is "how do I get my article published", in which case this question may be helpful.
    – cag51 ♦
    Apr 22 at 19:49

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If your main concern is the shortness of the article, there are journals accepting also quite short papers, as Comptes Rendus Mathématiques or PAMS (Proceedings of the American Mathematical society), but they are quite selective, and what in your opinion is "a fundamental discovery" could be considered something obvious/unimportant/wrong by the mathematical community.

I have to be honest and say that, based on what you say, this seems most likely. However, it could well be that you found something relevant. There are a bunch of such cases in the history of math. So the right thing to do is to let your paper acquire visibility, while making it clear that it is your original work.

Luckily enough, there are resources for that. For instance, did you put your article on ArXiv or something like that? This can let it have some visibility and, perhaps more importantly, can bring you some feedback.

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  • Yes, I did post it as a preprint on ResearchGate but as you say, I am well aware that it has a flavor that renders itself to be considered as either obvious or unimportant. In short, I came up with a mathematical counter-example to Wolfram's principle of computational equivalence.
    – Cel
    Apr 22 at 17:18
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    @Cel: No one takes Wolfram seriously (indeed on these sorts of topics he's considered basically a crank), so, yes, indeed, what you have done is unimportant. I won't judge obviousness until I've seen it.
    – Alexander Woo
    Apr 22 at 17:33
  • @AlexanderWoo indeed, I am aware of that perception. In my humble opinion, he is the closest we really have to a modern day Feynman and viewing Wolfram as a crank happens to those who may culturally never get the subtleties of Wolfram's research - that's what made him a billionaire and others namecallers ;)
    – Cel
    Apr 22 at 18:04
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    @Cel Can you add the RG link?
    – Alessandro Della Corte
    Apr 22 at 18:18
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    @Cel Even if the perception of Wolfram as a crank were completely false (which it isn't), clearly your problem has nothing to do with the length of the paper and everything to do with it being "a mathematical counter-example to Wolfram's principle of computational equivalence", regardless of the fact that some editor might have mentioned something about the length of the paper to you at some point. You're asking the wrong question here. In other words, Dan Romik's answer is spot on.
    – Adam Přenosil
    Apr 22 at 22:34
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There are great math journals that regularly publish short papers. The American Mathematical Monthly is one such.

However, you’re asking the wrong question, which is based on the premise that good journals will refuse to publish a paper containing a “fundamental discovery” because its editors are not “champions of publishing short mathematical discoveries” or because your particular paper does not “fit the mould of articles they usually receive”. This premise is completely false.

Before you go any further with trying to publish your paper, it is crucial that you ascertain that it indeed “contains a fundamental discovery”. Otherwise you are just wasting your own time and credibility. You must obtain objective evidence that there are other active math researchers out there who share your view about the paper’s importance. Find some mathematicians willing to look at your paper and get their opinions. Then, and only then, consider your next steps.

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  • To be clear, I am looking for a journal that exclusively publishes short math discoveries. A journal where there is a positive bias towards pictures and negative bias towards Bourbaki style reasoning (I think you get what I mean). Short Math articles of a style that could be found in a Nature journal (50+ years ago).
    – Cel
    Apr 22 at 21:10
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    @Cel as I said, you’re asking the wrong question, and need to be receptive to the possibility that you have some misconceptions about how math research publishing works. The journal you’re describing does not exist (not as a journal for research math at least). And the journals that do exist don’t have the negative qualities you’re attributing to them that make a journal like that a desirable thing to have in the first place. Anyway, good luck with the project.
    – Dan Romik
    Apr 22 at 21:27
  • let me sharpen my question even further, I am looking for editors who do not consider Wolfram a crank. We have plenty of objective evidence that Wolfram's work is supported by several active math researchers (and also opposed - I am aware).
    – Cel
    Apr 23 at 9:18
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    @Cel Stephen Wolfram is a very well-respected mathematician, for example he is a Fellow of the American Mathematical Society, and his work has around 1000 citations on MathSciNet. I don’t think anyone considers his work to be invalid in the way that work by cranks is typically simply not correct. The only thing that’s remotely crank-like about him is that he wildly overhypes the significance of his research, particularly in his book A New Kind of Science. Other than that, he’s a mathematician who has produced valid and quite innovative work, and not a crank by any means IMO.
    – Dan Romik
    Apr 23 at 14:55
  • Okay let me sharpen it even further, I am looking for editors who would consider a mathematical counter-example to Wolfram's principle of computational equivalence - to be a fundamental discovery!
    – Cel
    Apr 23 at 15:10
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I think you have to find a professional mathematician to take a quick look at your work. The busy editor of a prestigious journal won't do that for you. I suggest you start with a teacher (if you're in high school) or a professor (if you're in college).

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Without examining the premise of this question, here are a few reputable journal that welcome very short notes (some already mentioned in other answers):

  • The Comptes Rendus - Mathématique are a peer-reviewed, open-access diamond electronic journal that publishes original research articles, journal articles, and texts reflecting the activity of the Academy des sciences in the field of mathematics. They publish short articles, announcements of significant new results, but also updates, conference proceedings and thematic issues.
  • The Bulletin of the London Mathematical Society has been publishing leading research in a broad range of mathematical subject areas since 1969. Research articles accepted by the Bulletin are of high quality and well-written, with a maximum length of 20 pages. The Bulletin also publishes authoritative survey articles (of any length) and obituaries of distinguished mathematicians. The Bulletin welcomes short papers on subjects of general interest that represent a significant advance in mathematical knowledge, as well as submissions that are deemed to stimulate new interest and research activity.
  • Bulletin of the Australian Mathematical Society aims at quick publication of original research in all branches of mathematics. Papers are accepted only after peer review but editorial decisions on acceptance or otherwise are taken quickly, normally within a month of receipt of the paper. The Bulletin concentrates on presenting new and interesting results in a clear and attractive way.
  • Proceddings of the American Mathematical Society This journal is devoted to shorter research articles (not to exceed 15 printed pages) in all areas of pure and applied mathematics. To be published in the Proceedings, a paper must be correct, new, and significant. Further, it must be well written and of interest to a substantial number of mathematicians. Piecemeal results, such as an inconclusive step toward an unproved major theorem or a minor variation on a known result, are in general not acceptable for publication. Longer papers may be submitted to the Transactions of the American Mathematical Society. Published pages are the same size as those generated in the style files provided for AMS-LaTeX.
  • Archiv der Mathematik (AdM) publishes short high quality research papers in every area of mathematics which are addressed to a broad readership and not overly technical in nature. Articles should typically not exceed 10 pages.
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