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I've spent years writing a math paper I call "A study of Pythagorean Triples" and I would like to publish. I've written and re-written for accuracy and clarity and I ported it from Word to TexShop after having found that most publications require that format. My paper is currently 14 pages long including 8 [ small ] graphic Exhibits in .png format.

How do I begin to get peer review as a total amateur and how do I proceed from there?

Update: My work was original to me but comments have led me to links showing that some of it has been done by others. The only distinction my work still has is in showing how this or that function was developed and how it works. I should rename my paper something along those lines and reflect that in my abstract.

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    This is a duplicate of academia.stackexchange.com/q/3010/75368. Basically, anyone can publish simply be submitting to a journal and having it accepted. – Buffy Sep 7 '19 at 19:52
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    I’ve worked on this topic, if you email me a pdf of the paper I can have a look and let you know what I think. – Dan Romik Sep 7 '19 at 19:56
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    FYI, there's an enormous amount of literature on this topic that is widely scattered throughout books and non-research journals (e.g. this), and you'll want to apply due diligence in your literature review to avoid claims of novelty for things that are fairly well known to connoisseurs of the subject. For example, make sure you're familiar with Sierpinski's book (Polish original 1954, English translation 1962 that was reprinted in 2003) and easily googleable items that cite it. – Dave L Renfro Sep 7 '19 at 21:50
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    Frankly, this is a topic that I would be scared to death of working on without a collaborator who is very familiar with the area. There's about 400 years worth of literature on the topic, and chances are very high that whatever I would come up with is somewhere in there. – Alexander Woo Sep 7 '19 at 22:05
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    For references a little more recent than Sierpinski's book, see William L. Schaaf's 4-volume A Bibliography of Recreational Mathematics --- pp. 89-99 in Volume 1, pp. 108-113 in Volume 2, pp. 62-66 in Volume 3, pp. 75-79 in Volume 4. (I couldn't locate a digital copy of Volume 4 with a quick internet search.) – Dave L Renfro Sep 7 '19 at 22:15
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A partial answer: Every piece of scientific work builds on other people's publications (remember Newton's "standing on the shoulder of giants" quote), and so one can surmise that your paper also cites other publications -- and if it doesn't, it probably should.

So let me assume that you are already doing that, then a good approach is to see where these other references were published. Look up these journals: Every journal has a charter on their website that explains (i) what kinds of papers they publish, and (ii) how one can submit a paper to them.

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    One problem is that I got none of this from other publications. I did get a reference to Euclid's formula after I had invented my own different formula to generate distinct sets of triples. I did get help on MSE figuring out the combinatorics for counting primitives vs multiples. I did get help on MSE in the trigonometry I used to prove that 6 dissimilar triangles I found using my functions made a perfect Isosceles triangle. I will have to look hard to find where the work has been done. In the mean time, I'm rewriting to reflect the critiques I've received so far. – poetasis Sep 8 '19 at 10:22
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    Then at the very least you ought to cite the MSE sources. But the reality is -- and I don't want to sound dismissive, just realistic -- that it is really very very unlikely that nothing of what you've invented has been done before. I mean, it's possible, but statistically it just never happens in math that anyone comes up with something that's not at least informed and builds on other things. You really should spend time reading the literature of the area, or you will find the publication process rather frustrating. – Wolfgang Bangerth Sep 10 '19 at 5:16
  • Thank you and everyone else for the feedback. It has shown me that I need a major re-write in my abstract and modification of the body to reflect those changes. I know that it's rare that something hasn't been done before but in all my spare time searches and queries online, I haven't yet found anything resembling my Formula which generates only and all Pythagorean triples where GCD(A,B,C) is an odd square. I also haven't found prior work, for example, of 'how to' find triples given a side, perimeter, area, or area/perimeter ratio. I'm learning. Thanks again. – poetasis Sep 10 '19 at 16:36

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