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The Collatz Conjecture is an 80 year-old open Math problem. Recently, I made a remarkable discovery of the long sought visual pattern in the conjecture. This never-before-seen visual pattern led me to two significant results: (a) a natural proof that the Collatz conjecture has no non-trivial cycles, and (2) a direct link between the Collatz conjecture and prime numbers.

My question: If you have proven a major unresolved question in mathematics but you are out of touch with university professors, or someone who can endorse you on arXiv, how can you get your paper published and noticed by professional mathematicians?

My paper can be found here. I'm currently not interested in publishing in a journal, unless someone wants to pick up that challenge with me.

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    I have not followed your link. You may want to be careful to put an anonymous untimed link like that, you have at this stage no proof of priority, should the proof be real and someone try to scoop you.
    – Captain Emacs
    May 13, 2021 at 21:10
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    One thing to consider is if you live close to a university, you could ask their dean/head of dept. whether, if you would offer to give a seminar to their math faculty, they would be happy to host/criticize your talk. Not sure if they would agree, but it might be worth a try. At least you would have an audience, and proof of priority and possibly and endorser.
    – Captain Emacs
    May 13, 2021 at 21:12
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    Looking very briefly at your document, I have the impression that you give many examples. Not a bad thing, but: (1) this would be unpersuasive for Collatz, (2) makes your document much longer, (3) May give the impression that you believe that lots of examples are a proof. If nothing else, a shorter document will be read much more. Perhaps put the examples in an appendix, so that your proof ideas can be easily identified/isolated by interested readers.
    – paul garrett
    May 13, 2021 at 21:19
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    @Prof.SantaClaus They need an endorser.
    – Captain Emacs
    May 13, 2021 at 21:33
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    It would help if the introduction instead of being quotes about how hard the problem instead explained the ideas of the paper like a normal math paper’s intro.
    – Noah Snyder
    May 13, 2021 at 22:05

1 Answer 1

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Apply for postgraduate study at the closest university.

My advice would be to apply for postgraduate study at the nearest university to you; you'd most likely want to apply for either a PhD in Mathematics or a research-based Master's Degree, if your university offers the latter.

This way, helping you to get your discovery published would be a part of your supervisor's job, and they would thus be incentivised to do so, when compared with you being a random guy off the street. Academics are generally busy people, so time spent helping you when it's not their job to do so could be spent in a number of different ways.

Additionally, if you're a postgraduate student, it's likely that this paper, once published, would form a significant part of your thesis (often, a PhD thesis is composed of several papers stitched together), so you'd basically be walking in the door with a decent chunk of your degree already completed. Of course, different universities have different requirements for graduation, so this might not be 100% guaranteed.

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    Why would OP do a PhD if all they want to do is to provide a result? (assuming the writeup makes sense).
    – Captain Emacs
    May 13, 2021 at 23:13
  • I don't think this is how things work most places. Especially in the U.S., (my experience), there is emphasis on broad mathematical education. Even if "mathematicians" would be conceivably inclined to award a PhD "by acclaim", most administrations in the U.S. have lots of hoops to be jumped through...
    – paul garrett
    May 13, 2021 at 23:16
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    If they went to grad school then they could work out for themselves why this isn’t a valid proof, rather than needing to ask for feedback.
    – Noah Snyder
    May 13, 2021 at 23:31
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    @NoahSnyder Is it an invalid proof? I haven't read it, and I probably wouldn't be qualified to judge it if I did since I'm not a mathematician. I just assumed that it was a valid proof with insufficient formatting for publication based on other comments.
    – nick012000
    May 13, 2021 at 23:47
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    It's very rare, but "layman" discoveries are possible in math; Collatz may be a good candidate for that. To direct such authors to jump through a lengthy qualification process to publish just a single discovery comes across as one of these often criticised gatekeeper practices to keep the "unwashed masses" out of one's sanctuary. Not saying this answer intended it this way, but it still kind of has this vibe.
    – Captain Emacs
    May 14, 2021 at 1:05

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