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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.

Bryan Krause
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Math777
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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 '21 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 '21 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 '21 at 21:19
  • I would post it on ArXiV, and if you are correct, you'll know. – Prof. Santa Claus May 13 '21 at 21:22
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    @Prof.SantaClaus They need an endorser. – Captain Emacs May 13 '21 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 '21 at 22:05
  • I'd say to contact the guy who took over running Erdos' prizes, but he died in 2020, according to Wikipedia. – nick012000 May 13 '21 at 22:20
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    Thanks for the comments. I get the idea that professional mathematicians don't have time for things like these. I like @CaptainEmacs' comments to walk over to a university math department. – Math777 May 14 '21 at 00:40
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    @Math777 I second the idea of contacting professors directly. Maybe try looking for a young professor. They usually desperately need to publish, so they might jump on the opportunity. Alternatively, look for postdocs. – fredq May 14 '21 at 14:30
  • Update: The paper has been posted to arXiv. Thanks for all your help. It's great when you can find people willing to lend a helping hand. – Math777 May 20 '21 at 15:19

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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.

nick012000
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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 '21 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 '21 at 23:16
  • Well, if they're the sort of person who'd solve an open problem of mathematics for fun in their spare time, they might enjoy doing a PhD, and it would likely give them the opportunity to extend their result into new applications or areas. Alternatively, if they want a lower time investment, then they could pursue a research Master's Degree - depending on their university's requirements, it's possible that the result that they've already gotten might be enough to write into a Master's thesis. – nick012000 May 13 '21 at 23:20
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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 '21 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 '21 at 23:47
  • @paulgarrett I wasn't talking about awarding a degree by acclaim, but about turning the published version of this paper into Chapter 1 of a "stapler" thesis. – nick012000 May 13 '21 at 23:53
  • @nick012000, ah, well, in the U.S. at least, there are no "stapler theses" in math, currently. Coursework is a gateway thing, and so on. A different system than in engineering in the U.S., for example, yes. – paul garrett May 14 '21 at 00:19
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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 '21 at 01:05