When using google to find out about research results about the Collatz conjecture, I find numerous proofs by various people who seem to be experts of the topic and an abundance of proofs by amateurs. Here are 3 examples of such proofs, where at least the first two appear to be scientists with experience in relevant fields:

Wikipedia states that the conjecture is not proved, while for example Porras' proof is from 2018. I'm sure this proof has been checked and either considered correct or incorrect/incomplete, but I couldn't find anything substantial about checks of these proofs.

How to know what the current status is about the research here? Do I have to check all of those proofs on my own to know if one of them is correct?

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    $\begingroup$ An accepted proof will become very famous very quickly. It is, of course, possible that one of the huge number of claimed proofs is correct...nobody could possibly keep up with the stack of these, though you are welcome to try. Note that any proof writer is free to submit their paper to a peer-reviewed journal, though it is certainly difficult to get anyone to focus on Collatz arguments (just as, in the past, nobody wanted to look at the huge piles of Fermat "proofs"). $\endgroup$
    – lulu
    Jan 24, 2022 at 13:04
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    $\begingroup$ If it has been published in a journal it means it went through a professional review. So, check if these "proofs" have been publish outside authors personal web pages. $\endgroup$
    – Salcio
    Jan 24, 2022 at 13:07
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    $\begingroup$ "not accepted" is not a synonym for "wrong". If a mathematician asserts that a claim is not proved that means no proof has been accepted. I, for example, would say that the $abc$ conjecture is not proved yet, despite the (well publicized) existence of a claimed proof. $\endgroup$
    – lulu
    Jan 24, 2022 at 13:14
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    $\begingroup$ I couldn't find anything substantial about checks of these proofs -- There are many red flags one can look for, this being one of them. Others are whether (and how) the author's proof is discussed on mathoverflow and in some of the well known math blogs, as no mention there (or here) is telling. Also, look at the author's publications in MR and Zbl. Regarding someone unknown solving the problem, such a situation would generate more publicity than an expert solving it. $\endgroup$ Jan 24, 2022 at 13:16
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    $\begingroup$ @Peter I certainly agree it is a waste of time, though I don't think I encouraged anyone to try it. Didn't mean to, anyway. Rather, I encouraged the OP to try to find the errors in the "proofs" they linked to...that can be a useful exercise on its own, at least if the paper is tolerably well written. I recall one $300+$ page "proof" of Fermat that included a $50+$ page digression into martial arts lore, not to mention page after page of threats against those who would dare impugn the author's genius. That one got circulated widely, though not for its mathematical content. $\endgroup$
    – lulu
    Jan 24, 2022 at 13:39


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