I recently stumbled upon the following paper from April 2016: https://www.researchgate.net/publication/299749569_A_proof_of_the_Collatz_conjecture

Its researchers, who are university professors, claim it proves the Collatz conjetcture.

Since I have not been up to date with the status of this conjecture for a while, and because I found no disproofs of this document on the web, I was wondering if someone here can shed some light on this paper.


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    $\begingroup$ Compare the wording of the abstract there with the abstract arxiv.org/abs/1612.07820 by the same two authors (but later). I would say definitely no. $\endgroup$ – Tobias Kildetoft Jan 19 '17 at 12:42
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    $\begingroup$ The revised version sounds like it is likely to hold, but neither the insight or the involved probabilistic techniques are new. $\endgroup$ – Jack D'Aurizio Jan 19 '17 at 13:10
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    $\begingroup$ Those guys actually sent me (and presumably others who worked on the Collatz conjecture before) their "proof" several months ago. I told them as politely as I could that I do not believe it to be a proof, with pointers to the gap in their proof and references to literature with similar probabilistic claims which are not complete proofs. They responded rather rudely saying I was wrong, and I did not know what I am talking about. So yeah, some "university professors with established reputation" can be real assholes as well. $\endgroup$ – TMM Jan 24 '17 at 5:02
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    $\begingroup$ Interestingly, in their follow-up paper they thank a bunch of people for their "insightful" comments, but none of these people (as far as I can tell) have actually ever worked on the Collatz conjecture. So I guess the feedback they got from people who did work on the topic ("the proof is wrong and the results are not new") was not insightful enough :-) $\endgroup$ – TMM Jan 24 '17 at 8:21
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    $\begingroup$ Sentences like "in this paper, we provide a self-consistent argument to support the validity of the Collatz conjecture" and "the existence of diverging trajectories can be however ruled out by invoking an argument of internal consistency" strongly set off my bullshit detector - they're usually a good sign that a "proof" is nothing more than a heuristic, backed by "intuitively obvious" claims (which on further examination are usually anything but). $\endgroup$ – Noah Schweber Jan 27 '17 at 15:14

The authors claim that EVERY trajectory is asymptotic to a decreasing one, hence all trajectories tend to the $1,2,4$ cycle.

However any cycle that isn't, wouldn't affect the general asymptotic, and would effectively 'escape the radar'.


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