1
$\begingroup$

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.

Thanks.

  • 4
    Compare the wording of the abstract there with the abstract https://arxiv.org/abs/1612.07820 by the same two authors (but later). I would say definitely no. – 2017-01-19
  • 1
    Also, while it is true that they are professors, they are apparently mainly physicists, rather than mathematicians. – 2017-01-19
  • 4
    The revised version sounds like *it is likely to hold*, but neither the insight or the involved probabilistic techniques are new. – 2017-01-19
  • 0
    ... "...it supports..." ... says it is no proof. – 2017-01-22
  • 0
    @Gottfried The title says "A proof of the Collatz Conjecture*... – 2017-01-23
  • 2
    @Pickle - :-) . Well, if you buy fish in a paper and it is "fish" written on the paper you still would look inside to know what it is, and whether it is only very similar to a fish ("supporting" your intuition of what a fish is... ;-) ) - But well, don't take me too serious here. – 2017-01-23
  • 0
    So you would say university professors with established reputation would entitle their ground-breaking discovery with a lie? – 2017-01-23
  • 10
    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. – 2017-01-24
  • 5
    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 :-) – 2017-01-24
  • 0
    Thanks for your reply TMM! If you can post an answer with some minimal pointers to these gaps, I will award you the bounty. Quick question: why are such papers published in journals, before anyone can verify it? It seems like a document with such outrageous claims should have been reviewed better before being published... – 2017-01-24
  • 1
    Two notes: 1) I don't think either paper has been accepted for publication yet, they're just pre-prints. 2) I'm far from an expert in these things, but I think the fundamental flaw in the original paper is that despite observing that their approach does not preclude a non-empty, measure zero set of divergent trajectories, they don't provide a clear proof that such a set does not exist. Basically, I don't see how the "proofs" of Props. 7, 8, & 9 actually prove anything. But that could just be me. – 2017-01-25
  • 3
    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). – 2017-01-27

1 Answers 1

5

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'.