I am currently writing a paper on 3x+1 and realized that despite having enough knowledge to work on a singular facet of the problem I lack a more broad understanding of the problem. I have seen the thorough annotated bibliographies by Jeffrey C. Lagarias but I do not have the time to read most of them and I imagine plenty of them would not teach me much about the problem itself, even if I did take the time to dissect them. So what are the papers people feel I should read with my limited time to gain the best possible understanding of the Collatz Conjecture?

  • $\begingroup$ Perhaps the Wikipedia page would be a good starting place? $\endgroup$ Commented Jun 14, 2012 at 20:48
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    $\begingroup$ I don't understand asking for an annotated bibliography from us when you already have access to one by THE expert. By the way, do you know that Lagarias has published a book on the problem? Maybe that's the first thing to look at. $\endgroup$ Commented Jun 15, 2012 at 11:19
  • $\begingroup$ I meant one of significantly shorter length but I will remove that part of the post anyways to avoid confusion. No I did not know, any chance you could post a link to it I could not seem to find it via google. Thank you for your helpful comment $\endgroup$ Commented Jun 15, 2012 at 13:34

1 Answer 1


It's challenging to distill a required reading on the Collatz conjecture, because it's unsolved. What may or may not be necessary? As you might have noticed from Lagarias's annotated bibliographies, there is a lot of literature on the subject, and it seems as though Lagarias has already sifted through a whole lot. What would be more convenient than his bibliographies, with short explanations of what each paper has done? If I were you, and I was set on working on the problem, I would decide which of the papers were related to the methods I had in mind, or which ones at least sound interesting.

But to be sure, he was two bibliographies. Pre 2000 here and 2000-2009 here. As mentioned in the comments, he has a book, and an intro. Lagarias is the expert, and there's no better list.

I would also mention that the problem is unsolved, and so I recommend patience. Developing the patience to read a beautifully written set of annotated bibliographies might be a good place to start.


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