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I have some short questions I'd like to ask. I hope I'm asking in the right place.

  • Has there been any significant progress on the Collatz Conjecture to date?

What Tao really did was to set new bounds for the numbers for which the Collatz Conjecture was correct? In fact, was Jeffrey taking Lagarias' work to the next level? What exactly do we have explicit results now?

My last question:

  • Given the academic articles published so far, is there any possibility that the Collatz Conjecture is still correct?

What I know is that Jeffrey Lagarias has solved some finite loop probabilities and found the $ x ^ {0.84} $ lower bound.

Thank you very much.

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    $\begingroup$ You are just asking us to summarize the latest results for you? Why not look them up yourself? $\endgroup$ – lulu Dec 17 '19 at 23:46
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    $\begingroup$ I suggest staying away from the Collatz problem. I understand its hypnotic attraction, but just stay away from it. If you don't want to accept that advice, then google Tao and Collatz. $\endgroup$ – lulu Dec 17 '19 at 23:50
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    $\begingroup$ To your last question: The Collatz conjecture has not be disproven (or proven). The query remains open. $\endgroup$ – Mason Dec 18 '19 at 0:03
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    $\begingroup$ @lulu You are right. People who do not have an academic career or do not have serious university education (like me) should not be interested in this. So I'm just curious about the latest results..(maybe I missed) $\endgroup$ – NewUser Dec 18 '19 at 0:15
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    $\begingroup$ @lulu Okay, I understood what you said. Thank you. $\endgroup$ – NewUser Dec 18 '19 at 0:23