Collatz Conjecture solution using 4n+1
Channel: bob therriault
Date: 2022-05-03

An update:
As several have pointed out, this process does not actually prove Collatz, but only proves that if an integer is within the Collatz tree it converges to 0. Other integers not on the tree could still exist. 

As of July 26, 2023 I have posted a paper that shows my current approach and in the next while I will post a video here that walks through the paper. If you would like to read it, you can find it here: https://code.jsoftware.com/mediawiki/images/8/88/The_Upward_Path_of_3x%2B1.pdf

I am not a trained mathematician, which will become apparent to trained mathematicians as they listen to me use technical terms in inappropriate ways. Nonetheless, I put forward this 4n+1 method, which is a consequence of the original odd and even Collatz rules. This 4n+1 rule shows that the Collatz Tree as a tightly bound group of odd numbers. In fact the odd numbers are so tightly bound that the 4n+1 rule shows that the Collatz Tree must contain all of the odd numbers and by extension the even numbers. If every number is included in the Collatz Tree then the Collatz Conjecture is true. I am putting this out as a way to have the world look at my reasoning and I welcome comments that point out flaws in my analysis. 

For a really good video explaining the challenges of proving the Collatz Conjecture take a look at this Veritasium video https://www.youtube.com/watch?v=094y1Z2wpJg

If you are interested in  how I came up with this solution, look at some of my other videos concerning the J language. It is a programming language that I find is particularly well suited to playing with number theory problems like Collatz. It is a descendent of APL and a cousin of k which are often used in large scale financial programs. https://www.jsoftware.com/#/README

I also participate in the ArrayCast podcast which is about the different array programming languages. https://www.arraycast.com