Solving 3n+1, One Failure At A Time

My progress in describing and attempting to solve the Collatz Conjecture (an, as of yet, unsolved math problem)

[collatzproblems]

I’d like to give a shout out to @mr-pengu1n for helping me work through some (unfortunately) incorrect assumptions and misunderstandings. He’s definitely pointed me in the right direction, and I cannot thank him enough.

[collatzproblems]

I’ve been decidedly absent from here because I’ve been exceedingly defensive of my theory. I’ve spent the years writing, re-writing, re-re-writing, thinking, considering, contemplating, and all other manner of things related to the conjecture.

I do believe I’ve solved it, but the problem is that most people I trust are too busy to review the paper and logic, and those that can have a difficult time following (hence half the point of a peer review... that’s what I say, anyways).

I recently found LaTeX and am using that to write the paper now, and it is beautiful. The packages allow me to easily put trees into the paper to demonstrate points, as well as beautifully formatted formulae... my dream come true. Even though most people are scared away from the paper by the fact that it’s “math”, they look at it and say it’s professional looking.

Hopefully soon I can get someone to review the concepts and then move forward (or back to the drawing board) from there.

[collatzproblems]

I think I may have done it. I may have solved it. Testing and passing it through a PhD here soon.

[matthen]

Pick a whole number, if it is even divide it by 2, if it is odd then multiply it by 3 and add 1. Repeat. For example, 12 is even, so goes to 6, then 3 which is odd, so goes to 10, then 5, then 16, then 8, 4, 2, 1.  Your number will have also gone down to 1 (I imagine).  Will the numbers always go down to 1? This seemingly simple question hasn’t been answered yet, and is called the Collatz conjecture.  The image shows my visualisation of how the first few hundred numbers whittle down to 1.  It is such an easy question to ask, but we can’t prove it yet; a good example to show there is still plenty of work to be done in maths! [more]

[collatzproblems]

This blog is about the wonderfully annoying mathematical anomaly that is the Collatz Conjecture. Often described as the 3n+1 problem, this simple math problem has stumped people for years. It is the easiest to explain, and among the hardest to formally prove. The equation is seen in the first picture, and the question is if every positive integer will eventually result in 1. This is the expanded form of the equation, and other, more condensed, forms can be used as well, and those will be discussed later. As you can see, this problem is very simple to understand (requiring only knowledge of evens/odds, multiplication, division and addition), yet, given no one has solved it yet (and I started this blog as a diary of sorts) the "why" is far more complicated.