Two days ago Peter Schorer published a new proof of the famous mathematical problem named the Collatz Conjecture. This doesn’t mean it has been proven, though: new proofs for this particular problem appear with depressing regularity, only to be invalidated in a few weeks. But we can always hope for the best!
The problem itself can be stated in simple terms:
Take any positive integer n.
- If n is even, divide it by 2 to get n / 2
- If n is odd, multiply it by 3 and add 1 to obtain 3n + 1
Repeat the process (which has been called “Half Or Triple Plus One”, or HOTPO) indefinitely.
The conjecture is that no matter what number you start with, you will always eventually reach 1. This seems easy to prove, but the Collatz mapping above exhibits chaotic, even fractal behaviour. Thus, a proof has long been sought but not yet been found. Due to the relationship to several other longstanding mathematical problems, this problem has occupied mathematicians for at least a century, possibly much longer than that. Leading to frustration in some quarters.