On May of this year, Gerhard Opfer offered a paper to the public in which he claims to solve the Collatz conjecture. A month later, June
Oops, got interrrupted by a Jehova’s witness whom I had to educate about confirmation bias.
Anyway, a month later, June 17th, he withdrew his claim. The Collatz conjecture is a bitch because it looks deceptively easy but cannot be proven by methods such as natural induction. Because it looks so harmless, many people, including lay-mathematicians (such as myself), have attempted to solve it. Mind you, the conjecture was proposed in 1937, so people have been trying to solve it for over 74 years.
Like I said, I have been messing around with it as well, and the main problem is, quite appropriately, confirmation bias: You’re working towards verifying the conjecture and in doing so you overlook major points that can overthrow your proof. I’ve tried four or five times in the past year and each and every time I, halfway through, I forget all about the issue at hand: Making sure that 4, 2, 1, 4, 2, 1, … is the only cycle. Instead, you find all sorts of properties of the Collatz graph that you think are useful and after you sleep on it a night, you realize that these properties do not allow you to detect cycles… OMG it’s a bitch.
However, I’m still hopeful, like everyone else who is trying to solve it 😉 and on those occasions when I’m SURE I have the answer… I have no idea where to send it… :S Don’t get me wrong, that’s actually a GOOD thing, because the mess I write down is enough to make any mathematician cry and quit his job… But where do solutions to ancient never-proved conjectures actually go? :S