Jeffrey Lagarias has been maintaining a summary of work on the Collatz problem, which is arguably the easiest open problem in mathematics: The 3x+1 problem: An annotated bibliography. It’s disturbing that such a simple problem is unsolved.

Jeffrey Lagarias has been maintaining a summary of work on the Collatz problem, which is arguably the easiest open problem in mathematics: The 3x+1 problem: An annotated bibliography. It’s disturbing that such a simple problem is unsolved.

As it happens, I’ve actually been thinking and doing experiments on this problem in recent weeks.

I’m actually becoming optimistic that this will be solved very soon now (within two years say) . The approach that seems to be making progress is looking at the computational nitty gritty with lots and lots of computer experiments. For instance, see this and this.

Yet the thing about those two links is that the content is nearly imcomprehensible, yet you can obviously see that there is “stuff” there. I’m betting that it will be simplified and unified once the proper paradigm is discovered.