michael_nielsen

This is a really fun thread. The 3x+1 problem is deceptively simple: the kind of thing anyone can understand & play with, but which the world's best mathematicians can't solve. A very brief explanation:https://twitter.com/AlexKontorovich/status/1172715174786228224 …

Take a positive number. Let's give it a name: x. The rules of the game are this: (1) if x is even, replace it by x/2; and (2) if x is even, replace it by 3x+1. That's it, the complete rules of the game.

If you play this game starting with x = 5 (say), then here's what happens. 5 is odd, so it gets replaced by 3x+1 = 16. That's even, so gets replaced by 16/2 = 8. That's even, so gets replaced by 8/2 = 4. You've likely gotten the hang of this now, & can see the end: 4 -> 2 -> 1

Here's what the 3x+1 conjecture says: no matter what number you start with, eventually you'll end up at 1. It might take a very long time, but you'll get there.

It's easy to write a 5-line Python program to check this up to, say, x = a trillion (or much further). But proving it turns out to be something else entirely! Lots of mathematicians have worked on this, and failed to solve it.