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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.
It's a lovely problem, in part because you can goof around with it from first principles, & learn fun stuff. I did a lot of this when I was 18, 19 or so, & even today occasionally pull the problem out to relax. But people have also brought quite sophisticated mathematics...
... to bear on the problem. Much has been learned, but the problem remains unsolved!
More detail in the Wikipedia article: https://en.wikipedia.org/wiki/Collatz_conjecture … And, via @geomblog, the news that Terry Tao has recently made some very interesting progress:https://terrytao.wordpress.com/2019/09/10/almost-all-collatz-orbits-attain-almost-bounded-values/ …
Sigh. @nathanju34 points out that in case (2) above I should have written "odd", not even, of course. My kingdom for an edit button.https://twitter.com/michael_nielsen/status/1172916056496558080 …
(2) should be odd case
Thanks. What a pain.
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