If math is a such a definite subject with solid answers, how are there still unsolved math problems? How do people even come up with them?
In: Mathematics
My favorite unsolved problem, because it’s so easy to understand, is the Collatz Conjecture. We have a game that goes like this:
1) Pick any number and check if it’s even or odd.
2) a) If it’s even, divide by 2
2) b) If it’s odd, multiply by 3 and add 1
3) Take your new number and go to step 1.
For example, if you start with 10:
10 -> 5 -> 16 -> 8 -> 4 -> 2 -> 1 -> 4 -> 2 -> 1…
Starting with 10, you end up going to 1 and then getting stuck in a loop between 4, 2, and 1. If you start with 9, it takes 20 steps (and goes all the way up to 52 at one point), but it also goes to 1. The conjecture is:
**Every positive whole number eventually reaches 1 when using this pattern.**
To _disprove_ this, all you have to do is find some starting number that gets stuck in a different loop. We’ve tried that, though – we’ve tried every number up to 20 digits long, and they’ve _all_ hit the 4,2,1 loop. To _prove_ this is true, though, you’ll need to come up with some creative insight about the way that numbers relate to each other.
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