This story in Scientific American gets very technical very quickly, but the root scenario is [really] pretty simple:

Take a natural number. If it is odd, multiply it by 3 and add 1; if it is even, divide it by 2. Proceed in the same way with the result x: if x is odd, you calculate 3x + 1; otherwise calculate x/2. Repeat these instructions as many times as possible, and, according to the conjecture, you will always end up with the number 1.

Hard to believe with all the “smart” computing resources in the world, there is still an unsolved math problem. Also hard to believe I almost studied mathematics here.