The Collatz conjecture[a] is one of the most famous unsolved problems in mathematics. The conjecture asks whether repeating two simple arithmetic operations will eventually transform every positive integer into 1. It concerns sequences of integers in which each term is obtained from the previous term as follows: if the previous term is even, the next term is one half of the previous term. If the previous term is odd, the next term is 3 times the previous term plus 1. The conjecture is that these sequences always reach 1, no matter which positive integer is chosen to start the sequence. The conjecture has been shown to hold for all positive integers up to 2.95×1020, but no general proof has been found. Wiki
More vids on the Collatz Conjecture.
An example of how math can be addictive for some. The patterns are often deep and hidden but seem so close. A simple premise can go on forever. Its rules based order is often the basis of science and the universe.
A physics friend quoted a prof we both had that said he sometimes longed for a physics that was all math.
Max Tegmark did a book called Our Mathematical Universe that was an interesting read.