The document summarizes the Collatz conjecture, an unsolved problem in mathematics. The conjecture states that if you take any positive integer n and repeatedly perform the operation of taking n/2 if n is even or 3n + 1 if n is odd, you will eventually reach 1. The author believes an algorithm can be found to prove that this process always converges to 1, despite others claiming the problem is unsolvable. They provide examples of the Collatz sequence for even and odd starting integers. The author defines an algorithmic sequence an+b and shows how it can generate the Collatz sequence.