writes "A proof has been proposed for the Collatz conjecture about hailstone sequences. A hailstone sequence starts from any positive integer n the next number in the sequence is n/2 if n is even and 3n+1 if n is odd. The conjecture is that this simple sequence always ends in one.
Simple to state but very difficult to prove and it has taken more than 60 years to get close to a solution. Paul Erdos said "Mathematics is not yet ready for such problems" — so is it now?"Link to Original Source