Collatz conjecture, one of the most mysterious questions in the world of mathematics, suggests that every natural number greater than 1 will eventually reach 1 through a certain series of operations. This interesting problem is also known by different names among mathematicians such as 3n+1 problem, Ulam conjecture, Kakutani problem.
It is basically based on two simple rules: If the number is even, it is divided by two; if it is odd, one more than three times it is taken. As these two processes are repeated, the series is expected to eventually add up to 1, no matter what number you chose to begin with. Although the checks carried out so far have shown that this rule works for numbers above 2.36 quintillion, mathematicians have not yet been able to prove the universality of this assumption.
The origin of this assumption dates back to 1937, when mathematician Lothar Collatz put forward this concept after his doctoral study. Some mathematicians also use names such as "hailstone series" or "hailstone numbers", comparing the fluctuating structure of these number sequences to hailstones in a cloud. They are even called "wonderful numbers" due to the extraordinary progress in these series.
The words of the famous mathematician Paul Erdลs, "Mathematics may not be ready for such problems yet," reveal how difficult a problem the Collatz conjecture is. Jeffrey Lagarias, in an evaluation he made in 2010, described this assumption as "an extraordinarily difficult problem, completely outside of today's mathematics." Although the conjecture itself has not yet been solved, efforts to understand and solve this problem have encouraged mathematicians to develop new methods and reach many partial results.
