The Collatz Conjecture The Problem The Collatz conjecture (a.k.a the hailstone problem or the $3n + 1$ problem) was proposed by Lother Collatz in 1937. Although the problem on which the conjecture is based is really simple that even a fourth-grader can easily understand it, the behaviour of the conjecture makes it exceedingly difficult to prove(or disprove). First of all, lets define the Collatz map . Let $T : \mathbb{Z}^+ \rightarrow \mathbb{Z}^+$ be defined by The conjecture is that for every positive integer $n$, there exists a $k$ such that $T^k(n) = 1$. Let us consider an example. As mentioned above, the conjecture states that this is true for any positive integer n. But what makes this problem interesting is that even after 60 years since its proposal nobody has been able to prove (or disprove) it. Mathematicians say the "Mathematics is yet not ready to tackle such problems." So far the conjecture has been checked for all starting values up to $87 \times...
Mathematics made simple.