The 3n+1 Problem
One of mathematics' greatest unsolved mysteries
The Collatz Conjecture (also called the 3n+1 problem) is one of the most famous unsolved problems in mathematics. Despite its simple rules, no one has proven whether it's true for ALL positive integers!
The Conjecture: No matter what positive integer you start with, you will ALWAYS eventually reach 1.
Status: ⚠️ UNPROVEN - Verified for all numbers up to 2⁶⁸ (≈ 295 quintillion), but no general proof exists!
Why is it unsolved? The sequence behavior appears chaotic and unpredictable. Some numbers reach 1 quickly, others take hundreds of steps and reach enormous peak values before descending.
Famous Quote: "Mathematics is not yet ready for such problems." - Paul Erdős