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![The Collatz conjecture[a] is one of the most famous unsolved problems in mathematics. The conjecture asks whether repeating two simple arithmetic operations will eventually transform every positive integer into 1. It concerns sequences of integers in which each term is obtained from the previous term as follows: if a term is even, the next term is one half of it. If a term is odd, the next term is 3 times the previous term plus 1. The conjecture is that these sequences always reach 1, no matter which positive integer is chosen to start the sequence. The conjecture has been shown to hold for all positive integers up to 2.36×1021, but no general proof has been found. Unsolved problem in mathematics For even numbers, divide by 2; For odd numbers, multiply by 3 and add 1. With enough repetition, do all positive integers converge to 1? More unsolved problems in mathematics Directed graph showing the orbits of small numbers under the Collatz map, skipping even numbers. The Collatz conjecture states that all paths eventually lead to 1. It is named after the mathematician Lothar Collatz, who introduced the idea in 1937, two years after receiving his doctorate.[4] The sequence of numbers involved is sometimes referred to as the hailstone sequence, hailstone numbers or hailstone numerals (because the values are usually subject to multiple descents](/video/cover/7703291683513027861.webp)