The Collatz conjecture is a conjecture in mathematics named after Lothar Collatz, who first proposed it in 1937. The conjecture is also known as the 3n + 1 conjecture, the Ulam conjecture (after Stanisław Ulam), Kakutani's problem (after Shizuo Kakutani), the Thwaites conjecture (after Sir Bryan Thwaites), Hasse's algorithm (after Helmut Hasse), or the Syracuse problem; the sequence of numbers involved is referred to as the hailstone sequence or hailstone numbers, or as wondrous numbers.
Take any natural number n. If n is even, divide it by 2 to get n / 2. If n is odd, multiply it by 3 and add 1 to obtain 3n + 1. Repeat the process (which has been called "Half Or Triple Plus One", or HOTPO) indefinitely. The conjecture is that no matter what number you start with, you will always eventually reach 1. The property has also been called oneness.
Paul Erdős said, allegedly, about the Collatz conjecture: "Mathematics is not yet ripe for such problems" and also offered $500 for its solution.
In 2007, researchers Kurtz and Simon, building on earlier work by J.H. Conway in the 1970s, proved that a natural generalization of the Collatz problem is algorithmically undecidable.
Read more about Collatz Conjecture: Statement of The Problem, Examples, Visualizations, Program To Calculate Hailstone Sequences, M-cycles Cannot Occur, Methods of Proof, Supporting Arguments, Optimizations, Syracuse Function
Famous quotes containing the word conjecture:
“There is something fascinating about science. One gets such wholesale returns of conjecture out of such a trifling investment of fact.”
—Mark Twain [Samuel Langhorne Clemens] (1835–1910)