The Collatz conjecture
The Collatz conjecture is an unresolved conjecture in mathematics. It is named after Lothar Collatz, who first proposed it in 1937. The conjecture is also known as the 3n + 1 conjecture, the Ulam conjecture (after Stanislaw Ulam), the Syracuse problem, as the hailstone sequence or hailstone numbers, or as Wondrous numbers as per Gödel, Escher, Bach. It asks whether a certain kind of number sequence always ends in the same way, regardless of the starting number.
Paul Erdős said about the Collatz conjecture: “Mathematics is not yet ready for such problems.” He offered $500 for its solution.
Now go out and solve it and I’ll personally eat my own hat (if I had any).
