In computer science and mathematics, "undecidable" refers to problems or questions that cannot be definitively resolved by any algorithm or computational method. This means there is no systematic way to determine a yes or no answer for all possible inputs. A famous example of an undecidable problem is the Halting Problem, which asks whether a given program will eventually stop running or continue indefinitely. Undecidability is significant because it highlights the limitations of formal systems and algorithms. It shows that there are inherent boundaries to what can be computed or proven, as established by Kurt Gödel's incompleteness theorems. These theorems demonstrate that in any sufficiently complex mathematical system, there will always be true statements that cannot be proven within that system.