Unsolvability

Unsolvability refers to problems in mathematics and computer science that cannot be solved by any algorithm or systematic procedure. Despite a problem’s clear definition, no step-by-step process exists that can always provide a correct answer within finite time. An example is the Halting Problem, which asks whether a program will eventually stop or run forever; it’s proven that no general method can solve this for all possible programs. This concept highlights fundamental limits in computation, indicating that some questions are inherently unanswerable through algorithmic methods.