uncomputability

Uncomputability refers to problems that cannot be solved by any algorithm, no matter how much time or resources are available. This concept is central to computer science and mathematics, stemming from the work of mathematicians like Kurt Gödel and Alan Turing.123

Gödel's incompleteness theorems demonstrated that within any sufficiently complex formal system (like those used for arithmetic), there will always be true statements that cannot be proven within that system. Turing's work on the halting problem provided a concrete example of an unsolvable algorithmic problem: it's impossible to create a program that can determine whether any given program will eventually stop or run forever. These findings highlight fundamental limits to what can be computed.314