P versus NP is a fundamental question in computer science and mathematics that addresses the relationship between the complexity classes P and NP. The class P consists of problems that can be solved quickly (in polynomial time) by a deterministic Turing machine. In contrast, NP is the class of problems for which a given solution can be verified quickly (in polynomial time) by a deterministic Turing machine. The P vs NP problem asks whether every problem whose solution can be quickly verified can also be quickly solved. This question has profound implications for fields such as cryptography, algorithm design, artificial intelligence, and more. Despite significant efforts, it remains one of the most important unsolved problems in theoretical computer science.
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