Cook's Theorem
Cook's Theorem is a fundamental result in computational complexity theory, established by Stephen Cook in 1971. It states that the Boolean satisfiability problem (SAT) is NP-complete, meaning that it is at least as hard as the hardest problems in the class NP. If a polynomial-time algorithm exists for SAT, then it can be used to solve all NP problems efficiently.
The theorem implies that no known polynomial-time algorithm can solve all NP-complete problems, assuming P ≠ NP. This has significant implications for computer science, as it suggests that certain problems may inherently require more computational resources to solve than others.