During his PhD, Cook worked on complexity of functions, mainly on multiplication. In his seminal 1971 paper "The Complexity of Theorem Proving Procedures", Cook formalized the notions of polynomial-time reduction (a.k.a. Cook reduction) and NP-completeness, and proved the existence of an NP-complete problem by showing that the Boolean satisfiability problem (usually known as SAT) is NP-complete. This theorem was proven independently by Leonid Levin in the Soviet Union, and has thus been given the name the Cook-Levin theorem. The paper also formulated the most famous problem in computer science, the P vs. NP problem. Informally, the "P vs. NP" question asks whether every optimization problem whose answers can be efficiently verified for correctness/optimality can be solved optimally with an efficient algorithm. Given the abundance of such optimization problems in everyday life, a positive answer to the "P vs. NP" question would likely have profound practical and philosophical consequences.