The P vs. NP problem

The resounding success of computers has often led to some common misconceptions about “computer science” — namely that it is simply a technological endeavor driven by a search for better physical material and devices that can be used to build smaller, faster, computers. Without trivializing this important quest, this article would like to highlight the complementary science behind computing: namely the search for efficient algorithms (or programs or procedures or software, depending on the readers preference) and the profound implications of this science, not only to the technology of computing, but almost all other disciplines including mathematics, physics and other physical sciences, as well as the social sciences including economics, psychology and indeed, even philosophy! In this article we will attempt to introduce some of the very basic elements of the theory of computing starting with elementary examples of computational tasks that everyone is familiar with. We will then describe Turing’s contributions in the 1930s that led to the development of both computers and a theory of computers. We will conclude with a description of the more modern theory of efficient computing from the 1970s leading to the question “Is P = NP?”. We will explain the question, its significance and the important consequences of its resolution (depending on how the question is resolved).