Knowledge, Creativity and P versus NP

The human quest for efficiency is ancient and universal. Computational Complexity Theory is the mathematical study of the efficiency requirements of computational problems. In this note we attempt to convey the deep implications and connections of the results and goals of computational complexity, to the understanding of the most basic and general questions in science and technology. In particular, we will explain the P versus NP question of computer science, and explain the consequences of its possible resolution, P = NP or P 6= NP , to the power and security of computing, the human quest for knowledge, and beyond. The connection rests on formalizing the role of creativity in the discovery process. The seemingly abstract, philosophical question: Can creativity be automated? in its concrete, mathematical form: Does P = NP?, emerges as a central challenge of science. And the basic notions of space and time, studied as resources of efficient computation, emerge as key objects of study to solving this mystery, just like their physical counterparts hold the key to understanding the laws of nature. This article is prepared for non-specialists, so we attempt to be as non-technical as possible. Thus we focus on the intuitive, high level meaning of central definitions of computational notions. Necessarily, we will be sweeping many technical issues under the rug, and be content that the general picture painted here remains valid when these are carefully examined. Formal, mathematical definitions, as well as better historical account and more references to original works, can be found in any textbook, e.g. see [14, 17]. We further recommend the surveys [19, 3, 18, 11] for different perspectives on the P versus NP question, its history and importance.