Books like Theory of computation by Michael Sipser

In Meta Math!, Gregory Chaitin, one of the world's foremost mathematicians, leads us on a spellbinding journey of scientific discovery and illuminates the process by which he arrived at his groundbreaking theories.All of science is based on mathematics, but mathematicians have become painfully aware that math itself has serious limitations. This notion was first revealed in the work of two giants of twentieth-century mathematics: Kurt Godel and Alan Turing. Now their successor, Gregory Chaitin, digs even deeper into the foundations of mathematics, demonstrating that mathematics is riddled with randomness, enigmas, and paradoxes.Chaitin's revolutionary discovery, the Omega number, is an exquisitely complex representation of unknowability in mathematics. His investigations shed light on what, ultimately, we can know about the universe and the very nature of life. But if unknowability is at the core of Chaitin's theories, the great gift of his book is its completely engaging knowability. In an infectious and enthusiastic narrative, Chaitin introduces us to his passion for mathematics at its deepest and most philosophical level, and delineates the specific intellectual and intuitive steps he took toward the discovery of Omega. In the final analysis, he shows us that mathematics is as much art as logic, as much experimental science as pure reasoning. And by the end, he has helped us to see and appreciate the art--and the sheer beauty--in the science of math.In Meta Math!, Gregory Chaitin takes us to the very frontiers of scientific thinking. It is a thrilling ride.From the Hardcover edition.

361 p. : 25 cm

An accessible guide to the P‑NP problem, its history, and its impact on computing, economics, physics, biology, and everyday life.