# The Golden Ticket: P, NP, and the Search for the Impossible

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**Publisher:**Princeton University Press-
**Format:**Hardback | 192 pages -
**Dimensions:**163mm x 236mm x 20mm | 431g **Publication date:**1 May 2013**Publication City/Country:**New Jersey**ISBN 10:**0691156492**ISBN 13:**9780691156491**Illustrations note:**41 halftones. 41 line illus.**Sales rank:**192,259

### Product description

The P-NP problem is the most important open problem in computer science, if not all of mathematics. The Golden Ticket provides a nontechnical introduction to P-NP, its rich history, and its algorithmic implications for everything we do with computers and beyond. In this informative and entertaining book, Lance Fortnow traces how the problem arose during the Cold War on both sides of the Iron Curtain, and gives examples of the problem from a variety of disciplines, including economics, physics, and biology. He explores problems that capture the full difficulty of the P-NP dilemma, from discovering the shortest route through all the rides at Disney World to finding large groups of friends on Facebook. But difficulty also has its advantages. Hard problems allow us to safely conduct electronic commerce and maintain privacy in our online lives. The Golden Ticket explores what we truly can and cannot achieve computationally, describing the benefits and unexpected challenges of the P-NP problem.

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### Author information

Lance Fortnow is professor and chair of the School of Computer Science at the Georgia Institute of Technology. He founded and coauthors the Computational Complexity blog.

### Review quote

One of Amazon.com's 2013 Best Science Books One of Choice's Outstanding Academic Titles for 2013 Honorable Mention for the 2013 PROSE Award in Popular Science & Mathematics, Association of American Publishers "As Lance Fortnow describes in his new book, The Golden Ticket: P, NP and the Search for the Impossible, P versus NP is 'one of the great open problems in all of mathematics' not only because it is extremely difficult to solve but because it has such obvious practical applications. It is the dream of total ease, of the confidence that there is an efficient way to calculate nearly everything, 'from cures to deadly diseases to the nature of the universe,' even 'an algorithmic process to recognize greatness.'... To postulate that P ? NP, as Fortnow does, is to allow for a world of mystery, difficulty, and frustration--but also of discovery and inquiry, of pleasures pleasingly delayed."--Alexander Nazaryan, New Yorker "Fortnow effectively initiates readers into the seductive mystery and importance of P and NP problems."--Publishers Weekly "Fortnow's book is just the ticket for bringing one of the major theoretical problems of our time to the level of the average citizen--and yes, that includes elected officials."--Veit Elser, Science "Without bringing formulas or computer code into the narrative, Fortnow sketches the history of this class of questions, convincingly demonstrates their surprising equivalence, and reveals some of the most far-reaching implications that a proof of P = NP would bring about. These might include tremendous advances in biotechnology (for instance, more cures for cancer), information technology, and even the arts. Verdict: Through story and analogy, this relatively slim volume manages to provide a thorough, accessible explanation of a deep mathematical question and its myriad consequences. An engaging, informative read for a broad audience."--J.J.S. Boyce, Library Journal "[This] as-yet-unsolved problem--identified by mathematicians as the P-NP problem--raises fundamental questions about just how far society can ride the technological wave triggered by the computer revolution. Fortnow unfolds a fascinating dual-track story of how this problem first emerged, Western researchers encountering it while trying to maximize computer efficiency, Russian analysts confronting it while puzzling over the persistent need for perebor ('brute force search'). Readers watch as the P-NP problem attracts investigators in cryptography, biology, quantum physics, and social networking--and frustrates them all. Fortnow allows nonspecialist readers to glimpse the conceptual difficulties here (try 'nondeterministic polynomial time,' for example). But he mercifully frames his discussion largely in nontechnical terms. Even readers averse to mathematics will share in the intellectual stimulation of pondering a riddle compelling us to ask what we should hope for--and fear--in replacing human brains with computer algorithms. A provocative reminder of the real-world consequences of a theoretical enigma."--Bryce Christensen, Booklist "The definition of this problem is tricky and technical, but in The Golden Ticket, Lance Fortnow cleverly sidesteps the issue with a boiled-down version. P is the collection of problems we can solve quickly, NP is the collection of problems we would like to solve. If P = NP, computers can answer all the questions we pose and our world is changed forever. It is an oversimplification, but Fortnow, a computer scientist at Georgia Institute of Technology, Atlanta, knows his stuff and aptly illustrates why NP problems are so important."--Jacob Aron, New Scientist "Fortnow's book does a fine job of showing why the tantalizing question is an important one, with implications far beyond just computer science."--Rob Hardy, Commercial Dispatch "A great book... [Lance Fortnow] has written precisely the book about P vs. NP that the interested layperson or IT professional wants and needs."--Scott Aaronson, Shtetl-Optimized blog "[The Golden Ticket] is a book on a technical subject aimed at a general audience... Lance's mix of technical accuracy with evocative story telling works."--Michael Trick, Michael Trick's Operations Research Blog "Thoroughly researched and reviewed. Anyone from a smart high school student to a computer scientist is sure to get a lot of this book. The presentation is beautiful. There are few formulas but lots of facts."--Daniel Lemire's Blog "An entertaining discussion of the P versus NP problem."--Andrew Binstock, Dr. Dobb's "The Golden Ticket is an extremely accessible and enjoyable treatment of the most important question of theoretical computer science, namely whether P is equal to NP... [I]t is a very pleasant read for those specializing in discrete mathematics, and understandable to anyone with an undergraduate knowledge of mathematics."--Choice "The book is accessible and useful for practically anyone from smart high school students to specialists... [P]erhaps the interest sparked by this book will be the 'Golden Ticket' for further accessible work in this area. And perhaps P=NP will start to become as famous as E=mc2."--Michael Trick, INFORMS Journal of Computing "In any case, it is excellent to have a nontechnical book about the P versus NP question. The Golden Ticket offers an inspiring introduction for nontechnical readers to what is surely the most important open problem in computer science."--Leslie Ann Goldberg, LMS Newsletter "The Golden Ticket does a good job of explaining a complex concept in terms that a secondary-school student will understand--a hard problem in its own right, even if not quite NP."--Physics World "The whole book is fun to read and can be fully appreciated without any knowledge in (theoretical) computer science. Fortnow's efforts to make the difficult material accessible to non-experts should be commended... The book thus caters to all audiences: from novices with an interest in computational problems to experts with knowledge in theoretical computer science."--Andreas Maletti, Zentralblatt MATH

### Flap copy

"You will love this book. It's completely accessible and captures the thrill, potential, and heartbreak of an edgy mathematical problem in terms that nonmathematicians will appreciate. After reading The Golden Ticket, I sort of hope P isn't NP after all."--Vint Cerf, Google Vice President and Chief Internet Evangelist and one of the "Fathers of the Internet" "The P-NP problem is fundamental to computer science, and indeed all of mathematics. This book presents an engaging exposition of the problem, its history, and importance. In the process, it touches on major topics appearing in university computer science courses, all presented in an amusing style requiring no background in mathematics beyond the ability to solve Sudoku puzzles. I highly recommend it."--Stephen Cook, formulator of the P-NP problem "This book, written by a world-class master of the field, is a grand tour of the most celebrated and profound unsolved problem in computer science. Fortnow's many ingenious explanations make the mysteries of computational complexity accessible to anyone interested in the fundamental questions: what can be computed and how fast can we compute it?"--John MacCormick, author of "Nine Algorithms That Changed the Future" "This book is meticulous. Fortnow has really tracked down the history and background of this important and timely subject. Even complexity theorists will benefit from his fine scholarship. The Golden Ticket is the first of its kind--a book for general readers about complexity theory."--William Gasarch, University of Maryland "Nobody explains the importance of the P-NP problem better than Fortnow."--William J. Cook, author of "In Pursuit of the Traveling Salesman: Mathematics at the Limits of Computation"

### Table of contents

Preface ix Chapter 1 The Golden Ticket 1 Chapter 2 The Beautiful World 11 Chapter 3 P and NP 29 Chapter 4 The Hardest Problems in NP 51 Chapter 5 The Prehistory of P versus NP 71 Chapter 6 Dealing with Hardness 89 Chapter 7 Proving P NP 109 Chapter 8 Secrets 123 Chapter 9 Quantum 143 Chapter 10 The Future 155 Acknowledgments 163 Chapter Notes and Sources 165 Index 171