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

One of’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

Paperback | 2017 | $17.95 | £14.95 | ISBN: 9780691175782
Hardcover | 2013 | $26.95 | £21.95 | ISBN: 9780691156491
192 pp. | 6 x 9 1/4 | 41 halftones. 41 line illus.
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A Q&A with Lance Fortnow
Supplemental materials at Lance Fortnow's website

The P-NP problem is the most important open problem in computer science, if not all of mathematics. Simply stated, it asks whether every problem whose solution can be quickly checked by computer can also be quickly solved by computer. 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. Lance Fortnow traces the history and development of P-NP, giving examples 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. The Golden Ticket explores what we truly can and cannot achieve computationally, describing the benefits and unexpected challenges of this compelling problem.

Lance Fortnow is professor and chair of the School of Computer Science at Georgia Institute of Technology and the founder and coauthor of the Computational Complexity blog.


"As Fortnow describes. . . 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

"A provocative reminder of the real-world consequences of a theoretical enigma."--Booklist

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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

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