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

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*Starred Review* In 1956, mathematician Kurt Gödel wrote to computer scientist John von Neumann speculating about how “the mental work of a mathematician . . . could be completely replaced by a machine.” In Gödel’s speculation, Fortnow finds the kernel of what may be the most important mathematical problem of all time. That 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

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One of Amazon.com’s 2013 Best Science Books

"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

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Direct download links available for Free The Golden Ticket: P, NP, and the Search for the Impossible Hardcover

• Product Details
• Table of Contents
• Reviews

• Hardcover: 192 pages
• Publisher: Princeton University Press (March 31, 2013)
• Language: English
• ISBN-10: 0691156492
• ISBN-13: 978-0691156491
• Product Dimensions: 0.8 x 6.5 x 9.5 inches
• Shipping Weight: 1 pounds (View shipping rates and policies)

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

Everyone knows that computers are getting more powerful and better at doing almost anything. Finding you the fastest route cross country is easy. Translating a page of prose from one language to another is harder, but it's getting better all the time. Finding the shortest route that will get you to all of five different cities, no problem; finding the provably shortest route that will get you to all of a thousand cities - that's a toughie. It's so hard that perhaps no computer, no matter how big or how fast, can ever do it. Perhaps. Are there tasks beyond computing? It is a deep question bridging mathematics and computer science, and it is the subject of _The Golden Ticket: P, NP, and the Search for the Impossible_ (Princeton University Press) by Lance Fortnow. The question is so hard, and so important, that it is one of the seven Millennium Problems for which the Clay Mathematics Institute will give you one million dollars when you prove it. (Programming genius Donald Knuth will also give you a turkey.) This is deeper mathematical territory than most of us will ever penetrate, but Fortnow, a professor of computer science, keeps the explanations light, knowing that those of us reading this sort of book aren't really in the running for the prize, but at the same time showing how important the answer to the question might be for the future of computing.

It is best to call it the P/NP problem; the abbreviation P comes from "polynomial;" and in giving us the second, Fortnow jokes, "NP (which stands for `nondeterministic polynomial time,' if you really need to know)." He does not get much deeper into polynomials, but P is the group of problems we know computers can solve quickly.

What an awesome book! P-NP is essentially the question of whether we can find solutions quickly if we can define or know there is a solution quickly-- in layman's terms, it means we know, and then can solve, the traveling salesman problem in "P" -- polynomial -- rather than exponential or infinite time, or not at all. (MAHDI emailed and corrected this by saying: "The second sentence is wrong. P-NP is whether we can find solutions nearly as efficiently as we can verify them. The statement that we can find solutions if we can know there is a solution is a known fact and an easy exercise to prove").

There are a lot of technical books on the topic, but this is the first recent book that explores the golden ticket (finding the ONE in your batch of many that will allow you into Willy Wonka's factory tour) in layman's terms, but without talking down to the reader, and covering and focusing on all the aspects of the question. "How not to prove that P does not equal NP" as the author says, is an example of the complex and convoluted logic that's needed to explore the field of computational complexity.

Most authors, including this one, use public key crytography, factoring, etc. as examples of the "good" things about intractable problems, yet they also point out that if you could solve this problem, all the other millenium prize problems would likely also fall before you! That's more than $5 million US, so this book is definitely worth a careful read! (Ok, little tongue in cheek). The current "go to" text on the topic, from 2010, is Goldreich's

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