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

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From Booklist

*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""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 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)"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

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Product details

Hardcover: 192 pages

Publisher: Princeton University Press; First Edition edition (March 31, 2013)

Language: English

ISBN-10: 0691156492

ISBN-13: 978-0691156491

Product Dimensions:

6.5 x 1 x 9.5 inches

Shipping Weight: 15.2 ounces (View shipping rates and policies)

Average Customer Review:

3.9 out of 5 stars

41 customer reviews

Amazon Best Sellers Rank:

#667,466 in Books (See Top 100 in Books)

Having personally neglected computational theory for almost two decades since completing my doctorate in computer science, this read was a blast - not only reminding me of the main themes of the topic, but seeing a bigger perspective around it than I'd ever previously been taught - plus a lot of new aspects have developed over those years (e.g., I still thought of P/NP as being about deterministic versus non-deterministic, rather than today's more common vantage: recognizing versus finding a solution to a problem instance).The footnote on page 111 is my favorite footnote ever.Given my background, I wouldn't mind (for the Second Edition?) a 2- or 3-page appendix with a Wikipedia type of entry about the technical details, so I could remind myself and ruminate more deeply without interrupting my transcendental state by running back to an actual computer screen, but that is hardly a criticism of the book, given its purpose.My work is in machine learning (aka, predictive analytics), and the author touches upon how P/NP relates to my field; tantalizing food for thought. Machine learning is not just optimization, though; beyond optimizing over a training data set, you need to ensure it then continues to perform well over data not used to optimize it. Hmm, how does this play out if P=NP?Eric Siegel, Ph.D.Founder, Predictive Analytics WorldAuthor, Predictive Analytics: The Power to Predict Who Will Click, Buy, Lie, or Die

Everything is doing some computations. Everything in the whole universe. The computational flavours range from Math and Physics to Biology and Economics; bounded by our current science. Some computations are feasible within human timeframe (P - polynomial), some are not (NP-complete - non polynomial). For example, you can easily start a computation at home that will outlive yourself. What a messy universe! (Even light travels so slow here) The golden ticket to “paradise” is to proof that hard problems (NP) can be reduced to possible problems (P), then P = NP. Lance explores this magnificent challenge using several entertaning analogies (e.g., finding one ticket within many many chocolate bars). To conclude that, maybe, even ask if P=NP is completely nonsense but it is pushing us forward. Some of us are adventurous enough to try impossible things and civilization has been accumulating their results .

Lance Fortnow's new book is an inspiring, accessible, and imaginative overview of P versus NP that everyone can read and appreciate, which until now has been conspicuously missing from the literature. Within the "folklore" of complexity theory, people have long uttered intuitive phrases to motivate P versus NP in passing, such as "P versus NP is asking whether creativity can be automated by computers." Fortnow takes these intuitions and expands them, like no one else has before: really imagining a world where P = NP, exploring the magic of computing in that world, and arguing why that world is unlikely to exist. He also discusses a historical account of the problem's origins in both the East and West, how people cope with P versus NP in practice, some past attempts at resolving P versus NP, the applications to cryptography, and the relevance of quantum computing. All this in less than 200 pages!There is an intellectual cost to the immediate accessibility of this book: for example, P and NP are never really formally defined. If you would like to *work* on P versus NP, or (less ambitiously) are looking for a technical overview of the problem, there are many available books to recommend such as Scott Aaronson's new Quantum Computing since Democritus or Sipser's classic textbook Introduction to the Theory of Computation. However, if you're just looking for a high-level explanation of why P versus NP is so important, Fortnow's book is a great place to start.

I really enjoyed this book. It was a light enough read to finish in one sitting on a weeknight within a few hours, but also showed its importance by being able to connect the dots between the P = NP problem to issues in health care, economics, security, scheduling and a number of other problems. And instead of talking in a "professor-like" tone, the author creates illustrative examples in Chapters 2 and 3 that are easy to grasp. These examples form the basis for much of the problems addressed in the book.This is a book that needed to be written and needs to be on everyone's bookshelf, particularly for those asking questions like "what is mathematics" or "what is mathematics used for". This book answers those questions, and towards the end gives examples (in plain English) of the different branches of mathematics and theoretical computer science, without making it read like a text book.

The book contains no algorithms. It covers the history of complexity theory and speculates about a science fictionesque future in which cancer would be cured if only we could solve one NP-complete problem, but the author doubts it will happen. It reads like the script of a Discovery Channel program.

Worth reading for the clarification that Shor's factoring algorithm is not in fact an example of quantum computers solving an NP complete problem, a misconception I had going into the book. Reads like a magazine article.

I'm giving this 5 stars because:1.It was interesting enough to read straight through.2.I thought the author did a nice job balancing making it technical enough, but not too much, for the intended audience, an intelligent reader interested in the subject, but not wanting to be overwhelmed with technical items.3.It cost less that $10.00 (Kindle).

I especially liked the fact that the author explained the topic well, while resisting the temptation to create a giant book full of repetitious examples. I didn't fully understand some of the analogies but still feel like I have a better understanding of what the P vs. NP problem is - and why it matters to all of us.

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