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The Golden Ticket: P, NP, and the Search for the Impossible, by Lance Fortnow
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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.
- Sales Rank: #157600 in eBooks
- Published on: 2013-03-27
- Released on: 2013-03-27
- Format: Kindle eBook
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
Review
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
"This is a fabulous book for both educators and students at the secondary school level and above. It does not require any particular mathematical knowledge but, rather, the ability to think. Enjoy the world of abstract ideas as you experience an intriguing journey through mathematical thinking."--Gail Kaplan, Mathematics Teacher
"Fortnow's book provides much of the background and personal information on the main characters involved in this problem--notably Steven Cook, with a cameo appearance by Kurt Gödel--that one does not get in the more technical treatments. There is a lot of information in this book, and the serious computer science student is sure to learn from it."--James M. Cargal, UMAP Journal
From the Back Cover
"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
Most helpful customer reviews
31 of 33 people found the following review helpful.
The Million Dollar Problem
By Rob Hardy
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. NP is a possibly separate group of problems that cannot be solved quickly by any computer program we have now, but if P = NP, then a powerful computer could solve those NP problems as easily as computers are currently solving the P ones. One of the important parts of Fortnow's book is that he shows that the P/NP problem is not something just of interest to mathematicians and computer scientists. It is a critical question in fields as diverse as biology, economics, medicine, and physics. No one has been able to come up with an efficient algorithm that solves any NP problem, which seems to indicate there is no such thing, and that P is not equal to NP. It would be a real surprise if P = NP, but right now there is no proof either way. There are plenty of people working on it. Some of them are the same sort of people who are sure they have proved the classic (and unprovable) problem of trisecting an angle. One computer journal has ruled that it will accept such P/NP proofs from any one author no more often than every two years, because most such attempts are "unreadable or clearly wrong." Fortnow encourages readers to try proving P/NP, "for you cannot truly understand the difficulty of a problem without attempting to solve it," and while his book does not give formal definitions of P/NP that would be the basis for your proof, it has website citations that could start you off. But on the other hand: "Suppose you have actually found a solution to the P versus NP problem," he writes. "How do you get your $1 million check from the Clay Mathematics Institute? Slow down. You almost surely don't have a proof. Realize why your proof doesn't work, and you will have obtained enlightenment."
Not only are you unlikely to get a proof, Fortnow is pessimistic that any mathematician is going to be coming up with one anytime soon. He knows the state of current research on the problem, and says that there is no known line of attack currently being pursued that could lead to a successful proof. Things seem to be at a standstill. He reminds us that it took 357 years to get a proof of Fermat's Last Theorem. While we may continue to butt our heads up against NP problems with merely approximate answers, and while P will increasingly seem not to equal NP, there may be no proof out there ever. Fortnow's book does a fine job of showing why the tantalizing question is an important one, with implications far beyond just computer science.
36 of 42 people found the following review helpful.
FINALLY a Really Up to Date Survey of the Biggest Problem in Science
By Let's Compare Options Preptorial
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 P, NP, and NP-Completeness: The Basics of Computational Complexity -- which takes a kind of "text" approach, with problems, exercises, etc., and is a lot more technically oriented (interpret: dry) than Fortnow.
Contents include: The Golden Ticket, The Beautiful World, P and NP, The Hardest Problems in NP, The Prehistory of P vs. NP, Dealing with Hardness, Proving P does not equal NP (which this author believes), Secrets, Quantum, and The Future.
This book is truly FUN and READABLE-- Fortnow peppers every page with anecdotes, examples, side stories, cartoons, diagrams, and an amazing array of connections. Past explorations couldn't even have asked if it's possible to scan for the largest Facebook friends lists, because Facebook didn't exist during most of the past P/NP books frames!
If you want a more general intro to computational complexity, Neil Johnson's little triple reprint from 07 to 2012 is outstanding: Simply Complexity: A Clear Guide to Complexity Theory, and is under 10 bucks. For an exploration of how P/NP fits with the other current millenial problems, an outstanding new book is Ian Stewart's Visions of Infinity: The Great Mathematical Problems. To go a level higher, and see how computational complexity fits more generally in Systems Science and systems thinking, Flood's 2010 book is a gem: Dealing with Complexity: An Introduction to the Theory and Application of Systems Science (Language of Science).
NONE of these, however, are as gentle an introduction, with as complete and detailed coverage, as Fortnow. This is a must have if you have any interest in the biggest and toughest and perhaps most important problem of our age. The icing on the cake is the really fun read of a really dry topic!
EMAILERS-- update: For those who want more math on complexity than Fortnow gives, but not beyond advanced undergrad, check out this truly undiscovered gem by Sole: Phase Transitions (Primers in Complex Systems).
Library Picks reviews only for the benefit of Amazon shoppers and has nothing to do with Amazon, the authors, manufacturers or publishers of the items we review. We always buy the items we review for the sake of objectivity, and although we search for gems, are not shy about trashing an item if it's a waste of time or money for Amazon shoppers. If the reviewer identifies herself, her job or her field, it is only as a point of reference to help you gauge the background and any biases.
13 of 15 people found the following review helpful.
Popularizing P vs NP for the laymen
By haig shahinian
A rare popular science book about the P vs NP problem. The author takes care in using concrete examples and simplifying explanations as much as possible, though I think at times he makes it too simple. I especially liked that he included the history of how the problem developed on both sides of the iron curtain during the cold war. This book may be a nice read for people who don't have much of a science or math background, but for those who do I don't think they will get enough out of it compared with just reading some wikipedia articles.
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