A Beautiful Math: John Nash, Game Theory, and the Modern Quest for a Code of Nature [Hardcover]

Tom Siegfried (Author), Joseph Henry Press (Author)

Book Description

Publication Date: September 25, 2006

Millions have seen the movie and thousands have read the book but few have fully appreciated the mathematics developed by John Nash's beautiful mind. Today Nash's beautiful math has become a universal language for research in the social sciences and has infiltrated the realms of evolutionary biology, neuroscience, and even quantum physics. John Nash won the 1994 Nobel Prize in economics for pioneering research published in the 1950s on a new branch of mathematics known as game theory. At the time of Nash's early work, game theory was briefly popular among some mathematicians and Cold War analysts. But it remained obscure until the 1970s when evolutionary biologists began applying it to their work. In the 1980s economists began to embrace game theory. Since then it has found an ever expanding repertoire of applications among a wide range of scientific disciplines. Today neuroscientists peer into game players' brains, anthropologists play games with people from primitive cultures, biologists use games to explain the evolution of human language, and mathematicians exploit games to better understand social networks. A common thread connecting much of this research is its relevance to the ancient quest for a science of human social behavior, or a Code of Nature, in the spirit of the fictional science of psychohistory described in the famous Foundation novels by the late Isaac Asimov. In A Beautiful Math, acclaimed science writer Tom Siegfried describes how game theory links the life sciences, social sciences, and physical sciences in a way that may bring Asimov's dream closer to reality.

Editorial Reviews

From Publishers Weekly

The title capitalizes on the popularity of the Oscar-winning movie about Nobel Prize–winning mathematician John Nash. But this is a serious and adroit look at a branch of mathematics, influenced by Nash's work, that is steadily sending tendrils into nearly every area of science. It may even, says science journalist Siegfried, result in a mathematical description of nature of the sort imagined and called "psychohistory" by Isaac Asimov in his Foundation trilogy. Siegfried is talking about game theory, which was originally conceived as a model of economics predicting what rational people would do when competing for monetary gain. But with the help of the "Nash equilibrium," it has since evolved into a system that helps describe social networking, physics, evolution and more. In guiding the reader through the outgrowths of game theory, Siegfried steps nimbly around anything that would bog down the narrative, crisply painting the key concepts and framing them with pop culture, biographies of and conversations with giants in the field, and reacting ("Now, you have to admit, that's a little strange") to each new discovery. His clear and easy voice makes the content effortless and a pleasure to read. (Oct. 20)
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From the Author

You’re a science journalist who is interested in many topics. Why game theory?

It’s precisely because of the many different topics in science that game theory touches. It was invented for use in economics, but over the decades its applications have extended to biology, psychology, anthropology, neuroscience and even quantum physics. Science journalism ought to report new scientific insights, and game theory has become a spectacular tool for identifying many new insights.

What is it about science that really generates the passion necessary to explore it in such depth?

Science is the one common language for coping with the world that transcends personal preferences and prejudicial ideologies. Many people, even some scientists, nevertheless try to impose their preferences or ideologies on science. In my writings I try to cut through those prejudices to find the evidence, interpreted by sound reasoning, that tells nature’s true story. The search for that evidence and reasoning is what drives me.

The movie or the book – which did you like better?

The book, of course. The movie was very entertaining but bore very little resemblance to the true story and pretty much garbled what little it described about John Nash’s math. The book was a skillfully written biography that provided some flavor of the math, although it did not explore game theory’s widespread use across the spectrum of scientific disciplines.

See all Editorial Reviews

Product Details

• Hardcover: 272 pages
• Publisher: Joseph Henry Press; 1st ed edition (September 25, 2006)
• Language: English
• ISBN-10: 0309101921
• ISBN-13: 978-0309101929
• Product Dimensions: 6 x 1.1 x 9 inches
• Shipping Weight: 1.2 pounds (View shipping rates and policies)
• Average Customer Review: 3.7 out of 5 stars  See all reviews (10 customer reviews)
• Amazon Best Sellers Rank: #941,726 in Books (See Top 100 in Books)

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Most Helpful Customer Reviews

21 of 24 people found the following review helpful

1.0 out of 5 stars Journalistic hypes and some patently false claims August 3, 2007

By Sung H. Kim

Format:Hardcover

I am an academic economist who knows something about game theory, so when I bought this book I did not hope to learn anything new but just to be entertained by an "illuminating" author during my leisure hours. I was disappointed to the point of anger.

This book is basically a journalist's report based on interviews with a few (probably half a dozen) individuals as the pages are filled with quotes from several academics in good standing. I think it would have been better to simply present many illuminating quotes from these individuals without inserting additional insights that the author gleaned from them, because many of the author's insertions were at best misleading and at worst patently false.

Just for an example, the author keeps insisting that payoff numbers in games are "money" as economists are interested in monetary matters. It might probably be true that von Neumann preferred interpreting payoffs of a game as money, but most practicing economists and game theorists certaintly do not do that.

An annoying repeated phrase is that "xxx told me (in an exclusive interview) that..." where xxx is one of the half dozen individuals mentioned above. Most of what xxx told the author must be correct, relevant and have some meaning but these are simply taken out of context by bits and spread throughout the text.

Also the basic hype about game theory's possibility to be a Theory of Everything seems to come out of (as the author admits) one person's recent writings at Bell Labs.... The idea itself presented as such sounds simply outrageous (even to an academic economist like myself) but rather a surpring fact is that game theory's origins are in fact related to such an outrageous idea from physicists, mathematicians and "cyberneticians", one story of which is told in Mirowski, Machine Dreams. Mirowski's book has its own faults, and is a lot more heavy going (with some 500 + pages with small fonts and requiring a lot of knowledge), but at least it shows seriousness and a lot of research the author took to it. Read more ›

16 of 18 people found the following review helpful

1.0 out of 5 stars for the beginner and rather misleading June 19, 2007

By M. Mulhollam

Format:Hardcover

This is a 215 page book. If you are familiar with the Prisoner's Dilemma there just isn't a whole lot here for you. The discussion of statistical mechanics pales in comparison (and is rather similar to the outline of) Philip Ball's vastly superior "Critical Mass". Go there first. I know that is a different subject but a good chunk of this book discusses it. The author creates a ridiculous and unrealistic strawman of evolutionary pyschology and then repeatedly belittles it because human societies are variable (what a novel and unexpected concept!). Usuaully the author presents one example of work within each field he discusses - I suppose this keeps it readable but disappointing light fare. Go read "Critical Mass", don't waste your time with this.

11 of 12 people found the following review helpful

4.0 out of 5 stars I think I get it know March 12, 2007

By Jeffrey Leeper

Format:Hardcover

I first picked up this book because I thought it would be more of a biography of John Nash. The book is more a discussion of how game theory can be used to help understand nature.

The book was very readable and even gave me a historic perspective about where this trend is going. Although there is some very limited math in the book, it is very clearly explained. The books is very readable and engaging.

After reading this book, I know want to know more about game theory and its predictive capabilities. I would highly recommend this book.

9 of 10 people found the following review helpful

5.0 out of 5 stars Brilliant .. expert storytelling November 21, 2006

By SG

Format:Hardcover

If you read or saw "A Beautiful Mind" and think there was drama in John Nash's creative madness, wait until you plunge into the work that drove him. Even without a background in (or any natural talent for) math, this story swept me up completely and, like previous reviewers, I had a hard time putting the book down. Siegfried expertly ushers the reader into the heart of a branch of mathematics that influences everything from pop culture to Nobel-winning science .. and does so in a way that leaves you feeling awed, inspired, and eager for more.

6 of 7 people found the following review helpful

5.0 out of 5 stars Far-Reaching Theory Now Accessible December 12, 2006

By J Shamon

Format:Hardcover

The movie "A Beautiful Mind" was inspiring and touching. But, it really did not explain Nash's contributions to the world in the form of game theory. Now readers have a chance to understand the theory and practice behind this Nobel Prize winning discovery in Tom Siegfried's book, "A Beautiful Math."

This thorough, historical, mathematical, and metaphorical description of game theory really helps me to see the implications of Nash's discovery. This work influences psychology, evolutionary biology, sociology, anthropology, statistical physics, quantum physics and more. Its far-reaching implications are brought to life within an eloquent explanation that touches on all branches of science.

5.0 out of 5 stars interesting April 22, 2013

By F. Jafari

Format:Hardcover|Amazon Verified Purchase

A good introduction to game theory and its many applications. This, and other books like it (e.g. Brian Greene, etc) should become standard textbooks for high school students wanting to know where math goes.

3 of 5 people found the following review helpful

3.0 out of 5 stars Brilliantly understood and explained, questionably authored. July 2, 2007

By M. Rixman

Format:Hardcover

The book jacket tells us that Seigfried won an award "for interpreting [science] for the public." I'm sure that that award was well deserved, for he has a knack for taking complex ideas and presenting them to a less-educated crowd. His two or three page explanations of concepts that took me weeks (and loads of homework/study) to grasp are nothing short of amazing. He often uses examples or analogies rooted in works of fiction to illustrate his points. The way these works are summarized to include only relevant information, and yet still capture the essence of those stories, is marvelous. Also, unlike many books of this genre, after reading it I did not feel like I needed to re-take any classes or brush up on my math. In fact, the most in-depth math involved (calculating a Nash equilibrium) should be crystal clear to a tenth-grader, and it is conveniently relocated to an appendix so that it doesn't bother any take-your-word-for-it readers.

Why only three stars then? Because this is a book review, and explanatory prowess isn't the only thing that it takes to write a book.

The humor in the book is very hit-and-miss. I wouldn't remove it, because when it hits... it's wonderful, but perhaps he should've gotten a humor-editor, someone to help him decide what to include and what to leave out. For example, Seigfried goes about explaining the mathematical differences between what he calls a "Robinson Crusoe economy" (one in which a single person makes decisions about fixed values) and a "Gilligan's island economy" (one in which each person makes decisions based upon other people, who make decisions based on other people, who...). Seigfried states that,

"Mathematically, that meant that no longer could you simply compute ... for Robinson Crusoe.... Your calculations had to accommodate ... for Gilligan, the Skipper too, the millionaire, and his wife, the movie star, the Professor, and Mary Ann."

How cool! But then there are other instances. While using a game between fictional characters Alice and Bob to demonstrate some simple game theory, he inserts parenthetically: "(As I said, Alice would probably tell him to shove it)," directly between two rules of the game. We had already been told that this game was not in Alice's favor, and that it was simplified for the purpose of example. The text is peppered about equally with good, relevant, non-interrupting humor, as it is with not-so-good humor.

Furthermore, while he can explain very-high-level science to a high-school-graduate (and two thumbs up for that) his narration seems to be directed at an audience with a damaged memory. I say this because we are told at least four times that Colin Camerer is into Behavioral Game Theory, and that Neuroeconomics is a fledgling hybrid field.
The organization of the book favors the understanding of game theory over the understanding of its history. One is presented with concepts fundamental to game theory, some uses of it, some game theory developments, some views into advanced game theory; it works very well to foster understanding. With each chunk of theory work, Seigfried includes the history (which I was pleasantly surprised at--it's fascinating) that contributed to that chunk of theory. The problem here is that the first section takes place mostly in the eighteenth century, the second-to-last section in the twenty-first, and the last section in the seventeenth and also the twentieth. The jumping around in time was confusing. I can't say what the best organisational method is, but I don't think this is it.

Lastly, and most importantly, is the hype that he gives game theory. I am interested in it, that's why I picked up the book, and the occasional renewal of that interest was nice, but he takes it a step too far. The reader is told time and time again how freakin' amazing game theory is, it's all true. The problem is that after pages of this game theory hype, and a mid-book discrediting of some evolutionary psychologists who dared disagree, I begin to question how strongly his bias is affecting his writing. It doesn't come across too strongly until the final few pages (which, in my mind, bumped it down from a four-star) in which he compares game theory to a unified field theory, or physics' golden "theory of everything." He says game theory is the theory concerned with everything else (i.e. the social/biological/economic half of everything). I agree that it could be a framework to hold "everything else" together, but that's like saying that all baked goods can be divided between pie, and things-with-frosting. It doesn't include the whole picture, and it does so in a deceptive way.

I should, however, admit that I am subject to the same type of biases as the author. When I read, in that last few pages, that:

"Game theory is not, however, the same as the popular 'Theory of Everything' that theoretical physicists have long sought. That quest is mearly for the equations describing all of nature's basic particles and forces, the math describing the building blocks."

I became quite upset: MEARLY?! that theory is only one of the most important goals of science, ever! Well, you can see that my bias clouds my judgement too, interperet as you will...

So buy this book, I can't stress enough how great the explanations within are, but take it with a grain of salt (and perhaps some of your own research). Read more ›