The Unfinished Game: Pascal, Fermat, and the Seventeenth-Century Letter that Made the World Modern [Hardcover]

Keith Devlin (Author)

Book Description

Series: Basic Ideas | Publication Date: September 23, 2008

Before the mid-seventeenth century, scholars generally agreed that it was impossible to predict something by calculating mathematical outcomes. One simply could not put a numerical value on the likelihood that a particular event would occur. Even the outcome of something as simple as a dice roll or the likelihood of showers instead of sunshine was thought to lie in the realm of pure, unknowable chance.

The issue remained intractable until Blaise Pascal wrote to Pierre de Fermat in 1654, outlining a solution to the “unfinished game” problem: how do you divide the pot when players are forced to end a game of dice before someone has won? The idea turned out to be far more seminal than Pascal realized. From it, the two men developed the method known today as probability theory.

In The Unfinished Game, mathematician and NPR commentator Keith Devlin tells the story of this correspondence and its remarkable impact on the modern world: from insurance rates, to housing and job markets, to the safety of cars and planes, calculating probabilities allowed people, for the first time, to think rationally about how future events might unfold.

Editorial Reviews

From Publishers Weekly

Starred Review. Prior to the development of statistics in the late seventeenth and eighteenth centuries, even rationalists were convinced that no human could speculate on the future. Devlin, NPR's "Math Guy" and the author of numerous books on the subject, shows us how that belief was transformed through the 1654 correspondence between mathematicians Blaise Pascal and Pierre de Fermat. Devlin uses the critical letter from Pascal to Fermat in which he discusses "the problem of points"-that is, how to determine the probable outcome of a game of chance-as a framework for a history of probability theory and risk management, fields which now dominate our social, political and financial lives. Devlin interweaves the specific issues discussed in that famous letter with the work of other mathematicians, like the London businessman John Graunt, whose ingenious, groundbreaking work analyzing London parish death records helped predict a breakout of bubonic plague and essentially founded the science of epidemiology. Devlin also introduces the remarkable Bernoulli family, eight of whom were distinguished mathematicians, and the Reverend Thomas Bayes, whose formula has enabled the calculation of risk in a variety of fields. This informative book is a lively, quick read for anyone who wonders about the science of predicting what's next and how deeply it affects our lives.
Copyright © Reed Business Information, a division of Reed Elsevier Inc. All rights reserved.

Review

"PublishersWeekly.com"
"This informative book is a lively, quick read for anyone who wonders about the science of predicting what's next and how deeply it affects our lives."

"New Scientist"
"This breezy book shows why probability theory, though not Pascal and Fermat's last, was undoubtedly their most important theorem."

"Washington Times"
"Mr. Devlin shares the great mathematicians' correspondence, walks readers through critical mathematical problems and contextualizes it all in a lively narrative. The book is a refreshing testimony to the rewards of thinking rationally about how future events might unfold.... [A] rewarding read.... Mr. Devlin does a remarkable job of showing just how much derived from the history-changing Pascal-Fermat correspondence."

"MAA Online"
"This book is not only about mathematics. It is also a tale of how mathematics, and science in general, is really done.... Very well written and accessible to everyone.... This is highly recommended reading.... [It] should find a place in every mathematician's library."

"Booklist"
"Devlin depicts Fermat as leading Pascal toward correct understanding of probability's underlying logic, through quotation of the entire letter and a characteristically clear explanation of the logic of probability with which Pascal struggled. A rewarding account for math buffs."

David Berlinski, author of "The Devil's Delusion" and "A Tour of the Calculus"
"I've been a faithful reader of Keith Devlin's work for a long time, and this is the best thing I've seen from his pen. It combines a lightness of touch, an understanding of the sources, an absence of anysort of intrusive self, and a sensitive and error-free presentation of the mathematics."

William Dunham, author of "The Calculus Gallery" and "Journey Through Genius"
"Keith Devlin's delightful little book traces the origins of probability theory and introduces the mathematicians--from Pascal and Fermat to Bernoulli and de Moivre--who created it."

Amir Aczel, author of "Fermat's Last Theorem" and "Chance"
"In this enchanting romp through the early history of probability theory, Devlin does a great job explaining the role probability plays in modern life, and shows how probabilistic reasoning, which we almost take for granted today, was a product of the minds of brilliant mathematicians almost four centuries ago."

"Entertainment Weekly"
"Surprisingly engaging."

See all Editorial Reviews

Product Details

• Reading level: Ages 16 and up
  
• Hardcover: 208 pages
• Publisher: Basic Books; 1 edition (September 23, 2008)
• Language: English
• ISBN-10: 0465009107
• ISBN-13: 978-0465009107
• Product Dimensions: 8.5 x 5.7 x 1 inches
• Shipping Weight: 12 ounces
• Average Customer Review: 4.3 out of 5 stars  See all reviews (9 customer reviews)
• Amazon Best Sellers Rank: #865,878 in Books (See Top 100 in Books)

More About the Author

Dr. Keith Devlin is a mathematician at Stanford University in California. He is a co-founder and Executive Director of the university's H-STAR institute, a co-founder of the Stanford Media X research network, and a Senior Researcher at CSLI. He has written 31 books and over 80 published research articles. His books have been awarded the Pythagoras Prize and the Peano Prize, and his writing has earned him the Carl Sagan Award, and the Joint Policy Board for Mathematics Communications Award. In 2003, he was recognized by the California State Assembly for his "innovative work and longtime service in the field of mathematics and its relation to logic and linguistics." He is "the Math Guy" on National Public Radio. (Archived at http://www.stanford.edu/~kdevlin/MathGuy.html.)

He is a World Economic Forum Fellow and a Fellow of the American Association for the Advancement of Science. His current research is focused on the use of different media to teach and communicate mathematics to diverse audiences. He also works on the design of information/reasoning systems for intelligence analysis. Other research interests include: theory of information, models of reasoning, applications of mathematical techniques in the study of communication, and mathematical cognition.

He writes a monthly column for the Mathematical Association of America, "Devlin's Angle": http://www.maa.org/devlin/devangle.html

Customer Reviews

Most Helpful Customer Reviews

35 of 36 people found the following review helpful:

4.0 out of 5 stars Valuable detailed account of an oft-mentioned episode in the history of probability, September 26, 2008

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David J. Aldous "gentleman scholar" (Alameda, CA USA) - See all my reviews
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This review is from: The Unfinished Game: Pascal, Fermat, and the Seventeenth-Century Letter that Made the World Modern (Hardcover)

Many textbooks on mathematical probability mention as a brief aside the correspondence between Pascal and Fermat on the subject of settling fairly a wager on an unfinished game. And many of the popular science style books on probability which have substantial historical components (amongst my favorites, Against the Gods: The Remarkable Story of Risk and Chances Are: Adventures in Probability) devote a few pages to this topic. The first half of Devlin's book, whose style positions it slightly more toward the "serious" end of the popular science spectrum, presents and discusses the correspondence, accompanied by background about the lives of the two principals and their contemporaries. Having a detailed yet easy to read account of this subject is a very welcome addition to the literature.

I'm less enthusiastic about the second half, consisting of briefer accounts of the contributions of people such as Graunt, the Bernoullis, Gauss, Bayes and fast forwarding to DNA testimony and Black-Scholes. Much of this material is similar in spirit to that in existing books (such as the two mentioned above) which paint a broader and richer historical picture. Moreover the implication that there's some kind of meaningful direct line from Pascal-Fermat to the present mathematical understanding of probability, risk etc seems to me just misleading. In core areas of mathematics (geometry, algebra, calculus ..) there was a continuous historical development, in that people consciously learned and built upon what was known before. In contrast, pre 20th century mathematical probability was more a disjointed collection of small topics initiated by different individuals with different motivations -- metaphorically, an archipelago not a continent.

Note: The listing as 208 pages may be misleading (the pages are smallish and the typeface large), though the price is still very reasonable.

15 of 15 people found the following review helpful:

5.0 out of 5 stars Mathematics Makes Modernity, November 3, 2008

By 

R. Hardy "Rob Hardy" (Columbus, Mississippi USA) - See all my reviews
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This review is from: The Unfinished Game: Pascal, Fermat, and the Seventeenth-Century Letter that Made the World Modern (Hardcover)

Many years ago, I can remember that the weatherman on television would give us a forecast for the next day, and he'd make his blunt prediction that it was going to rain or shine. That was it; you had his prediction, and he turned out either to be wrong or right. A couple of decades ago, this changed, and the weatherman started giving us percentage chances of rain. If he says there is a ninety percent chance of rain, you make your decision accordingly about whether to take the umbrella, and if it doesn't rain, the weatherman wasn't wrong; it was just that other ten percent chance creeping through. We take predictions about the weather, and stocks, and countless other things for granted, but that we can predict the future and take such predictions seriously represents a philosophical shift based on pure and applied mathematics. Keith Devlin wants us non-mathematicians to understand how important this shift was, and how it got started from a letter from one mathematician to another written on 24 August 1654. In _The Unfinished Game: Pascal, Fermat, and the Seventeenth-Century Letter That Made the World Modern_ (Basic Books), Devlin has given a quick history of the beginning of probability theory, and more important, has shown how the mathematics was done and how it really did change everyone's outlook on the way the world works. Devlin, well known as "The Math Guy" on National Public Radio who tries to make complicated mathematical ideas understandable for the rest of us, does much the same thing here, making complicated and sometimes counterintuitive mathematical themes understandable, and even more important, relevant.

Before the letter, Devlin says, scholars and even leading mathematicians believed that any attempt to predict the likelihood of future events was futile; the future was known by God alone. Gamblers would particularly have liked to have predicted the future, and Pascal and Fermat were taking on a gambling problem: Two players are betting on a game in which they are going to toss a coin five times, and the one who calls the most tosses correctly wins a pot. What happens if the game gets interrupted before the fifth toss? How should they divide the pot? It is a matter of examining the possible outcomes, figuring the odds of each, calculating the chance each player would have had of winning if the game had continued, and dividing the pot according to their respective odds. The problem is not complicated (looking back on it!), but it required subtle reasoning. At no point did they attempt to solve the problem empirically, tossing coins for many simulated games to find out how often each outcome might happen; this was an effort of pure mathematics, applied to a real-world problem.

Neither Pascal nor Fermat could have known how real-world it was. For them it was a puzzle, a bit of mathematics inspired by gambling. What they were laying down, though, was the basics of risk management, and directly because of their correspondence, people started behaving in different ways. Within only a few decades, the solution to the unfinished game was being applied to life-expectancy calculations, and the business of selling life annuities began. Such calculations and such businesses are still going on, with insurance being sold on far more than just people's lives. Engineers can calculate risk of bridges or airplanes falling down. Quantifying risks means that investors can calculate expected gain, or that pharmaceutical companies can compare different drugs. And of course, back to gambling, casinos know just how much they can expect to make for every dollar wagered, and they can mathematically plan on that outcome. There is still randomness; no one knows exactly what tomorrow will bring. Devlin's clearly-written and entertaining book, however, shows that the intellectual effort of two mathematical giants enabled us to quantify what might happen, and to plan accordingly. The future would never be the same.

12 of 13 people found the following review helpful:

5.0 out of 5 stars The Birth of Probability Theory, October 24, 2008

By 

G. Poirier (Orleans, ON, Canada) - See all my reviews
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This review is from: The Unfinished Game: Pascal, Fermat, and the Seventeenth-Century Letter that Made the World Modern (Hardcover)

In this most engaging book, the author focuses on correspondence between Blaise Pascal and Pierre de Fermat - two great mathematicians of the seventeenth century. The subject of this correspondence deals with a particular problem in gambling. The resolution of this problem, as detailed in this exchange between these two geniuses, is viewed by mathematicians as the birth of probability theory as we know it today. As another reviewer as already pointed out, the author's analysis of this exchange, one letter in particular, occupies the better part of about half the book. The rest involves subsequent developments in this field due to other great luminaries in mathematics, as well as resulting applications in everyday life. Throughout the book, the author has included historical/biographical snippets which add an important human element to what could otherwise be viewed by some as a rather dry subject. I have read other books by this author, and I find this one to be clearly his best thus far. The writing style is clear, friendly, authoritative, quite engaging and accessible to a wide audience. Nevertheless, this book will likely be savored the most by math and science buffs.