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The Unfinished Game: Pascal, Fermat, and the Seventeenth-Century Letter That Made the World Modern [Englisch] [Taschenbuch]

Keith Devlin

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23. März 2010
In the early seventeenth century, the outcome of something as simple as a dice roll was consigned to the realm of unknowable chance. Mathematicians largely agreed that it was impossible to predict the probability of an occurrence. Then, in 1654, Blaise Pascal wrote to Pierre de Fermat explaining that he had discovered how to calculate risk. The two collaborated to develop what is now known as probability theory--a concept that allows us to think rationally about decisions and events. In The Unfinished Game, Keith Devlin masterfully chronicles Pascal and Fermat's mathematical breakthrough, connecting a centuries-old discovery with its remarkable impact on the modern world.

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The Unfinished Game: Pascal, Fermat, and the Seventeenth-Century Letter That Made the World Modern + Introduction to Mathematical Thinking
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"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."

"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." -- Dieser Text bezieht sich auf eine vergriffene oder nicht verfügbare Ausgabe dieses Titels.


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. -- Dieser Text bezieht sich auf eine vergriffene oder nicht verfügbare Ausgabe dieses Titels.

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38 von 39 Kunden fanden die folgende Rezension hilfreich
4.0 von 5 Sternen Valuable detailed account of an oft-mentioned episode in the history of probability 27. September 2008
Von David J. Aldous - Veröffentlicht auf
Format:Gebundene Ausgabe|Verifizierter Kauf
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.
17 von 17 Kunden fanden die folgende Rezension hilfreich
5.0 von 5 Sternen Mathematics Makes Modernity 3. November 2008
Von R. Hardy - Veröffentlicht auf
Format:Gebundene Ausgabe
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.
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5.0 von 5 Sternen The Birth of Probability Theory 24. Oktober 2008
Von G. Poirier - Veröffentlicht auf
Format:Gebundene Ausgabe
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.
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4.0 von 5 Sternen Lacking in Social Context But Valuable 7. Oktober 2013
Von David Milliern - Veröffentlicht auf
This book was by no means exciting, but it was moderately interesting. I think this is one in which the reader will have to be sufficiently interested in reading beforehand, because I don't think it is bound to inspire anyone to new levels of interest. I am a little torn between whether this book should have been an article in a journal, rather than being a book. The print size is such that it would have made for a long article, but I guess the accessibility of such a book is a positive, given that there are bound to be a number of laypeople interested in the founding of probability.

The writing is okay, the research is pretty well done, and so I would recommend this book to anyone seeking the history surrounding this mathematical subdiscipline's formation. This history finds its setting in a communication (and critical letter) between Blaise Pascal and Pierre de Fermat. Therefore, anyone also interested in the lives and thought of these thinkers may also be interested.

My single point of criticize is that the history is presented in a vacuum, discussing some preceding issues that exist before Pascal and Fermat deal with the "unfinished game," however, no significant social context was established, which would have inexorably driven the discussion as much as the preceding history of probability. I think any history of science and mathematics is simply incomplete without this, and probably misleading, as I have found in other cases. Nonetheless, this is a valuable book.
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5.0 von 5 Sternen The Unfinished game 9. August 2013
Von Janet Gallin - Veröffentlicht auf
Verifizierter Kauf
Anything by Keith Devlin is perfect. If you want a really grand weekend, buy several of his books, turn off your cellphone, lock yourself away from the world with a pot of coffee or tea, a couple of Snickers bars and dive right in. His writing is wonderful, clear as can be and what could be more fun than a pile of beautifully written math books. Mathematicians are, in general, exquisite writers. You might want to try Men of Mathematics by E.T. Bell in this weekend as well. And, anything Simon Singh. If I know you will get Keith's book I will be very happy for you.
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