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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 rea 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.


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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 rea 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.

30 review for The Unfinished Game: Pascal, Fermat, and the Seventeenth-Century Letter that Made the World Modern

  1. 5 out of 5

    Ben

    I've been reading some books recently with a new sort of question in mind: would I ever give this book to a kid I was teaching? In the case of _The Unfinished Game_, Keith Devlin's little riff on the 17th century exchange between Blaise Pascal and Pierre de Fermat and its role in the history of risk management, the answer is absolutely not. I did not fail to find anything of value in this book. I read it because I've become increasingly interested as an educator in the history of math, especially I've been reading some books recently with a new sort of question in mind: would I ever give this book to a kid I was teaching? In the case of _The Unfinished Game_, Keith Devlin's little riff on the 17th century exchange between Blaise Pascal and Pierre de Fermat and its role in the history of risk management, the answer is absolutely not. I did not fail to find anything of value in this book. I read it because I've become increasingly interested as an educator in the history of math, especially at key moments, and in relation to that interest, the book did give me a useful sense of the historical trajectory of the idea of probability, and Fermat's and Pascal's roles in it. Also, it includes the full text (translated, of course) of a key letter from Pascal to Fermat dated August 24, 1654, and this primary source document, with its human in addition to mathematical content, was for me the most exciting thing in the book. However, I have several deep complaints, that matter to me all the more as a person working to make math more readily accessed and appreciated. First, the book succumbs to the trade publisher's temptation to sensationalize a story that is plenty important enough already. This lends the whole book a "look what a big deal this is!!!!" quality. Since probability is at the core of every facet of modern life (as Devlin rightly notes), it is really not necessary to talk, for example, about its role in predicting terrorist attacks. This is especially true since the technical details are omitted, so Devlin's description of the use of probability theory in such high-stakes situations is in awed terms that completely mystify the actual math at work and so deny the reader the right to think about it for herself. This would bother me in any case but it is especially galling from the point of view of a math educator. I spend my whole professional life working to have people see math as something that their reasoning applies to; that they have the right to engage with. Huddling in cowed submission in the face of a claim to scientific authority that hides the content of the ideas being presented is a posture most non-mathematical adults are used to when it comes to math, and it's the exact opposite of the posture they need to actually understand it. Devlin invites them right into this powerless role with his "I'm-not-gonna-tell-you-any-details-but-look-how-important-this-is!!!" discussions, especially the one about terrorism. But actually, there is a second problem that is even greater. The book's framing device is the 1654 correspondence between Pascal and Fermat, and throughout the book, Devlin seems intent on judging them against each other. He repeats several times throughout the book that Fermat was the greater mathematician, and that Pascal appreciated this. There is a fair amount of fawning over both of them and their prowess, which is exceedingly common in writings on math history much to my chagrin, but the insistence on raising up Fermat by putting Pascal down strikes me as immature whether the book is seen as a work of literature or history. More than immature, though, it is pernicious and damaging to math and our society's relationship to it. Devlin is not personally responsible for this. He is only acting out a perversity that is already present in how math is understood, at least in the USA and England. We as a society insist on ranking mathematicians - "Gauss was the greatest ever"; "Euler was the greatest of the 18th century"; "Hilbert the greatest of the turn of the 20th"; and so on. Why do we do this? What good does it do anyone? But lest you think it does no harm, consider that this ranking extends all the way downward, to schoolchildren. I have been a teacher for close to a decade now and I have hardly met the student who has not gotten from somewhere a strong idea of where she stands when it comes to math - "I'm good at math" or "I suck at math" as the case may be. And good or bad, this idea only serves to hurt her. For those who have the sense that they are less, I hope it is already obvious that this sense they carry is an obstacle; but for those who have the sense that they are greater, it is an obstacle as well. For if you think you're good at it, what happens when you hit a problem that really challenges you - that makes you struggle? Most kids with the idea that they're "good at math" do their best to avoid such problems altogether, because they automatically cause a crisis: if I'm struggling, doesn't that mean I wasn't so good after all? The problem is radically compounded by the _grounds_ on which Devlin declares Fermat the greater mathematician. Just as he harps on this relative evaluation of the two, he also harps on the fact that in the letter that frames the book, Pascal is visibly struggling to understand what Fermat is saying, and it is on this basis that Fermat is judged superior. Devlin gives us to understand that Fermat probably solved the problem quickly and had no confusions about it, but humored Pascal's slow process of making sense of his elegant solution. Now, the primary sources Devlin provides us do not force this interpretation of the story, but more importantly, Devlin is implying to his readership that struggling with an idea makes you lesser. In order to be truly great, we are being told, you have to solve the problem quickly, without struggle. A student fed on such ideas is doomed as a creator of original mathematics because no great idea was ever arrived at without struggle. There is a venerable history of hiding this fact, but the fact remains. (I read elsewhere that the great Simon de Laplace used to write "it is easy to see" about conclusions that he would wrestle with for an hour.) What leaves me particluarly mad about this is that the story Devlin tells is clearly an opportunity for the opposite lesson. I was drawn to the book in the bookstore partly because of this. It has a sub-subtitle: "A Tale of How Mathematics Is Really Done," and it shows us (in the form of the Fermat-Pascal correspondence) a snapshot of a mathematical idea _in the process of being made_. It is the natural state of such an idea to be not entirely worked out, not yet cleaned up, still being struggled with. Of course Pascal was struggling with Fermat's solution. I feel utterly certain that Fermat struggled with it too, even if by the time of the correspondence he had sorted things out for himself. My point is that this could have been a story that revealed the creation of original, groundbreaking, in fact world-changing mathematics to be a human activity that the reader can relate to. How empowering, how uplifting, for anyone who has ever struggled with a mathematical idea (and all of us have) to watch one of the _inventors_ of that idea go through the same process? That radical, exciting possibility is what this book could have been. Instead, it is one more voice telling all of us (since we have all struggled) that we are fundamentally different and lesser beings than the Math Gods like Fermat who originated everything we obediently consume. At one point Devlin does invite us to sympathize with Pascal's struggle - but in the context of his repeated judgement of him as lesser, this invitation comes off as condescending. "Even Pascal was nothing next to the great Fermat! It's okay that you are nothing too." So I'm not sorry I read it - the letter itself was fascinating, and I have a better sense of where I would look to learn more about how the idea of probability came into being. But never in my lifetime would I visit on a student of mine the harm of exposing them to this book's idea of what makes a mathematician.

  2. 4 out of 5

    S.

    The book illustrates the history of probability, not dense with equation's, in fact all of which are made easier to understand with all the examples and explanations that the author used. Why don't we go on learning maths this way, fun, simple and tightly related to the 'real' world ? The book illustrates the history of probability, not dense with equation's, in fact all of which are made easier to understand with all the examples and explanations that the author used. Why don't we go on learning maths this way, fun, simple and tightly related to the 'real' world ?

  3. 4 out of 5

    Valerie

    Letter writing is most certainly a lost art. "I beg you to inform me how you would proceed in your research on this problem. I shall receive your reply with respect and joy, even if your opinion should be contrary to mine." contrasted with today's modern flame wars. Having just taken a class in decision quality at Stanford, I found the discussions of Baye's formula and assessing risk by using probability very interesting. It is difficult to imagine a time before probability mathematics. Letter writing is most certainly a lost art. "I beg you to inform me how you would proceed in your research on this problem. I shall receive your reply with respect and joy, even if your opinion should be contrary to mine." contrasted with today's modern flame wars. Having just taken a class in decision quality at Stanford, I found the discussions of Baye's formula and assessing risk by using probability very interesting. It is difficult to imagine a time before probability mathematics.

  4. 4 out of 5

    Marius Bancila

    The title is a little bit misleading as the book is not entirely about the letters Pascal and Fermat have exchanged in 1654, but rather a history of the science of probabilities that started with the problem of the unfinished game. Devlin does focus on the letters of the two great French mathematicians but also shows how others have drawn inspiration from the methods Pascal and Fermat have established and how they developed and applied math to real world problems (not only gaming). The book is n The title is a little bit misleading as the book is not entirely about the letters Pascal and Fermat have exchanged in 1654, but rather a history of the science of probabilities that started with the problem of the unfinished game. Devlin does focus on the letters of the two great French mathematicians but also shows how others have drawn inspiration from the methods Pascal and Fermat have established and how they developed and applied math to real world problems (not only gaming). The book is nicely spiced with short biographies of many mathematicians. Overall Devlin makes a good case showing how hard it was for the great thinkers of 17th century to overstep what seemed rationale and develop correct mathematics for determining the chances of an event to occur.

  5. 5 out of 5

    William Schram

    The Problem of Points taunted humanity for centuries. A letter between Blaise Pascal and Pierre de Fermat changed all of that forever. In "The Unfinished Game," Keith Devlin goes over the paradigm-shattering piece of correspondence that introduced the world to Probability Theory. Devlin explains the reasoning of each side and the points that each person made in previous letters. The game-changing idea was to predict what would happen if the game continued. People assumed that games of chance were The Problem of Points taunted humanity for centuries. A letter between Blaise Pascal and Pierre de Fermat changed all of that forever. In "The Unfinished Game," Keith Devlin goes over the paradigm-shattering piece of correspondence that introduced the world to Probability Theory. Devlin explains the reasoning of each side and the points that each person made in previous letters. The game-changing idea was to predict what would happen if the game continued. People assumed that games of chance were all up to the gods and did not realize that it was possible to predict events. Devlin discusses other aspects of Probability Theory as well. For example, in the same period as the correspondence, John Graunt developed a method to read statistics from raw data. Graunt was surprisingly accurate for the time and used for decades to make actuarial predictions. We can't discuss this era without some mention of the Bernoulli family, and we get that too. Finally, Devlin talks a bit about Bayes' Rule. Conditional Probability was far too tedious before computers were widespread. Devlin does not include too many equations in the book. He mainly discusses the methods employed.

  6. 5 out of 5

    Vishal Katariya

    Nice history of probability theory.

  7. 5 out of 5

    Kelly Vincent

    This book tells the story of the origins of probability, which emerged more recently than you would expect for such a fundamental field. It's somewhat famous among certain types of nerds that probability theory came from a handful of mathematicians pondering certain types of gambling. Specifically, the real origins are documented in a series of letters between Blaise Pascal and Pierre de Fermat. So this book includes selections from the (extant) letters and explains and discusses them, giving th This book tells the story of the origins of probability, which emerged more recently than you would expect for such a fundamental field. It's somewhat famous among certain types of nerds that probability theory came from a handful of mathematicians pondering certain types of gambling. Specifically, the real origins are documented in a series of letters between Blaise Pascal and Pierre de Fermat. So this book includes selections from the (extant) letters and explains and discusses them, giving the historical context and then continuing on to what the letters inspired. It's an interesting book, and it's always cool to actually see the primary sources that history books are relying on. It's also a fairly slim book. The math isn't extremely difficult to follow (this is no "calculus-based probability and statistics" textbook) and I don't think a full understanding of all of it is critical to an appreciation of the book, anyway. Prior to the events kicked off by the exchange of letters, virtually everyone thought the future was impossible to predict (well, in a secular sense, anyway). So while some avid gamblers tried to pay attention to the behavior of the games they played to figure out how to best bet, it seemed rather pointless. The late-fifteenth century mathematician Pacioli published a book that included the "problem of the unfinished game" (also called the "problem of the points"), which asks what the fair way to distribute the money when a game has to be aborted before its intended conclusion. For instance, if two players decide to play the best of 7 but have to stop after only 4 games, with 1 player with 1 win and the other with 3, how much of the pot should each walk away with? The only really obvious scenario is when they are exactly tied. All others seemed unknowable. The Chevalier de Mere was good enough at calculating odds that he used the modern casino long haul strategy of identifying games with probability just slightly in his favor (i.e., around 51% for him) and just playing a whole bunch of times. He contacted Pascal with several questions relating to games of chance, including the problem of the unfinished game. Pascal tried to solve it and then wrote to Fermat to get a second opinion on his solution. Thus, the exchange. Devlin walks us through the letters, Pascal's solution, Fermat's superior solution, and Fermat's patient attempts to explain the revolutionary ideas embedded in his solution to Pascal, who struggled to grasp it. I found this pretty interesting, because Pascal is one of the Greats, yet he just could not wrap his head around what Fermat was proposing. Sometimes math is hard, even when you're good at it. This certainly fits with my own experience of trying to learn probability theory--it is probably (heh) as counter-intuitive as any accurate idea can be. The most novel part of Fermat's approach, the one Pascal had so much trouble accepting because it seemed illogical, is the idea that when you are calculating probabilities on a game of say, best of 7, you have to calculate the odds based on 7 plays--not just 5 if one player would have won and the game would have finished. So with the unfinished game problem, if one player is leading after 3 plays, you still have to calculate the odds on 7 plays to get the right answers. Devlin goes on to discuss what happened with the new ideas. This includes (among other things): the first real instance of applied statistics (a 1662 pamphlet analyzing mortality rates in London), the landmark text that Huygens wrote on probability theory (starting with Fermat and Pascal but adding his own), the (amazing and numerous) Bernoullis, psychology and risk, probability in courts, the Normal distribution, annuities and insurance, Bayes, Site Profiler (the DoD system that predicted the events of 9/11, along with many other incidents that didn't happen), DNA profiling, and financial derivatives.

  8. 5 out of 5

    Claudia

    It will never cease to amaze me how few hundred years ago, when relying almost exclusively on their minds, people where able to develop and discover such things. This book details how the theory of probabilities emerged from the question on how the pot should be divided between two players, when one of them leads with 2 to 1 and they stop playing. Keith Devlin, professor of mathematics at Stanford University, dissects the correspondence between Blaise Pascal and Pierre de Fermat and explains, in It will never cease to amaze me how few hundred years ago, when relying almost exclusively on their minds, people where able to develop and discover such things. This book details how the theory of probabilities emerged from the question on how the pot should be divided between two players, when one of them leads with 2 to 1 and they stop playing. Keith Devlin, professor of mathematics at Stanford University, dissects the correspondence between Blaise Pascal and Pierre de Fermat and explains, in a very simple and understandable way, all the thinking and connections which led to that discovery and, later on, to statistics, risk management and many other predictions used today, from financial trends to terrorist’s attacks. He also reviews the roles others had in this matter, which are not as famous as these two, but had, nonetheless, a major contribution to this particular field. And the letter between the two is just a piece of art… too bad these days we resume ourselves to electronic succinct messages. A highly enjoyable and interesting book.

  9. 4 out of 5

    Kelly Jackson

    I do have a math background for disclosure purposes. I found the subject matter and historical context interesting. The writing style was a little grating. There was a lot of condescension in the prose. It's OK if you don't understand it... I do have a math background for disclosure purposes. I found the subject matter and historical context interesting. The writing style was a little grating. There was a lot of condescension in the prose. It's OK if you don't understand it...

  10. 5 out of 5

    Elizabeth

    Not as entertaining or efficiently informative as The Man of Numbers. Felt a bit disjointed and speculative at times, as though Devlin thought, "Oh, yes, one other thing while I'm at it" many times throughout. Not as entertaining or efficiently informative as The Man of Numbers. Felt a bit disjointed and speculative at times, as though Devlin thought, "Oh, yes, one other thing while I'm at it" many times throughout.

  11. 5 out of 5

    John Landis

    A complete waste of my time. I would rather they chose either the math or the people involved to concentrate on instead of focusing on both and failing twice.

  12. 5 out of 5

    Fred Cheyunski

    Basis of Probability/Statistics for Our Modern World (and Limitations) - In under 200 pages, Keith Devlin goes over the key letter of Pascal to Fermat in 1654, which is well known by mathematicians but not usually read; the letter is included, related history and implications are discussed in very readable manner. That is, in a Preface and 10 chapters, the book goes into the origins of probability, statistics, and the modern world; it addresses the ability to predict the future, or at least the l Basis of Probability/Statistics for Our Modern World (and Limitations) - In under 200 pages, Keith Devlin goes over the key letter of Pascal to Fermat in 1654, which is well known by mathematicians but not usually read; the letter is included, related history and implications are discussed in very readable manner. That is, in a Preface and 10 chapters, the book goes into the origins of probability, statistics, and the modern world; it addresses the ability to predict the future, or at least the likelihood of different events based on similar ones in the past. Pascal’s correspondence with Fermat began with the problem of how to award points if a game of chance could not be completed as first stated earlier in the 15th century. The book also provides fascinating background on Pascal and Fermat as well as showing how the use of numbers progressed from Fibonacci (for additional information see my review of Devlin’s book on this subject that appeared in 2012). Among my favorite parts of the book are those that talk about the development of our ability to quantify risk which made insurance, liquid capital markets, and global corporations like Amazon, Google, and Microsoft possible. There is the discussion of Graunt’s work on mortality rolls during rein of Charles II (1676) to help warn about the spread of bubonic plague and bring probability theory out of the gaming room. Then, Huygens’s formalization/improvement of methods, and advances by Jacob Bernoulli with his 1713 “law of large numbers” enabled sampling and prediction. Also, receiving attention are de Moivre discovery of the bell curve in1733 as well as Gauss’s and Bayes’ later contributions. Devlin even mentions the Black Scholes formula which permitted financial derivatives valuation (and the Nobel economics prize in 1997) that lead to so much difficulty in 2008 around the time this book first appeared (due to the publication date we can forgive the author for more attention to such ills). Along the lines of probability and statistics underlying assumptions and limitations, a good companion to this book could be Nazism Taleb’s “The Black Swan: Second Edition: The Impact of the Highly Improbable” (2012). Some of my favorite parts from that book include recognizing narrative’s strength in promoting and storytelling for completion and being wary of its use for prediction. The added segments on the four quadrants, when to use typical statistics, and when to look for black swans or improbable events is also most pertinent. So, for a good read on the basis of probability and statistics for the modern world consider “The Unfinished Game.”

  13. 4 out of 5

    Ed Terrell

    Mathematics is anything but boring. Knights gambling over pots of gold combined with intrigue and suspense, where what seems obviously to be true just isn't so. It's not that we are irrational, its just that we don't know how to ask the right questions. "The Unfinished Game" is a quest to calculate how the pot or winnings should be divided if the game was not able to be played to completion. The key insight provide by Fermat was to focus on future rather than past outcomes. Along the way, he and Mathematics is anything but boring. Knights gambling over pots of gold combined with intrigue and suspense, where what seems obviously to be true just isn't so. It's not that we are irrational, its just that we don't know how to ask the right questions. "The Unfinished Game" is a quest to calculate how the pot or winnings should be divided if the game was not able to be played to completion. The key insight provide by Fermat was to focus on future rather than past outcomes. Along the way, he and Pascal created a new branch of mathematics: probability and statistics. Devlin casts a wide net to ensure that we get introduced to a consortium of mathematical wizards such as the Bernoullis, Huygens and Bayes. The book ties in the historical development of ideas with clear and concise mathematical explanations. It is worth reading for his discussion of Bayes rule alone. Clearly five stars.

  14. 5 out of 5

    Xin

    This review has been hidden because it contains spoilers. To view it, click here. First Mathematics history book I have encountered. Definitely the most nerdy book I have read. The premise of the book is about how Pascal and Fermat discovered the earliest version of probability through the “game of points.” Can’t help but to notice Pascal is a genius, but tragically died young. The content is inherently interesting, but became more repetitive as there is only one central theme. I did however have a good conversation with the neighbor math professor, who is excited about using First Mathematics history book I have encountered. Definitely the most nerdy book I have read. The premise of the book is about how Pascal and Fermat discovered the earliest version of probability through the “game of points.” Can’t help but to notice Pascal is a genius, but tragically died young. The content is inherently interesting, but became more repetitive as there is only one central theme. I did however have a good conversation with the neighbor math professor, who is excited about using the game of points to teach his students about expected value next week in his class. The book overall is so-so, but I can tell the author is more excited about the content than the average reader. I can admire people who love what they do.

  15. 5 out of 5

    Jeroen

    An easy to read book on the origin of probability theory. The theory is explained well and established based on a letter between Pascal and Fermat. Easy to read for people that don't already know some of the probability theory basics and interesting background reading for those who do. Main drawback of the book is the easy way the author uses historic dates to set context of developments after the start by Fermat/Pascal. Those dates sometimes feel a bit chaotic and unstructured. An easy to read book on the origin of probability theory. The theory is explained well and established based on a letter between Pascal and Fermat. Easy to read for people that don't already know some of the probability theory basics and interesting background reading for those who do. Main drawback of the book is the easy way the author uses historic dates to set context of developments after the start by Fermat/Pascal. Those dates sometimes feel a bit chaotic and unstructured.

  16. 4 out of 5

    Sonya Mann

    Pretty good Moderately entertaining and fairly informative. But not exceptionally written. I know a little more about the origins and anatomy of probability theory, so that makes me happy.

  17. 4 out of 5

    Kiora Nield

    Super quick read with introductions to a lot of mathematicians that influenced probability theory. My favorite part was how he delved into the thinking they had to overcome to get to the breakthrough.

  18. 4 out of 5

    Nikos Koukis

    This review has been hidden because it contains spoilers. To view it, click here. Meh, not really interesting. The only fact worth knowing is that Fermat and Pascal developed the modern theory of probabilities in 1654 via a series of mail correspondences. There you go. I saved you from going through 200 boring pages

  19. 5 out of 5

    Brett

    Pascal and Fermat are two fascinating characters in the history of math. However, I simply wasn't interested in the story here. Pascal and Fermat are two fascinating characters in the history of math. However, I simply wasn't interested in the story here.

  20. 5 out of 5

    Lars Guthrie

    The low rating (for me, I know I rate high but I like to think I read what I'm interested in and know about so that my discrimintion is shown as much by my selection as my evaluation) is more due to my weaknesses in math than Devlin's style or story. I would have liked more context (and I mean non-mathematical context)--like the mise en scène of late Seventeeth Century France and the other eras and locales included here. I once had a European history prof who made the development of annuities re The low rating (for me, I know I rate high but I like to think I read what I'm interested in and know about so that my discrimintion is shown as much by my selection as my evaluation) is more due to my weaknesses in math than Devlin's style or story. I would have liked more context (and I mean non-mathematical context)--like the mise en scène of late Seventeeth Century France and the other eras and locales included here. I once had a European history prof who made the development of annuities really exciting. Annuities are around because of the letters about the probabilities in coin toss games sent between Blaise Pascal and Pierre de Fermat, the focus of this little book. Devlin does get into the same stuff as that professor, but it wasn't as engaging for me. He also probably regrets the books came out before derivatives were denigrated. But the "math guy" on NPR is adept with words and witty, and made me feel better when he noted that many calculus students don't understand what they are doing, even though they are doing it. I sometimes didn't understand what I was reading here, even though I was reading it (sometime with bemused enjoyment). I did get a better idea of what a "standard deviation" is, which helps me to explain normed standardized testing for kids better.

  21. 4 out of 5

    Eric

    I’ve got a dirty secret - I’m mathematically challenged, and it has always been so. I’ve had to work extra hard to be extra average at math. Secretly, I’d like to be good at math, and understand some of the advanced compression, encryption, and other algorithms that kick around the interwebs. Every now and then, I’ll pick up a math-oriented book, and I usually put it down in despair. Not so The Unfinished Game, which is as much about history as it is about probability. In a nutshell, the book des I’ve got a dirty secret - I’m mathematically challenged, and it has always been so. I’ve had to work extra hard to be extra average at math. Secretly, I’d like to be good at math, and understand some of the advanced compression, encryption, and other algorithms that kick around the interwebs. Every now and then, I’ll pick up a math-oriented book, and I usually put it down in despair. Not so The Unfinished Game, which is as much about history as it is about probability. In a nutshell, the book describes a snail mail conversation - an ancient form of collaboartion - between Pascal and Fermat regarding the correct way to devise the payment of a wager on an unfinished game of dice. The narrative weaves mathematical explanations between discussion of the time, place, and personalities of the story. A quick and compelling read, you’ll come out of it feeling that you’ve learned something truly important, borne of a discovery that took ages by modern standards. It is striking to consider how quickly we are able to use the social Web to iterate over interestin ideas, in comparison to the pen and paper ways of old. Strongly recommended.

  22. 4 out of 5

    Gary Fixler

    Can one ever really finish "The Unfinished Game?" I admit, I did not read the full correspondence between Fermat and Pascal at the end of the book; I got much of it in pieces throughout. I'll save the 10 or so pages for a rainy day. I am impressed—and admittedly puzzled—by the praise each heaps upon the other in his letters. Modern teenagers in love fail to reach such heights of extended, floral flattery. Perhaps, owing to the slowness of communication-by-post, such admiration was delivered in b Can one ever really finish "The Unfinished Game?" I admit, I did not read the full correspondence between Fermat and Pascal at the end of the book; I got much of it in pieces throughout. I'll save the 10 or so pages for a rainy day. I am impressed—and admittedly puzzled—by the praise each heaps upon the other in his letters. Modern teenagers in love fail to reach such heights of extended, floral flattery. Perhaps, owing to the slowness of communication-by-post, such admiration was delivered in bulk, and metered out in doses by the recipient over the course of the following weeks. I can't say. What I can say is that this was a very fun read, and a nice peek into the lives behind a good number of names I've known for years. I really enjoyed following the connections back, from things I've known (and math I've [albeit indirectly] used) to the life and times of the 17th century. Math is timeless.

  23. 5 out of 5

    Doug

    I loved this book. Pascal and Fermat never met in person but their exchange of letters started a revolution in terms of how mankind sees the world - in terms of risk management. Devlin documents the exchange and highlights significant topics in the discussion. I think his characterization of the problem of points, Pascal's probabilistic argument for believing in God, and his numerous examples of how Baye's theorem is used (especially in health care) are some of the best I've seen. And, he does a I loved this book. Pascal and Fermat never met in person but their exchange of letters started a revolution in terms of how mankind sees the world - in terms of risk management. Devlin documents the exchange and highlights significant topics in the discussion. I think his characterization of the problem of points, Pascal's probabilistic argument for believing in God, and his numerous examples of how Baye's theorem is used (especially in health care) are some of the best I've seen. And, he does a good job of identifying a priori and a posteriori probability, and the different ways that distinction is used. If you're interested in history and how our modern world has been shaped, pick up and read. You don't have to be mathematically inclined to enjoy it.

  24. 4 out of 5

    mandy

    While this is book is meant to appeal to "regular" people, and not mathematicians, I found that the math that is included was at times hard to grasp. Luckily, Devlin has a knack for explaining the principles behind the formulas with real world examples, which helped a great deal. We also find out a lot of history about various 17th century mathematicians, so history buffs might enjoy this as well. Overall an interesting read. While this is book is meant to appeal to "regular" people, and not mathematicians, I found that the math that is included was at times hard to grasp. Luckily, Devlin has a knack for explaining the principles behind the formulas with real world examples, which helped a great deal. We also find out a lot of history about various 17th century mathematicians, so history buffs might enjoy this as well. Overall an interesting read.

  25. 5 out of 5

    David Robertus

    A generally well done look at the origins of probability theory, the implications for the insurance industry and so on. The author takes a very interesting look at the mindset (or lack thereof) of people prior to the wide spread use of statistics and probability theory in modern every day life. This is intriguing to me in two ways- first,what life is like without it, and two, how frequently misused it is today (which is also addressed albeit briefly).

  26. 5 out of 5

    Kathy

    Probability is such a part of modern life that it is hard to believe it wasn't until the 17th century that it started to be studied. The book is written in a way that can be understood by someone who has forgotten high school math. There are mathematical formulas in the book but the author lets you know you can skip them without losing the flow of the book. For someone with more mathematical background it lets you see how the familiar statistical formulas came about. Probability is such a part of modern life that it is hard to believe it wasn't until the 17th century that it started to be studied. The book is written in a way that can be understood by someone who has forgotten high school math. There are mathematical formulas in the book but the author lets you know you can skip them without losing the flow of the book. For someone with more mathematical background it lets you see how the familiar statistical formulas came about.

  27. 4 out of 5

    Thom

    I appreciate the import of this idea, and the math behind it. I mostly liked the presentation - bits of the letters and the history behind them. Something about the writing - the style perhaps - didn't sit right with me. Will read some of Devlin's online column to see if I can narrow it down sometime. I appreciate the import of this idea, and the math behind it. I mostly liked the presentation - bits of the letters and the history behind them. Something about the writing - the style perhaps - didn't sit right with me. Will read some of Devlin's online column to see if I can narrow it down sometime.

  28. 4 out of 5

    Michael Artin

    So far...the book is compelling simply because of the subject matter. But Devlin's style is so smug and sensationalistic that it gets in the way of digging into the interesting history. He spends so much time telling you "this was really important" and assuring you, "Don't worry if you don't get this...they didn't either!" Speaks down to the reader. So far...the book is compelling simply because of the subject matter. But Devlin's style is so smug and sensationalistic that it gets in the way of digging into the interesting history. He spends so much time telling you "this was really important" and assuring you, "Don't worry if you don't get this...they didn't either!" Speaks down to the reader.

  29. 5 out of 5

    Lauren Hutchinson

    I really like statistics so I may be a bit biased. At times the book did get into some complex but the examples helped to convey the complex math that was being discussed. It was nice getting to learn a bit more about Pascal and Fermat, plus a whole lot of other characters. I'm not sure this book would be that enjoyable for anyone without an appreciation for vague mathematics. I really like statistics so I may be a bit biased. At times the book did get into some complex but the examples helped to convey the complex math that was being discussed. It was nice getting to learn a bit more about Pascal and Fermat, plus a whole lot of other characters. I'm not sure this book would be that enjoyable for anyone without an appreciation for vague mathematics.

  30. 4 out of 5

    Fraser Sherman

    An interesting story about how the great mathematical thinkers Pascal and Fermat tackled an old problem (the Unfinished Game problem of the title) and developed the concept of probability to solve it. Devlin traces the growth of probability and statistics from that breakthrough (though a lot of independent ideas contributed too) through to the present age. Fascinating.

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