Rating: 
Summary: Important book of diminishing appeal
Review: The message of the book -- that mathematics (in particular what the author considers essential: a sense for "large" numbers, estimation, probability, and statistics) is too important to be left to mathematicians -- is clear, relevant, and important as ever. However in my opinion the examples Paulos adopts for illustration are currently too widely publicized to stir interest among readers with even a slight interest in the topic. Examples of such examples are: 1) spouse-choosing schemes (assuming that a lady is sequentially screening N spouse candidates, and that she cannot choose a candidate who she had previously rejected, what is the best strategy for the lady to pick the one she most prefers?), 2) can a baseball player whose batting average is better than another player for two seasons nevertheless have lower overall batting average than the other? 3) stock newsletter scam (suppose you wish to charge N number of people a fixed amount of subscription fee. In order to win subscription, you have to make X consecutive correct weekly predictions. During the first week send out newsletters to N*2^X people, half of letters stating that the market will be up, the other half stating the opposite. Either of the predictions will be true. Divide the group that received the correct prediction to two and deliver again opposing predictions the next week. Repeat till you reach the desired N number of people.)Some notes to be fair. 1) There are many, many interesting examples (a là Paulos: (more than 20 per chapter) * (5 chapters) = (more than 100 examples overall)). 2) Many of these numerous examples are Paulos' own (including the stock newsletter scam above, I believe). 3) At the time of initial print (1988) the examples evidently were not as well publicized as now (2003). If you haven't heard any of the examples above and never read any Paulos publications, then the book will be of value to you, especially given Paulos' clean exposition and wit. On the other hand if you've either read some other book by Paulos or heard of any such examples then you might be better off reading his monthly column on ABCNews at http://abcnews.go.com/sections/science/whoscounting_index/whoscounting_index.html.
Rating:
Summary: interesting book, but lacking focus
Review: The problem that resulted in this book is far-reaching: the public simply doesn't understand mathematics. Statistics, ranging from a 10%-off sale to the sort found in opinion polls, are unfathomable to the general populace. Probability, especially in the context of gambling, is understood by only a scant handful of people. The list of misunderstood mathematics is nearly endless. In the first few chapters of the book, Paulos describes various issues that the innumerate (that is, those who don't understand numbers and math) often have issues understanding. He describes the issue to a reasonable level of detail, then derives answers for them. Don't let the use of the word 'derive' scare you off: the answers are readable and readily understandable to a general audience. In some cases, if you're really rusty, you might need to read them a second time to grasp the solution. Later chapters, however, are not written for the innumerate. They are attempts to convince the reader that mathematical education needs to be improved. I think that everyone agrees that education should be improved, but he offers suggestions that are impractical or nonsensical. Ultimately, the problem of this book is a lack of focus. Paulos could have written either a book that tackles basic mathematical issues that the general public doesn't understand, or he could have written a book that describes the consequences of innumeracy. He tried to do both, and stuffed both topics into a single slim volume. In doing so, he shortchanges both audiences. The result is a book that is good, but does not fully address the needs of anyone. If you find yourself uncomfortable with mathematics, pick up a copy of this book and read up to chapter five. If you are comfortable with mathematics and are looking for fodder to prove the point that improving mathematical knowledge at any level is productive, this book will not serve your purpose.
Rating:
Summary: Innumeracy as irrationality
Review: This book is an extended rant about instances involving numbers where people act irrationally. It begins with a long enumeration of examples such as the inability to comprehend the immensity of extremely large numbers, the misinterpretation of statistics and probability, and various types of what Paulos terms 'pseudoscience' (including fire-walking, whose relevance for a book of this type is not clear). Following this extended introduction, there is a short section where Paulos points his finger at the ones to blame for our blatant disregard for numbers, especially elementary school teachers. Then he goes on to discuss a few points about how numbers should be interpreted. Many of Paulos' examples are engaging or even amusing. However, the book wasn't quite what I was expecting, given its title. For me, a word like 'innumeracy' sounds like 'illiteracy', so I thought the book would be about people who are unable to do simple everyday math, and the consequences of this problem. For example, what about people who can't balance a checkbook, who go to a sale and can't determine whether $100 off or 15% off of a $1000 purchase is a better deal, who can't estimate how it will take them to drive 30 miles at 65 mph? To me, these people are truly the 'innumerate', and the consequences of their ignorance are far more serious for them and for society than the people Paulos rails against. Paulos doesn't discuss such problems at all. Instead, he complains about people's irrational interpretations of probability, such as when people avoid travel because of fear of a terrorist attack, but think nothing of the much greater probability of injury or death while commuting in their cars every day. Paulos points out the large differences in the probabilities of engaging in activities such as these, and he seems to expect that "numerate" people should calculate the corresponding probabilities and act logically, like computers. He seems to miss the really interesting point- -why do people act the way they do? Why do they persist in irrational behavior when they know the numbers? At one point, Paulos does describe some psychology research, in which investigators found that given exactly the same odds, people are more likely to take risks in order to avoid loss, and less likely to take risks in order to gain something. But in the rest of Paulos' examples, he simply describes the irrational behavior of humans, and assumes that the irrational behavior is due entirely to a lack of an ability to deal with numbers, rather than having a deeper psychological explanation. One example of "innumerate" behavior that Paulos cites is a sports writer, who suggests that a baseball manager could create the perfect team by trying out every possible combination of players and positions on the team until he finds the optimal combination. As Paulos points out, when you calculate the number of possible combinations in this case, it would be so high that the players would be dead long before the trials were over. But ordinary people, who aren't necessarily 'innumerate', understand what the journalist meant- -that the manager should try out only those possible combinations that make sense, and to use his intuition to try out the more likely possibilities first. By using intellect and intuition, the manager might be able to complete the task in a few seasons, perhaps. This ability is quite fascinating, but after dismissing the mathematical absurdity of following the suggestion literally, Paulos does not go on to investigate what was actually meant, or how people can hone in on good choices and reject bad ones out right in such a situation. In his blame-assigning section, Paulos goes as far as to suggest that elementary schoolteachers and university professors should be required to exchange places for a few weeks every year. Paulos suggests that the schoolteachers would improve their math skills by learning from the university students in the classes they would take over, and that the professors would make classroom math fun for elementary students by bringing in games and such. Get real! I'm sorry, but it is the schoolteachers who bring to the classroom creative approaches to teaching math, not university professors. When was the last time you ever heard of a university professor playing games in math class? The vast majority of them simply stand at the board with a piece of chalk and write out example problems and solutions for students to copy in their notebooks. It's no wonder that many of the schoolteachers, who were supposed to learn math in college, didn't master the skills they needed. What is really needed is better math instruction at the tertiary level for elementary school teachers, who are in general, very good teachers, even if their math skills may be weak. All in all, while this book is occasionally interesting, it is much more a discussion of probability and statistics and how people choose to interpret them rather than a discussion of a general lack of math skills in society.
Rating:
Summary: Needs a bit of direction
Review: This book is very good, but it seems that he could have done a better job by giving specific examples that were found in real life. On one hand, the topic of debunking is something done-to-death. On the other, it is nice when you read a book about something that disproves something that you've always thought wrong and you can say "Oh! That's why that is so!" This book does not go in that direction. Thematic organization would have been immensely useful to an otherwise very good idea. Also, some of the topics that he brought up were not supported by numbers. Like his mentioning that math education majors were the worst in all of his math classes. How *much* worse were they? Was their score 2% below the average or 20% below? On the good side, it was a short book. There was not much wasted space in the sense that he didn't simultaneously write and assert *nothing* (as anyone who's ever read an Ayn Rand book knows is possible).
Rating: 
Summary: A must read for the numerate and innumerate alike
Review: This book offers valuable common sense advice that can be used in a broad array of every day situations. The narrative is very readable and easily accessible to all, only requiring an occasional minimum of mathematical reasoning.
For those who are already familiar with the concepts, it is a refreshing summary of the pitfalls of the innumerate. And for those of you who have always considered mathematics to be 'one of your worst subjects', then this book may very well give you a new perpective and teach you something to boot.
I found it to be refreshing and entertaining read and recommend it to all.
Rating:
Summary: Are you innumerate?
Review: This book was a pretty quick read, and while it covered a lot of ground, the book generally dealt with the issues on a pretty basic level that should be easy for almost everyone to follow. There are important issues in here, dealing with people's inability to properly comprehend probabilities and statistics, as well as the common problems associated with comparing relative magnitudes. The inability of people to grasp some of these concepts has an impact on their ability to make good decisions, and leads them to develop beliefs that aren't strongly based in reality. A worthwhile read, if only to emphasize the importance of these concepts.
Rating:
Summary: Great book that re-ignite my interest in mathematics,
Review: This is a great book, i bought it in Bali airport, and enjoy it very much. I even bought several other books by Paulo: BEYOND NUMERACY which deals with more "numbers n mathematics" and two others coming in soon. I also started to search trough the mathematics section and got THE JOY OF MATHEMATICS. So, in short, the book ignite my interest again in mathematics...., it is a great book well written and enjoyable to read. It is about all the things we see in life that connect to mathematics. It teach us to use mathematics into our thinking. It is very interesting and alive. It is amazing how a good writer can turn a dry material into such an "entertainment". I bought several copies and giveaway to several friends. Yeach, it is that good.
Rating:
Summary: Should be Required Reading
Review: This is a humorous, entertaining and frequently depressing book about the mathematical ignorance in the modern world. Just the confusion among million, billion and trillion is enough to set one's teeth on edge but the rest of the real-world examples...
Do you laugh or cry? What is infinitely sad is that the very people who need this book the most are the ones who most likely get their reading from the super market checkout line. I hear this type all the time...."Hey, Marge, look at this bat-baby." Even some of the reviewers who would be most prone to pick up a book like this complain at the "difficult" nature and condescending attitude. So what is the answer - do we leave them blissfully unaware of their stupidity? Gardner answers with a decided, "No" and this is the result - a splendid accomplishment.
Rating:
Summary: The consequences of numerical ineptitude
Review: This is one of those books I wish everyone would read. In this wonderful and very readable little book, John Allen Paulos addresses an ever-growing but little-acknowledged problem: the pervasiveness of "innumeracy", a sibling malady of illiteracy. Paulos defines innumeracy as "an inability to deal comfortably with the fundamental notions of number and chance...", and I can safely say, without much fear of contradiction, that it afflicts the vast majority of the human race. But why is it a problem? What does it matter if people get a little confused over numbers and probabilities? Well, just consider how many important decisions we are faced with, almost on a daily basis, that involve numbers and probabilities. Nearly all political discussions these days involve mention of millions, billions, or even trillions of dollars, so it would be prudent to have some familiarity with those concepts. Nearly all discussions of product safety and drug efficacy involve the results or studies, which require some understanding of probability and statistics. Yet another reason to get a grip on numerical reasoning, Paulos claims, is that innumeracy is linked with belief in pseudoscience and other outright nonsense. As Paulos points out, "...a significant portion of our adult population still believes in Tarot cards, channeling mediums, and crystal power." With a bit more quantitative savvy, these ruses would not hold sway. Paulos writes in a very engaging style, although he admits at the outset that "Because the book is largely concerned with various inadequacies--a lack of numerical perspective, an exaggerated appreciation for meaningless coincidence, a credulous acceptance of pseudosciences, an inability to recognize social trade-offs, and so on--much of the writing has a debunking flavor to it." Yet, Paulos's method of debunking is friendly and even comical. He typically uses social scenarios to make his points. For example, he relates the following story: "...we were watching the news, and the TV weathercaster announced that there was a 50 percent chance of rain for Saturday and a 50 percent chance of rain for Sunday, and concluded that there was therefore a 100 percent chance of rain that weekend." Paulos notes that he had to explain the error to others who were listening to the weathercaster; and even then, one of the listeners "wasn't nearly as indignant as he would have been had the weathercaster left a dangling participle." Given the generally sad state of literacy in this country, anecdotes like this should make one wonder just how deplorable the state of numeracy is. If you are looking for a friendly and readable book that will help you to make sense of the ever-increasing use of numerical data and probabilistic thinking that is appearing in public discussions of all forms, I recommend this book very highly. If you are yourself a "numerate" person (perhaps even an instructor of mathematics), it behooves you to understand just how ill-prepared the majority of our population is to deal with such reasoning; you need to know what you are up against. It will shock you.
Rating:
Summary: Get smart!
Review: This is the second book that I have read by Paulos, and consistent with the previous book that I read (Once Upon A Number), this work is nothing less than superb. It is short and to the point (can be read in less than a day). Although Innumeracy may be short, it does not skimp on providing plenty of detail and evidence to support Paulos' claim that many people living in American society have a problem when it comes to interpreting statistics and understanding large numbers. Innumeracy takes you on a journey through the world of math and helps you understand things that used to seem so mystical. Paulos does a great job at chopping down the institutions (i.e. astrology, ESP, and other pseudosciences) that have grown as a result of our lack of basic mathematical understanding. If probabilities can seem foreign to you at times, this book is for you, too. Thanks to this book, I am well more aware of the differences between large numbers (millions, billions, trillions - don't confuse them!). What makes this book fun is its inclusion of relevant, exciting topics that you probably think about often, but may not fully grasp. I recommend this to anyone who may feel intimidated by certain fundamental mathematics. I certainly enjoyed learning all about how to choose a spouse, running pyramid scams, and gambling. If you think this kind of stuff might interest you, give Innumeracy a shot.
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