One thing that most people will appreciate in this book is a better understanding of their mathematics professor's strange sense of humor. I agree with the author that most mathematicians do show a certain, recognizable style of humor. He goes on to explain the ways that mathematical reasoning resembles, and therefore illuminates humor. This book provides an entertaining introduction to mathematical concepts and theory. I'm not sure that I would recommend it as highly on the other side--to comedians. This is more of a philosopher's approach to humor.

Given the book's title I was surprised at its contents. It contains a lot of very good jokes, to be sure, but it is a serious study of the mathematical structure of certain kinds of jokes. The introductory discussion of the history of ideas about humor was particularly valuable. Very satisfying read!

Pretty nice offering from Paulos, but kind of thin. A lot of good illustrative jokes are scattered throughout, but the analysis isn't really all that interesting. At any rate, I would still recommend it, with some reservation.

This is a wonderful joining of laughter (which nearly everyone does) and mathematics/logic (which not as many do well as they should be able to - me included). I would hesitate to use it as a supporting text in a mathematics, logic or philosophy class but many of the examples given would be great teacher's aids. (The book is sometimes too technical for students and its technical details may alienate some of them - in my estimation anyway.) But I have written elsewhere (see 'Zero: The Biography of a Dangerous Idea') that I believe mathematics education will be greatly assisted by humanising it, putting people back into it (who could not be fascinated by Ramanujan, Erdos, Gauss and company?). The writings of Paulos would be a great tool in this direction and I wouldn't hesitate in prescribing 'Innumeracy', for example, as a required text. This book, however, would be a great source of ideas for a teacher or an interested reader like myself. And there are some very good laughs too!

Paulos is entertaining, awesome, etc. My first book by him I couldn't put down. I was so intrigued with Innumeracy that I even had a hard time finding time to do my math homework. Ironically, Innumeracy was "advertised" in the math book that I was working in. Really, any books by this genius is worth your time and money. "I Think" reminds me a little of Lewis Carroll, word and math games. Paulos does what all of these math wizards out there claim they can do: make math more palatable and interesting. I tried, "Laugh With Math." What? I wasn't laughing! Paulos, I believe, doesn't even have to try.

I thought this a good book that showed how math is valuable in the real world. The author tries to avoid reading like a text book to try and make math come alive. He is moderately successful, but it is hard not to have some mathy jargon and notation, which I think will discourage those who don't have some motivation to think about math to start with. Overall a good book and I will try to read his first book if I get a chance.

I always tell people they don't realize how much mathematics they use in everyday life. Beyond Numeracy really makes that clear. It's a kind of mini-encyclopedia for most everything a recreational mathematician would find interesting, the nature of pi and e, prime numbers, matrices, elementary probability and logic, functions, game theory, statistics, paradoxes, chaos theory, combinatorics and so on and so forth.

I thoroughly enjoyed "Innumeracy," Paulos's first contribution to educating the general public in math. "Beyond Numeracy" picks up where "Innumeracy" left off, but the book does not continue the excellence so characteristic of the Paulos's first. Many of the explanations are less than perfectly clear (very much unlike the case in "Innumeracy"), and the later chapters on more obscure topics, while still interesting, can get tedious and repetitive.

Don't get me wrong-"Beyond Numeracy"'s flaws do not make it unworthy of a read. It's a fun book, and one capable of illuminating many topics in math. If you do choose to read the work, however, don't worry too much about skipping a chapter here and there. The short chapters ensure that you don't miss too much, and again, the repetition that I mentioned can get tiresome.

Overall, an interesting read; I have found no better work about math "in general." Paulos is for the most part clear, concise, focused, and capable of relating the subjects of his many chapters to the real world. Good stuff.

Another solid John Allen Paulos book.

If you would like an objective view of the stock market, are comfortable with math and enjoy a little irreverence in your investment reading, you will love this book. The material is easily accessible for anyone who finds algebra not too taxing. Professor Paulos minimizes the formulas for you by using anecdotes, simple brain teasers and practical examples instead.

What makes the book delightful is his self-effacing sense of humor. I cannot remember reading another book in which a writer is as candid and funny about his own failings as an investor. Only Andy Tobias comes anywhere close. The book's running joke is the professor's disastrous obsession with buying WorldCom stock using borrowed money before it became apparent that the company's reported earnings had more to do with wishful thinking than reality. It is this example that makes the book also insightful for the reader because it shows how easily our emotions and instincts can lead us astray, even when we understand as much about the stock market as Professor Paulos does.

I have read dozens of stock market books that have attempted to explain the "numbers" aspect of stock-market investing. None of them covered as much ground or did so as succinctly as this book does. I was very impressed by the depth of reading that this book reflects. Although it is not an academic book, the rigor is impressive.

The basic point is that the stock market is a lot more complicated than anyone can hope to understand, and likely to be more volatile than almost anyone will be comfortable with. Professor Paulos provides potential remedies for both (index investing, diversifying active portfolios, and using derivatives as insurance against large risks).

One of the many brilliant math examples shows how some games cannot be won with "success" strategies, but if you can combine a certain two "failure" strategies you will be a guaranteed success. With that wonderful point, the idea of being a contrarian was better expressed than in anything else I have read on the subject.

By inserting himself in the book through the WorldCom example, Professor Paulos powerfully introduces the element of individual and market psychology. Although he is neither a psychiatrist nor a psychologist, the book abounds with material about the psychology of how the market works and why investors make mistakes. To me, the ultimate lesson here was that one's stock market approach has to be one that fits emotionally well . . . or you will never execute it successfully.

Ultimately, successful active investing requires you to correctly pick what everyone else will find irresistible not too long before that compulsion hits them. I came away, once again, delighted that index fund investing is available as a sure-fired way to outperform more than 90 percent of all professional portfolio managers while sleeping soundly at night.

After you finish enjoying the book, I suggest that you also think about where else you commit your financial resources in large measure more due to your emotions than to your sense of how to calculate an advantage. How could you change your approach in that other area to be more emotionally and financially rewarding?

Donald Mitchell
Co-author of The 2,000 Percent Solution, The Irresistible Growth Enterprise and The Ultimate Competitive Advantage

Summary:
This is an excellent book on investment theory. It reviews fundamental analysis, technical analysis, option theory and many other topics. The author explains exceptionally well the Efficient Market Hypothesis and the debate surrounding it. He also introduces basic concepts of behavioral finance. And, he touches on the cutting edge of more complex models explaining stock price movements, including chaos theory, power laws, and even cellular automata from Stephen Wolfram's famous book 'A New Kind of Science.' And, he did all that in 200 pages, meanwhile spending pages sharing his self depreciating humorous narrative on his disastrous investment in WorldCom.

Abstract.
As a mathematician having studied the stock market, he believes the stock market is pretty efficient; and that technical analysis is of virtually no value. He gives slightly more credibility to fundamental analysis. Thus, it creates an interesting internal debate in his mind to what degree the stock market is efficient. This internal debate on the Efficient Market Hypothesis is actually one of the most fascinating part of this book. As a result, Mr. Paulos develops a far better understanding of this issue than anyone else I have come across.

Technical analysis according to him should be renamed trend analysis, as it consists in graphing and extrapolating current stock price trends. He covers the major strategies technical analysts use such as buying stocks when their current price breaks through its moving average, and selling them when they fall under this same moving average.

He covers fundamental analysis and their associated metrics in good details. Reading this section, you will become familiar with all the usual metrics, including P/E, PEG, P/Book value, P/Sales. He also mentions Robert Shiller's work on 'Market Volatility' that questions both the Efficient Market Hypothesis and fundamental analysis. Shiller noticed that stock prices are more volatile than the underlying fundamentals of their respective companies. For Shiller, the stock market is just irrational. Shiller later wrote 'Irrational Exuberance' and became both rich and famous due to the perfect timing of this book, which came out at the peak of the market in the first quarter of 2000.

Mr. Paulos makes a case that the stock market captures the aggregate of all our psychological foibles, and goes on giving a good introduction in behavioral finance. He illustrates the common psychological flaws associated with investor behavior, including: the confirmation bias, anchoring effect, status quo bias, endowment effect, and Richard Thaler's mental accounts. He also illustrates flaws we incur when doing investment research, such as: data mining back testing, and the survivor bias. But, in aggregate these human errors partly cancel themselves out rendering the stock market pretty efficient.

The book's gem is the debate on the Efficient Market Hypothesis (EMH). The fewer the investors believe in EMH, the more they will engage in technical and fundamental analysis to extract excess return above the index. These 'active' investors will render the market increasingly efficient, and negate their opportunities to earn excess return. The opposite is also true. If investors believe in EMH, they will become 'passive' and just buy the stock index through a Vanguard fund or an ETF. As a result, the market will not be so efficient, and the EMH will not hold up in such a situation. So if you believe in EMH, it is false. But, if you don't believe in it, it is valid.

Paulos argues that enough active investors do not believe in the EMH to render it valid. This argument is convincing when you think of the thousands of equity mutual funds, closed end funds, hedge funds, and private managers on Wall Street. Thus, there is plenty of professional active investors to render the market very efficient. But, Paulos does not deny that certain markets at certain times, temporarily ignored by Wall Street, may be less than efficient. Thus, for him the EMH debate is not just a true or false question, it is a matter of degree.

'Active' investors play a crucial role in making the market efficient. Paulos makes an interesting distinction between the technical analyst and fundamental analyst. He states that technical analysts are essentially momentum investors. Thus, they cause market volatility to increase. When stock prices increase, these guys buy even more. When stock prices decrease, they sell. Thus, they accentuate the swings in stock movements. Notice that they break the rule of 'Buy Low Sell High.' The fundamental analysts are really value investors or contrarians. They do just the opposite of the technical analysts, and cause stock price movements to moderate. Thus, the two types of analysts/investors play a different role. But, together their active analysis make the stock market very efficient. The EMH states that all information is disseminated and absorbed immediately within the investment community, and thus is fully reflected within stock prices. But, somebody has to process this information. And, that is what the technical and fundamental analysts do. This is how these 'active' investors who are EMH skeptics are its actual underpinning. Ironic is not it.

One of Paulos other big concept concerns the statistical distribution of stock price movements. According to the EMH, stock price movements are random. And, this is true as confirmed by the autocorrelation on any time series of stock prices that is typically very close to zero. If stock prices move randomly, they should assume a normal distribution. But, Paulos indicates it is not always the case. In other words, extreme events (stock crashes or booms) happen more frequently than in a normal distribution. He adds that at the tails, the price movement of stocks is better captured by the 'power laws.' Check page 178 for a detailed explanation on power laws. This is fascinating, and it may represent an upgrade to the EMH that relies solely on the normal distribution.

The book did nothing more than explaining some basic probability concepts (law of multiplicity, conditional probability, binomial distribution) and expressing the author's "anger" over innumeracy.

However, because of author's academic background and his condescending attitude towards the innumerates, the writing style could be quite intimidating to the general audience, who was supposed to be the target audience of the book.

Consequently, the stated objective of the book - to try to instill mathematical thinking to the general public has not been achieved.

For some who is interested in mathematics, this could be a good read. However, smart ones definitely are not going to gain much insight from this book.

There are other 2 books by Paulos. "Mathematician reads newspaper" is not bad (probably as good as this could get.) "Once upon a number" is a complete waste of time...

I read this book several years ago and believe it to be a classic that would enhance any mathematics study course by making it topical and a part of the reader/student's everyday environment. What mathematics teaching needs is humanising - this book could go some way towards doing this.

This short review follows a review I have just written for 'I Think Therefore I Laugh' - another of Mr Paulos' books. Because I rate 'Innumeracy' so highly I decided to look at Customer Reviews for it, and found some clashed with my own assessment.

Some reviewrs are offended by Mr Paulos' perceived attitude towards the innumerate - believing that he is condescending in an off-putting way. I don't see it that way except inasmuch as we are all innumerate at some level and have to learn to become more numerate - just as a golfer has to learn to read the cut of the green if they want to be a good putter. And numeracy skills will certainly enhance the way we see the world and respond to its mysteries as Mr Paulos shows so cleary.

To me, the most intriguing aspect of this book was Professor Paulos's ability to take simple math concepts that I learned way back when . . . and to show how they could enrich and expand my appreciation of the world around me. It was like Alice going through the looking glass in the sequel to Alice in Wonderland. There's a lot there that I never imagined. For example, the way disease rates are often described is for those who have survived to 85 years old. If you are younger, your current probability of incidence will be much lower (possibly more than 90 percent lower). Also, you can use the way you design your questions and sample to help eliminate bias (such as by asking about the results of a coin flip and dangerous sexual behavior in the same population). You can also find great humor in the errors of authority figures who misquote probabilities and risks. Plus, you can answer questions that I would never have thought of (such as the likelihood of breathing in an atom that Caesar did).

If you are feeling cowed about your math ability, take heart! Most of the concepts here you can handle. For example, can you multiply two numbers together? You can answer "yes" to my question if you can do so with a calculator. If so, you can appreciate almost all of the examples in the book.

Professor Paulos has a mind that works differently and more inquisitively from mine, but I enjoyed learning how his thoughts. He thinks about topics like how long it would take dump trucks to excavate Mount Fuji, how many times a deck of cards need to be shuffled to become random, and what the Earned Run Average is for a pitcher who lasts one-third inning and gives up 5 runs. I realized that if I thought about more things like this, I would develop new perspectives on the world.

He makes a helpful attempt to create solutions so that more people can appreciate the world in a quantitative sense. These include using exponents to indicate the size of numbers (such as the Richter Scale does for earthquake strength), refocusing secondary math education to practical applications rather than teaching calculus earlier and earlier, having talented mathematicians teach younger people, and disciplining those who communicate in public to check the mathematical accuracy of what they say.

What do we lose if we don't? Well, those who don't learn a little math will end up in careers that pay a lot less. Social resources will be misapplied to problems that are less serious (obscure diseases and terrorism get a lot more attention to reducing accidental deaths among young people, which is a greater danger). We will make bad resource decisions in our own lives (such as by playing the lottery without realizing that 50% of the money is not paid out to anyone buying a ticket).

I also appreciated how few people can use mathematics in creative ways, to solve problems. For instance, in our professional practice we developed a new way to forecast certain forms of investment behavior. Over 20 years of doing this work, I have never found anyone who could make a single useful suggestion for how to improve the mathematics of our approach, despite having had conversations with dozens of people with advanced math and statistics degrees who would get benefit from an improved approach. I suspect from this experience that there's a higher level of mathematical thinking that Professor Paulos did not explain in his book that we would all benefit from learning. Where do we start? I can hardly wait to learn!

The author deals in an original way with the difficult nexus between statistics and stories, between alpha- and betascience, without favouring one of them, and indeed arguing that both are complementary. This striking impartiality creates the space for original ideas about everyday-situations that every reader will certainly recognize. To be original about (seeming) banality, that is the work of a true great mind. The reason why I do not rate this book with the maximum score, is that it sometimes misses an overarching line of reasoning. The discursive path may strike some readers (like me) as too associative. Needless to say that such a style has its charms, but perhaps due to my Europe-continental education, I am a bit more at ease with a clear thesis and a transparant construction. Nevertheless: it is absolutely imperative to buy this book!

Of all the science books that I have read, there are only a few that I would classify as a must-read. I definitely put this book in that category. I have never read a Paulos before, and was amazed at how facinating the world of probability and statistics is when it is described this well! Authors of books about the wonders of the universe would be lucky if they could make their subjects as interesting as Paulos makes his.

There are four major concepts described in this book: the origins of probability and statistics (in particular how these subjects grew out of our natural observations of the world), the effect of subjective perspectives on our interpretation of both story and statistics, intensional logic (the still little-understood logical structure of this subjective interpretation), and information theory. The book takes a fast-paced, entertaining tour through these topics, and Paulos adds interesting personal anecdotes and bad (intentioanlly) jokes. The book concludes with a discussion of the chasm between the arts and sciences (and those who like to keep it that way).

If your looking for a detailed study of any of these topics, however, then this book may not be for you. But this is a good introduction to subjects you may no little about, but will most likely by facinated by when you finish reading.

I'll see with different eyes after reading this book. Paulos has such a fresh, different take on the world and story-telling - lying at Twenty Questions and its relation to "magical realism," the mathematics of con games, even the autobiographical asides. Superb!

This book read as if Paulos began with a list of common mathematical fallacies and went looking for archetypal examples of them. In many places he doesn't even use specific examples, instead describing a type of story without referring to any particular ones. I really missed the sense that he was reacting to real articles; it seemed more like he was contriving neatly exemplary, and hermetically sealed, examples.

Paulos should have concentrated on a collection of the newspapers that went out on a given day, or on a single paper over time. That way he could have stumbled across some of the more muddled and spontaneous uses of number in the news, and his math primer reactions could have been less pat.

Ultimately this book failed to surprise me with anything. It was pleasant, but not delightful.

I found Professor Paulos's book, Innumeracy, to be a delightful expression of the key elements of mathematical ignorance that can be harmful, along with many new ways to see and think about the world around. You can imagine how much more pleased I was to find that A Mathematician Reads the Newspaper is an improvement over that valuable book. Every editor and newspaper writer should be required to read and apply this book before beginning their careers. Almost all those who love the news will find some new appreciation for how it could be better reported. Those who will benefit most are those with the least amount of background in math, logic and psychology. Although the subjects are often related to math, if you can multiple two numbers together using a calculator you will probably understand almost all of the sections. If you already know math well, this book will probably only provide amusement in isolated examples and you may not find it has enough new to really educate you. Most of the points are regularly treated in the mathematics literature.

In the introduction, Professor Paulos reveals a long and abiding love for newspapers. And he reads a lot of them. He subscribes to the Philadelphia Inquirer and the New York Times, skims the Wall Street Journal and the Philadelphia Daily News, and occasionally looks at USA Today (he likes weather maps in color on occasion), the Washington Post, the suburban Ambler Gazette, the Bar Harbor Times, the local paper of any city he is in, and the tabloids.

This knowledge is reflected in the book's structure. There are four sections, reflecting the typical four section format of many weekday papers. The four sections are:

(1) Politics, Economics and the Nation

(2) Local, Business and Social Issues

(3) Lifestyle, Spin and Soft News

(4) Science, Medicine and the Environment

Then, within each section, he uses a headline and subtitle for each subsection to capture the essence of a story type that we have all read lots of. For example, "Lani 'Quota Queen' Guinier: Voting, Power, and Mathematics" is the subsection that looks at how different ways of compiling votes would affect the power of individual interest groups and minorities. "SAT Top Quartile Score Declines: Correlation, Prediction and Improvement" examines all of those many stories we read about the SAT and what they really mean. Each subsection tends to run from 2-5 pages. As a result, this book can be read in 10 minute intervals very comfortably. In that sense, it's an ideal book for commuters who've finished reading their daily paper and still have more time on their hands.

This book covers many of the same topics as Innumeracy. I suggest that if you feel you really understand that subject that you skip the relevant subsection here unless you find the treatment amusing in its opening lines. Professor Paulos tends to repeat examples from Innumeracy and while that makes the book easier to understand, the repetition can dull your interest.

I found the book to be most appealing when it pointed out the fundamental absurdity of some approach that is commonly used now. One of the most powerful examples involved pointing out that putting one pint of toxic material into the ocean would create a frequency of molecules in the entire ocean that would sound scary to anyone, even though the material would be extremely dilute. Naturally, as an author, I was in complete agreement with his point about the too infrequent reviewing of new books (except on Amazon.com, of course!). My mind was also expanded by the problem of whether Moslems should pray towards Mecca straight through the Earth or as though they were traveling over the top of the Earth.

You probably won't agree with all of his solutions . . . or even think that all of the problems he cites are important ones. But you'll find yourself amused and informed more often than not. That's better than you can expect from all but a tiny fraction of nonfiction books. Take a peek at "Recession Forecast If Steps Not Taken" as a test of your potential interest in the book. This subsection explores chaos theory and why it's not possible to forecast accurately all of the things that people regularly claim to forecast (such as the weather, the economy and many social trends).

After you finish the book, I suggest that you pick out a newspaper article that falls into some of these errors . . . and write a letter to the editor suggesting how it could have been improved. If we all did that even once a year, newspaper reporting would soon improve and we would all be better informed.

Paulos' warm and inviting style and his relationship with newspapers made me reminisce of the evenings I spent reading the "green pages" while visiting my grandparents in Milwaukee. I enjoyed his tour of scientific journalism and working through his math puzzlers. This book provides perfect examples for applying statistical knowledge in the real world. It's a wonderful tool for demonstrating the fruits of critical thinking. I especially like the short chapter format. Any stats instructor (or any social science instructor for that matter) will be glad they read it