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How Not to Be Wrong: The Power of Mathematical Thinking

by Jordan Ellenberg

3.89 of 5 stars 3.89 · rating details · 2,331 ratings · 308 reviews

The Freakonomics of math—a math-world superstar unveils the hidden beauty and logic of the world and puts its power in our hands

The math we learn in school can seem like a dull set of rules, laid down by the ancients and not to be questioned. In How Not to Be Wrong, Jordan Ellenberg shows us how terribly limiting this view is: Math isn’t confined to abstract incidents that The Freakonomics of math—a math-world superstar unveils the hidden beauty and logic of the world and puts its power in our hands

The math we learn in school can seem like a dull set of rules, laid down by the ancients and not to be questioned. In How Not to Be Wrong, Jordan Ellenberg shows us how terribly limiting this view is: Math isn’t confined to abstract incidents that never occur in real life, but rather touches everything we do—the whole world is shot through with it.

Math allows us to see the hidden structures underneath the messy and chaotic surface of our world. It’s a science of not being wrong, hammered out by centuries of hard work and argument. Armed with the tools of mathematics, we can see through to the true meaning of information we take for granted: How early should you get to the airport? What does “public opinion” really represent? Why do tall parents have shorter children? Who really won Florida in 2000? And how likely are you, really, to develop cancer?

How Not to Be Wrong presents the surprising revelations behind all of these questions and many more, using the mathematician’s method of analyzing life and exposing the hard-won insights of the academic community to the layman—minus the jargon. Ellenberg chases mathematical threads through a vast range of time and space, from the everyday to the cosmic, encountering, among other things, baseball, Reaganomics, daring lottery schemes, Voltaire, the replicability crisis in psychology, Italian Renaissance painting, artificial languages, the development of non-Euclidean geometry, the coming obesity apocalypse, Antonin Scalia’s views on crime and punishment, the psychology of slime molds, what Facebook can and can’t figure out about you, and the existence of God.

Ellenberg pulls from history as well as from the latest theoretical developments to provide those not trained in math with the knowledge they need. Math, as Ellenberg says, is “an atomic-powered prosthesis that you attach to your common sense, vastly multiplying its reach and strength.” With the tools of mathematics in hand, you can understand the world in a deeper, more meaningful way. How Not to Be Wrong will show you how. ...more

Hardcover, 480 pages

Published May 29th 2014 by Penguin Press (first published 2014)

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Jul 10, 2015 David rated it 5 of 5 stars

Shelves: mathematics, nonfiction

This is a wonderful book about mathematics and its application to everyday life. Jordan Ellenberg shows that the certainty that people associate with math is often misplaced; some areas of math are devoted to uncertainty, and that's where things get very interesting.

Ellenberg starts the book with a beautiful example of application of mathematics, logic, and thinking out of the box. During World War II, a group of mathematicians working for the Statistical Research Group were given a problem by s This is a wonderful book about mathematics and its application to everyday life. Jordan Ellenberg shows that the certainty that people associate with math is often misplaced; some areas of math are devoted to uncertainty, and that's where things get very interesting.

Ellenberg starts the book with a beautiful example of application of mathematics, logic, and thinking out of the box. During World War II, a group of mathematicians working for the Statistical Research Group were given a problem by some Air Force officers. Fighter planes returning from missions were analyzed for bullet holes. The number of bullet holes per square foot were counted. For example, there were 1.11 bullet holes per square foot in the vicinity of the engine, 1.73 in the fuselage, 1.55 in the fuel system, and 1.8 in the rest of the plane. The officers wanted to add some armor to the planes; the question was where? The planes could only support so much weight, and where would additional armor be most advantageous? The officers thought that since the fuselage had the greatest density of bullets, that would be the logical location for more armor. A mathematician named Abraham Wald said exactly the opposite; more armor is needed where the bullet holes aren't, namely, around the engines. Planes with lots of bullet holes in the engine did not return at all!

The book discusses the issue of statistical significance. Scientific experiment often use a 95% confidence threshold as an indicator of statistical significance. This means that if a truly random outcome were expected, a positive correlation would be seen only 5% of the time. Ellenberg includes an xkcd cartoon that shows how easy it would be to perform a set of experiments that could come up with statistically significant results like "Green jelly beans linked to acne! at the 95% confidence level.

Some of the section and chapter titles are hilarious. For example, in the chapter titled "Are you there, God? It's me, Bayesian Inference", Ellenberg brings up a scary example of the use of "big data". Based on a teen-age girl's purchases of unscented lotion, mineral supplements, and cotton balls, the retail store "Target" began sending her coupons for baby gear, because of the (correct) inference that she was pregnant. Another great section title is "One more thing about God, then I promise we're done."

Another interesting title is "The Cat in the Hat, the Cleanest man in school, and the creation of the universe", in which Ellenberg reviews some of the probabilistic arguments for and against the existence of god. And I love the famous quote by Richard Feynman:

You know, the most amazing thing happened to me tonight. I was coming here, on the way to the lecture, and I came in through the parking lot. And you won't believe what happened. I saw a car with the license plate ARW375. Can you imagine? Of all the millions of license plates in the state, what was the chance that I would see that particular one tonight? Amazing!

I also love the chapter title, "If Gambling is exciting, you're doing it wrong". Ellenberg describes how several groups capitalized on several state lotteries. Due to some strange lottery rules, it is (was?) possible to reliably make a profit, given enough investment of resources. No illegal shenanigans--the states make money no matter what you do. You could make a profit by taking advantage of the rules, and of the people who buy lottery tickets without a coherent strategy. And, I did not realize that Voltaire made his fortune by taking advantage of state lotteries!

Ellenberg brings up the phenomenon of Nate Silver predicting the outcome of the Obama-vs.-Romney election. Silver predicted the probability of both candidates winning state by state, along with the margin of error. By adding up the probable errors, he estimated that he would be wrong by 2.83 states. Critics seemed to have ignored the fact that he was not wrong by this many states--in fact he correctly predicted the outcome in all 50 states!

I highly recommend this book to all people who are even vaguely interested in math, probability, logic, and the application to everyday life. This is an excellent book! ...more

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Apr 18, 2014 Stuart added it

Shelves: more-stuff-like-this-please

Here's the deal. If you're a social scientist or a physical scientist (me) who works outside the world of controlled laboratory data, you have to make sense of the world with imperfect experiments. You often have limited data, you can't repeat your experiments, and the differences between your subject and control are sometimes very fuzzy. Yet you have to try to make some inferences even though imperfect data are all you have. How do you do that in an honest and careful way? That's what How Not T ...more

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Jun 19, 2014 Ian rated it 5 of 5 stars

This book was an excellent guide to the many ways in which our intuitions and poorly understood statistical training can lead us astray. One of the areas that it covers is regression to the mean, a concept which pretty much everyone needs to be aware of, since a better awareness of its ubiquity would prevent a lot of errors. Among other things, this concept explains why a successful pilot study is likely to give worse results when rolled out, why a good performance is often followed by a worse p This book was an excellent guide to the many ways in which our intuitions and poorly understood statistical training can lead us astray. One of the areas that it covers is regression to the mean, a concept which pretty much everyone needs to be aware of, since a better awareness of its ubiquity would prevent a lot of errors. Among other things, this concept explains why a successful pilot study is likely to give worse results when rolled out, why a good performance is often followed by a worse performance (and vice versa), why sequels are less successful and so on. The book also explains why a lot of medical research is effectively inconclusive despite statistically significant results and how p-values are generally misinterpreted, so we should take medical research with a large grain of salt. Some of the other areas the author discusses are counter-intuitive. One topical example is that if there are three or more options then unless one option has an absolute majority in its favour then ALL of the options will have a majority opposing them, which explains why politicians can never please everyone. For example, if the government offers three options for reducing the deficit: (a) increase taxes (b) cut health funding (c) cut welfare funding and equal numbers of people favor each option then 66% of people will be opposed to each option, so nothing the government does will please a majority.

This book is full of gold for anyone who hasn't encountered some of these concepts before, such as the story of Abraham Wald's insight regarding how the missing bullet holes determined where bombers should be armoured during WWII or how the Laffer curve governs a lot of phenomena rather than linearity or how a zero correlation doesn't necessarily mean that there is no relationship between two variables ( correlation co-efficient does not detect non-linear relationships) or the story of why scientists took so long to be certain of a link between smoking and lung cancer (not because of obstruction by the tobacco companies).

Although I am trained both as a mathematician and statistician, you don't need a strong mathematical background to understand and benefit from this book. Most examples require basic arithmetic and the author has a talent for producing crude but enlightening graphics that help to guide the reader's intuitions.

In addition to this book, I would recommend pretty much any recent book by Gerd Gigerenzer, whose work shows how scarily ignorant doctors are of how to properly interpret results of medical tests and why mass screening programs do significant harm while not significantly reducing mortality. ...more

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Aug 09, 2014 Ben Babcock rated it 5 of 5 stars · review of another edition

Shelves: 2014-read, economics, mathematics, non-fiction, owned, to-buy

I math for a living. I mathed, both amateurly and professionally, at school. I math quite a bit. And as a math teacher, I like reading "pop math" books that try to do for math what many science writers have done for science. So picking up How Not to Be Wrong was a no-brainer when I saw it on that bookstore shelf. I’ve read and enjoyed some of Jordan Ellenberg’s columns on Slate and elsewhere (some of them appear or are adapted as chapters of this book). And he doesn’t disappoint.

I should make on ...more

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Oct 20, 2014 สฤณี อาชวานันทกุล rated it 5 of 5 stars

หนังสือเกียวกับคณิตศาสตรและหลักสถิติเบืองตนทีดีทีสุดเลมหนึงทีเคยอาน อธิบายดวยภาษาทีเขาใจงาย ตัวอยางนาสนใจ แถมคนเขียนยังมีลีลาแพรวพราว เชือมโยงตอจุดเรืองราวตางๆ ทีตอนแรกดูไมรูวาเกียวอะไรกัน เขาดวยกันอยางสนุกสนาน (ตอนอานทำใหนึกถึงสารคดีโทรทัศนชุด Connections ของ James Burke ทีเคยดูตอนเดกๆ)

ชอบครึงแรกของหนังสือมากเปนพิเศษ โดยเฉพาะบททีอธิบายแนวคิด expected value ผานการเลาเรืองกลุมคนฉลาดทีรวยจากลอตเตอรีไดเพราะคำนวณ expected value เปน, บททีอธิบายความแตกตางระหวาง “สหสัมพันธ” (correlation) กับ “ความเปนเ หนังสือเกี่ยวกับคณิตศาสตร์และหลักสถิติเบื้องต้นที่ดีที่สุดเล่มหนึ่งที่เคยอ่าน อธิบายด้วยภาษาที่เข้าใจง่าย ตัวอย่างน่าสนใจ แถมคนเขียนยังมีลีลาแพรวพราว เชื่อมโยงต่อจุดเรื่องราวต่างๆ ที่ตอนแรกดูไม่รู้ว่าเกี่ยวอะไรกัน เข้าด้วยกันอย่างสนุกสนาน (ตอนอ่านทำให้นึกถึงสารคดีโทรทัศน์ชุด Connections ของ James Burke ที่เคยดูตอนเด็กๆ)

ชอบครึ่งแรกของหนังสือมากเป็นพิเศษ โดยเฉพาะบทที่อธิบายแนวคิด expected value ผ่านการเล่าเรื่องกลุ่มคนฉลาดที่รวยจากล็อตเตอรี่ได้เพราะคำนวณ expected value เป็น, บทที่อธิบายความแตกต่างระหว่าง “สหสัมพันธ์” (correlation) กับ “ความเป็นเหตุเป็นผล” (causation), คำอธิบายเข้าใจง่ายเรื่องข้อจำกัดของการทดสอบสมมุติฐาน (hypothesis testing) ผ่านการเล่าทฤษฎีเกี่ยวกับงานเขียนของเชคสเปียร์ ฯลฯ ฯลฯ

น่าสนใจว่าหนังสือเกี่ยวกับวิชาที่คนทั่วไปมองว่ามีตรรกะแน่นหนักปานภูผาอย่างคณิตศาสตร์จะให้ความสำคัญกับประเด็นความน่าจะเป็น ความไม่แน่นอน และขีดจำกัดของวิชานี้ มากกว่าเรื่องกฎหรือทฤษฎี แต่เรื่องนี้ก็สะท้อนความตั้งใจของคนเขียนที่กล่าวไว้ตั้งแต่บทนำว่า อยากให้คนอ่านเข้าใจว่าคณิตศาสตร์และนักคณิตศาสตร์จริงๆ ทำงานอย่างไร

บางตัวอย่างในเล่มไม่ค่อยเวิร์ค อย่าง Zeno’s Paradox อ่านแล้วยังไม่ค่อยเข้าใจ ส่วนประเด็น “ความเป็นสวีเดน” ของนโยบายรัฐ (ระดับการเก็บภาษีไปใช้จ่ายในสวัสดิการสาธารณะ) ก็ดูจะเป็นตัวอย่างที่ยกมาเพื่อหลอกด่า (หรือด่าตรงๆ) เศรษฐศาสตร์สำนักเสรีนิยมใหม่ มากกว่าจะเป็นตัวอย่างที่ดีของ nonlinearity อย่างที่ผู้เขียนอ้าง (ส่วนตัวไม่ได้ชอบเสรีนิยมใหม่ แต่มีหนังสือเศรษฐศาสตร์ที่ด่าอย่างมีเหตุมีผลและตรงประเด็นกว่าเล่มนี้มาก) แต่โดยรวมแล้วก็ต้องนับถือผู้เขียนที่สามารถย่อยเรื่องยากให้คนทั่วไปเข้าใจได้อย่างแจ่มแจ้ง และฝากเกร็ดเล็กเกร็ดน้อยทางประวัติศาสตร์ที่น่าสนใจเป็นของแถมคนอ่านมาหลายเรื่อง
...more

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Sep 02, 2014 Fortunr rated it 4 of 5 stars

Shelves: science-and-maths

Enjoyable, entry-level book, particularly recommended to any lover of applied maths who did not get prior significant exposure to the main concepts of statistics and probability calculus.
The author writes in a very engaging and conversational manner, and his enthusiasm for maths is quite contagious; I like how he manages to compellingly convey the message that math is a creative process, not a sterile, procedural slog.
While the book is designed to be understood by a wide audience, so it is neces ...more

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Jun 27, 2014 Maryanne rated it 4 of 5 stars

Shelves: non-fiction

Where language and math meet is where my head explodes.

That's this book.

Fortunately, the author has a funny, down-to-earth style that keeps me going even when my eyes glaze over and start to roll back into my head. That has nothing to do with him; it's all me. He and I have a fundamental difference in wiring: he loves numbers and the things they can do. For him they sing. For me, they are instruments of torment and deceit.

Let me give you an example. Here's one from page 44 et seq., where he dem ...more

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Dec 08, 2014 Paul rated it 2 of 5 stars · review of another edition

Shelves: books-read-2014

Almost everything that we do these days has some sort of mathematical element to it, from analysis by companies that are looking for patterns, voting, the stock market and ways of winning the lottery.

Ellenberg does make some reasonable arguments; I particularly liked the explanations on the three way voting where the favoured guy can end up being eliminated purely because of the first past the post method, and the way that groups were able to exploit a badly designed lottery.

And most of the tim ...more

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Oct 11, 2014 E rated it 3 of 5 stars

The press for this book seems a little overblown. It is decidedly not the "freakonomics of mathematics." Rather than hitting a plethora of topics, like Innumeracy and other popular books have done, Ellenberg homes in on just a few: linearity (consider: most trend lines are Laffer curves, not straight lines); inference (consider: an FBI algorithm determines that you are probably a terrorist; what are the odds that you are a terrorist? very very low; false positives almost always vastly outnumber ...more

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Aug 27, 2015 Brian Clegg rated it 4 of 5 stars · review of another edition

In the preface to Jordan Ellenberg's chunky maths book (441 pages before the notes in the version I read) we are introduced to a hypothetical student moaning about having to work through a series of definite integrals and complaining 'When am I going to use this?' What Ellenberg sets out do is to show how we use mathematics all the time - and how important it is to understand it if we are not to get the wrong idea about the world. We'll see how well he does.

It was very interesting to read this b In the preface to Jordan Ellenberg's chunky maths book (441 pages before the notes in the version I read) we are introduced to a hypothetical student moaning about having to work through a series of definite integrals and complaining 'When am I going to use this?' What Ellenberg sets out do is to show how we use mathematics all the time - and how important it is to understand it if we are not to get the wrong idea about the world. We'll see how well he does.

It was very interesting to read this book quite soon after Richard Nisbett's Mindware. Both cover how to interact with life better thanks to the support of mathematics. Nisbett drives from the psychology side and improving decision making, while this book drives from the maths. Perhaps surprisingly, How Not to be Wrong is the easier read of the two. Ellenberg has a delightful light touch and is often genuinely funny (it's important to read the footnotes, which Ellenberg, like Terry Pratchett, uses for a lot of his jokes).

Along the way he shows us the uses and risks of straight lines in forecasting and understanding data, the power (and danger) of using methods of inference, how to use expected value, the realities of regression to the mean and the interplay between correlation and causality, and some fascinating observations on why traditional statistics can be very misleading when it comes to public opinion. Here it is often not applied to either/or situations, and it's quite possible, for instance, for the public to both support the idea of cutting taxes while simultaneously supporting raising expenditure. Although there are a few cases where we lose the plot and the connection to the real world, mostly this all driven by real world examples - from lotteries where an appropriate strategy can result in big wins to the apparent prediction that everyone in America would be obese before the end of the century.

While I don't think is this as practical a book as Nisbett's, it is full of fascination for anyone who likes a bit of applied mathematics, but can't be bothered with the formulae - there is very little that is scary in that line here. What's more, if you have any exposure to scientists, this book contains by far the best explanation of p-values, what they really mean and where they are meaningless that I've ever seen.

So would the student from the preface feel after reading this book that there's no need to complain? Satisfyingly for a book that doesn't limit us to predictable mathematical answers, the response is both yes and no. Yes, because it becomes very clear that maths is hugely useful in understanding the world and responding to it. No, because the vast majority of maths you will have suffered at school and may have suffered at university, isn't required here. At least 90 per cent of the content depends on probability and statistics, topics that are rarely covered well enough in the curriculum, given how important they are in getting a grip on reality.

Although it felt a bit too long and used US sports rather too often as examples for my liking, this is a book for anyone with an interest in the way that mathematics can give us a better understanding of what's really happening in our complex world. ...more

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Jun 07, 2015 Will Once rated it 3 of 5 stars

I so wanted to like this book.

It's a topic I enjoy. I flicked through the book and the author was saying things that I agree with. Jordan clearly knows what he is talking about. All the signs were good.

So why the 3 stars? Because the book is unfortunately quite dull. There are long sections where Jordan spends ages proving some mathematical point or other, but then he doesn't draw any conclusions from it.

He starts with a story about school kids not liking mathematics because they can't see the r ...more

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Apr 11, 2015 Lisa Biskup rated it 4 of 5 stars

Though I never went beyond high school calculus, I always enjoyed math. I liked this book and gave it four stars because it is both educational and entertaining. Many other reviewers have written quite extensively about the stories and ideas presented in this book, which are all quite interesting and intriguing, especially the one about how the MIT students who were able to win the lottery.

I like books that expose the problems we have in our thinking and explain better ways to form our conclusi ...more

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Jul 25, 2014 Steven rated it 5 of 5 stars

Of the several books I've read recently in an effort to boost my motivation to re-learn all the math I've forgotten, most of them get bogged down in formulas and obscure theories. This book, while there is some of that, keeps the big picture in mind and doesn't get too technical for lay readers.

Aside from this, there were two big takeaways from this book that I will carry with me for the rest of my life:

1) We often talk about countries as if they are individual people like this: "China thinks __ ...more

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Dec 07, 2014 Aku rated it 5 of 5 stars · review of another edition

What a read!

Jordan Ellenberg has quite the talent for explaining mathematical concepts in a clear manner. If you have read his columns in Slate, you know what to expect from this book. The central theme of the book is how mathematics surrounds us in our everyday lives, showing up everywhere where reasoning is used to get closer to truth.

I will start recommending this book to people I meet who are proud of their mathematical ignorance and who say they never use the mathematics they've learned in What a read!

Jordan Ellenberg has quite the talent for explaining mathematical concepts in a clear manner. If you have read his columns in Slate, you know what to expect from this book. The central theme of the book is how mathematics surrounds us in our everyday lives, showing up everywhere where reasoning is used to get closer to truth.

I will start recommending this book to people I meet who are proud of their mathematical ignorance and who say they never use the mathematics they've learned in schools, to gently guide them to see how wrong that is.

The book has been divided into five parts: Linearity, Inference, Expectation, Regression and Existence. In each chapter the author brings up some problem of mathematical nature related to that part, maybe a few mathematicians from history and how they've paved the way for our current understanding of these issues, and ultimately how the problem should be solved. There is a great variety of topics covered in this manner. I found once again that I enjoyed the biographic parts a
lot, as they tie the otherwise abstract material into our world and culture.

In retrospective, the book suffers from one problem: it shies away from showing much of the mathematical language and notation behind these magnificent ideas. I fully understand that this is due to the genre, format and publisher's wishes, but I felt some compact formulas here and there would not have been "too much". I'm afraid the publishing world underestimates how much mathematical notation readers would be comfortable with, especially when it's so clearly spelled out that this is indeed a book about mathematics. Any reader should challenge themselves by looking up the referenced theorems and formulas from the Internet and seeing if they can understand what's going on.

There is also fairly heavy emphasis on American cultural concepts and politics in this book, but that's something I've learned to tolerate more and more. Each book from the United States teaches me something new about baseball: thanks to this book I now know what an umpire is, and how their calls might change the outcome of games. Maybe one day I will try to watch a game to see how much I've already gathered from books like this! ...more

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Jun 23, 2014 Michelle rated it 2 of 5 stars

Shelves: science-issues

Missed his own title in the very first chapter, where he is absolutely, spectacularly wrong. How can anyone read the quite-easy-reading Daniel J. Mitchell so horribly wrong? I'm NOT a math professor, but I understand the Laffer Curve quite well, and Ellenberg got practically nothing RIGHT here. Mitchell is actually one of the Curve's biggest PROPONENTS and he has mustered quite a bit of evidence about it. I even remember that column! Oh, and Ellenberg, how is all this great spending-tons-and-ton ...more

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Jul 13, 2015 R. rated it 5 of 5 stars

A great read on the importance of math. It ultimately helps us find the answer to many a high school math students’ favorite question: “when am I ever going to use this?” by showing how mathematical concepts help us understand and how they work in every day situations. I've noticed several comparisons this book has received with Freakonomics and think it's unfair. While Freakonomics makes fast and loose use of statistics to establish its hypothesis and make conjectures, HNTBW shows us how statis ...more

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Aug 10, 2014 Eileen rated it 4 of 5 stars

Brendan and I found this book at Tatnuck Booksellers in Westborough one day when he was home and we were book exploring. I said I would read it first and then give it to him and I have been reading a few chapters a night. I thoroughly enjoyed delving into my inner math psyche! The first chapter is something I have always asked Brendan when we talked math-“When Am I Going To Use This?” The author does a great job explaining the need for math and how we use math and that math is “the extension of Brendan and I found this book at Tatnuck Booksellers in Westborough one day when he was home and we were book exploring. I said I would read it first and then give it to him and I have been reading a few chapters a night. I thoroughly enjoyed delving into my inner math psyche! The first chapter is something I have always asked Brendan when we talked math-“When Am I Going To Use This?” The author does a great job explaining the need for math and how we use math and that math is “the extension of common sense by other means.” I was sold on reading more as long as I didn’t have to really DO complex math, so I read on….I learned about calculus with diagrams of a missile path (see page 39) and then enjoyed the deliberation about “everyone is obese” with theories. Ok-I admit that in some chapters I was a little lost, even with the down to earth explanations about some theories but I really liked READING about how math is actually a part of everything we do. Particularly felt comfortable with the chapter about statistics and the explanation and cartoon with the jelly beans was great. I learned many new words and math theories and concepts, but towards the end of the book I felt overloaded. The author was successful in connecting math to my world with connections to Facebook (Bayesian Inference), playing the lottery and gambling (Expected Value), and then Chapter Twelve about missing your plane-sorry but I was lost here. I remember doing regression in grad school but the stories here were much fun than the textbooks I used in school. Then I earned about Galton’s Ellipse, and also the use of percentages, numbers, and data in public polls and surveys. (Actually this part of the book reminded me of a little book we read and talked about when I was in grad school many moons ago-How to Lie With Statistics by Darrell Huff.) I am so glad the author had a good ending to the book as he brought me back to earth with talking about the importance of math. He writes, “When are you going to use it? You’ve been using mathematics since you were born and you’ll probably never stop. Use it well.” Final thoughts-I enjoyed the book but it still was a little difficult to read and digest some of the many theories and concepts presented. Off to use some math as I examine numbers about student teaching placements and to see how many have registered for my professional development training for cooperating teachers. I am eager to pass this book onto Brendan and hear his thoughts about the book. ...more

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Aug 30, 2015 Fred Forbes rated it 3 of 5 stars

The item that attracted me to this book is the chapter one discussion of a comment on Obamacare by the Cato institute that says Sweden is backing off on the benefits and high taxes of their healthcare system so why would the U.S. duplicate their mistakes? The author then constructs a graph, a view of the world from the perspective of the conservative Cato Institute. It shows "Swedishness" along the horizontal axis and "prosperity" along the vertical axis. The line thereon is straight, going from ...more

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May 05, 2015 Eva Thieme rated it 5 of 5 stars

My son, who is planning to major in math, gave me this book to read. Needless to say, I didn’t quite breeze through it as quickly as he did, but nevertheless greatly enjoyed it, even though I didn’t totally understand every last detail.

The reason it was so enjoyable: First, the subject matter. As promised, the book shows us how math touches everything we do, with a ton of real-world examples where one might not even suspect math played a role. We get to look at such varied topics as where on a ...more

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Apr 28, 2015 Robert rated it 5 of 5 stars

How Not to Be Wrong is a very funny and beautiful book about math and is my favorite book of the year so far. It's very rare that when I finish a book, I have the urge to read it again. But, that's how I felt after finishing How Not to Be Wrong, and I did end up giving it a fast, second read. I had bought a copy when I was supposed to be shopping for Xmas gifts for others, but it somehow ended up on my bookshelf. Sometimes selfishness pays off.

Ellenberg tells many fascinating stories related to ...more

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Mar 15, 2015 Doris rated it 4 of 5 stars

Ellenberg has an engaging writing style and plenty of good stories with mathematical underpinnings. The title, How Not to Be Wrong, is based on his assertion that "mathematics is the extension of common sense by other means." There are a lot of ways in which mathematics can surprise us though, and Ellenberg delights in doing that.

I really liked this book. It took me months to work my way through it, in large part because I was reading alternately a library hardcover copy and a library ebook. Ea ...more

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Jan 02, 2015 Rebecca Schwartz rated it 5 of 5 stars

It is hard to sum this book up because Ellenberg hits on quite a few mathematical topics (linearity and lack thereof, statistics, combinatorics, Euclidean and non-euclidean geometry, etc.) and their applications to areas such as economics, scientific studies, the lottery, error-correcting codes, politics, and voting, just to name the ones I recall off the top of my head.

I have never read Ellenberg's column on Slate, or his blog, but I intend to start. He mentions at the end that a lot of the ma It is hard to sum this book up because Ellenberg hits on quite a few mathematical topics (linearity and lack thereof, statistics, combinatorics, Euclidean and non-euclidean geometry, etc.) and their applications to areas such as economics, scientific studies, the lottery, error-correcting codes, politics, and voting, just to name the ones I recall off the top of my head.

I have never read Ellenberg's column on Slate, or his blog, but I intend to start. He mentions at the end that a lot of the material in this book was adapted from his Slate column, which may explain why the book reads like a collection of essays centering around the theme of sound mathematical and statistical reasoning but and how it applies to the real world, but doesn't have a particularly focused narrative arc. In other words, I would describe it as a bit non-linear. His overall intention seemed to be convincing people of the value of mathematical reasoning and how to use it properly to interpret data and avoid common fallacies. He did a good job of tying up the loose ends in the final chapter and leaving the reader with some solid, general insights about how the study of mathematics works, and addressing the question posed by the title of how not to be wrong.

I have a strong mathematical background, which helped tremendously in reading this book. Although the book is marketed towards laypeople, Ellenberg does not pull any punches when it comes to getting into detail about the mathematical concepts. I found it fairly dense and in some cases had to linger on a page for a while to grasp what he was saying. However, the clarity of his writing, as well as his sense of humor, makes it easier to digest. And fear not, you do not have to remember anything about algebra to understand his arguments. I imagine that if there were anything in this book too technical for readers to grasp, they could skim over some of the more challenging parts and still get the overall gist of the applications.

As a math professor who teaches non-majors (basic statistics in particular) I plan to read this book again to mine it for digestible nuggets of wisdom that I can sprinkle into my curriculum to help my students see the study of math and its applications from a fresher perspective. The book as a whole certainly did that for me.

Everyone could benefit from reading this book, and I would strongly recommend it to anyone who enjoys scientific writing, or anyone who isn't strongly averse to mathematical or logical thinking. ...more

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Nov 25, 2014 Doug Clark rated it 5 of 5 stars

I am, by training, a mathematician. However, for the most part, although still fascinated by the beauty and power of mathematics, I don’t read mathematical books for pleasure. But every once in a while, a new mathematical book is published and I read it, and often enjoy it immensely. The last such book I truly liked and had trouble putting down was Here Comes Euclid by Alex Bellos. Jordan Ellenberg’s How Not To Be Wrong: The Power of Mathematical Thinking falls into that category. I found this t ...more

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Nov 18, 2014 Converse rated it 4 of 5 stars

Shelves: mathematics, non-fiction, statistics

How not to be wrong by Jordan Ellenberg is the best mathematics book for the general reader than I've read. Ellenberg sees mathematics as the careful examination of assumptions and their consequences. The story of how Abraham Wald, who during the Second World War improved the armoring of US Air Force planes by focusing not on where the planes that came back were damaged, but rather on those parts of plane from which no one returned with damage (because they had all been shot down) illustrates th ...more

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Aug 01, 2015 Augusto rated it 5 of 5 stars · review of another edition

Shelves: estatistica, favoritos, matematica, não-ficção, politica

Informal sem descambar para o terreno do superficialismo, bem-humorado e lança mão de muitas ilustrações, analogias e metáforas que nunca havia lido em nenhuma obra ou que foram revisitadas com clareza e leveza absolutas.

Ellenberg é professor da Universidade de Wisconsin e colunista na Salon, o que reflete inúmeras vezes um viés político e humor sardônico que, assintoticamente, coincide com o meu. Sua condição profissional talvez tenha motivado a premissa inicial do livro: em um proto-prefácio d Informal sem descambar para o terreno do superficialismo, bem-humorado e lança mão de muitas ilustrações, analogias e metáforas que nunca havia lido em nenhuma obra ou que foram revisitadas com clareza e leveza absolutas.

Ellenberg é professor da Universidade de Wisconsin e colunista na Salon, o que reflete inúmeras vezes um viés político e humor sardônico que, assintoticamente, coincide com o meu. Sua condição profissional talvez tenha motivado a premissa inicial do livro: em um proto-prefácio de título oportuno WHEN AM I GOING TO USE THIS uma aluna, vitimizada por uma das intermináveis tabelas de integrais definidas do Cálculo 1, vira-se para o autor e dispara a conhecida pergunta para um professor hipótetico. Que poderia ser, e talvez tenha sido, o próprio Ellenberg. A resposta do autor compara o aprendizado e execução monótona e eventualmente mecânica de exercícios matemáticos com a preparação exaustiva de um atleta que, eventualmente, colocará seu expertise técnico e preparação física em uso durante uma competição. Em nenhum jogo de futebol os jogadores correm entre cones ou treinam passes exaustivamente. Para ele, a matemática faz parte do tecido da razão. Uma afirmação epistemológica que certamente vai deixar muita gente de cabelo em pé, mas que passa incólume para os propósitos do autor.

Uma possível reticência seria de que o contexto do livro é essencialmente EUA-cêntrico. O que, em si, é totalmente compreensível e em algumas partes, especialmente nas três primeiras, é mais evidente. Pode até mesmo ser um recurso literário para prender o leitor. Mas a última parte (Parte V), além de oferecer um cenário mundial mais abrangente em relação à avaliação de opinião e sistemas de votação, fecha o livro com chave de ouro.

Tem tudo para se tornar um dos grandes livros de divulgação matemática do século XXI, ombro a ombro com The Drunkard's Walk: How Randomness Rules Our Lives (publicado no Brasil como O Andar do Bêbado) e The Poincare Conjecture: In Search of the Shape of the Universe (A Conjectura de Poincaré), que são imbatíveis. ...more

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Nov 06, 2014 Katia Nosenko rated it 4 of 5 stars

Interesting and elegant book about Maths (and data) and its applications in our daily life. I would not call it very original as there are quite a few recent books on the topic. But it was quite refreshing to read the book on the topic by the proper mathematician. He managed to explain Bayesian theory very clearly so I finally understood it while Nate Silver failed to do it for me in his book.

Overall if you read "Thinking fast and slow" by Daniel Kahneman and "The signal and the Noise" by Nate ...more

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Aug 05, 2015 Bonny rated it 5 of 5 stars

Shelves: math, all-time-absolute-favorites, book-bingo-2014, non-fiction

I run across a lot of books that I add to my to-be-read list and then forget about until after their publication dates or I stumble upon the book in the library or bookstore. How Not to Be Wrong was initially one of those books, but it sounded so good that I found myself obsessively thinking about it and started a search for a pre-publication copy. Since I'm not a librarian, didn't win a copy via First Reads, and don't have friends at Penguin Press, it took some time and effort, but having procu ...more

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Jan 23, 2015 Lisa rated it 2 of 5 stars

Shelves: booksburgh, non-fiction

Have you ever heard the joke, "I'm an English Major. You do the math." or "There are three kinds of people in this world. Those who are good at math, and those who aren't."?

Both of those apply to me. Anyone who knows me knows that I hate math, that my mind draws blanks when it comes to anything relating to it. So why did I read this book? It was a book club selection that I wouldn't have picked up otherwise.

I respect what Eilenberg is trying to do, which is to make math more accessible. He succ ...more

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Sep 07, 2015 notabattlechick rated it 4 of 5 stars · review of another edition

Another solid examination of mathematical thinking in the real world

More philosophical than some of the author's other works, it tackles issues such as probability and uncertainty and ways of thinking with grace and elegance. There's plenty of math, but I would recommend it to anyone interested in rigorous thinking more broadly. Would be an interesting book to teach from, I think.

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Jun 14, 2015 Angela Groves rated it 5 of 5 stars

if this guy had been my maths teacher, i'd have been a straight A student. i found math boring, this, this, well this is fantastic! it made me see the point of maths, which was always my problem, i found equations for physics interesting, because i saw the point, now i can see the point to a lot more. even for a math novice, this book is one you just can't put down.

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