How Not to Be Wrong: The Power of Mathematical Thinking
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- Create Date：2021-03-29 13:17:12
- Update Date：2025-09-07
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- Author：Jordan Ellenberg
- ISBN：0143127535
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Summary
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。
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。
Reviews
Nick Davies
，
Perhaps I have read too many of this type of book。 Perhaps I'm not in a 'reading' mood at the moment， or perhaps it was the wrong book at the wrong time。 For whatever reason， I was underwhelmed with this - as opposed to objectively thinking it was a bad book。Jordan Ellenberg aims to highlight and discuss many of the more common mathematical biases and misunderstandings。 He does a good job of covering a good range - it's just that I found his chatty writing style a bit 'off' at times （maybe I pre Perhaps I have read too many of this type of book。 Perhaps I'm not in a 'reading' mood at the moment， or perhaps it was the wrong book at the wrong time。 For whatever reason， I was underwhelmed with this - as opposed to objectively thinking it was a bad book。Jordan Ellenberg aims to highlight and discuss many of the more common mathematical biases and misunderstandings。 He does a good job of covering a good range - it's just that I found his chatty writing style a bit 'off' at times （maybe I prefer non-fiction to be 'straight' and factual） and his little hand-drawn graphs a bit offputting。 There's a whiff of Matt Parker here。 Though much of what was discussed was new and interesting， much was a little 'this is the paradigm example of that kind of thing' and I had read about it before elsewhere on more than once occasion。So not bad， but also not compelling - read over the course of a week and a half only consuming a chapter or two a day。 。。。more
Mala Ashok
，
Sep 06， 2014Prof。 Jordan Ellenberg has written a book which shows the stark beauty of Mathematics。 He uses examples to show that pure Math can be applied to real life situations to make complex and often paradoxical situations simple。 He mentions that non-linear thinking really explains a lot of anomalies and says succinctly that "which way you should go depends on where you already are。"Some of his examples like the Baltimore Stockbroker are just fascinating。 All in all an eminently readable b Sep 06， 2014Prof。 Jordan Ellenberg has written a book which shows the stark beauty of Mathematics。 He uses examples to show that pure Math can be applied to real life situations to make complex and often paradoxical situations simple。 He mentions that non-linear thinking really explains a lot of anomalies and says succinctly that "which way you should go depends on where you already are。"Some of his examples like the Baltimore Stockbroker are just fascinating。 All in all an eminently readable book; however， the Math in it is a little tougher than one is led to believe:-） 。。。more
Or Lowi
，
I’m sure that someone who loves math would love this book。 I’m not that person unfortunately。。。
Chao
，
Written in a very humorous， witty， and accessible way， How Not to Be Wrong confirmed my love for mathematical and statistical reasoning。 The joyous feeling when finally being able to articulate the nature of the world is real， and Jordan Ellenberg conveyed just that with interestingly-framed practical problems， the right amount of human-centered academic history， and straightforward proofs and applications of mathematical principles。
Phat Nguyen
，
Funny and practicle。 I love the book but could not acknowledge the last part。 It seems to be about math and philosophy。 To me this particular session has strayed away from my original purpose that got me to the book。 But it's not bad and overall， the book is wonderful。 Highly recommended！ Funny and practicle。 I love the book but could not acknowledge the last part。 It seems to be about math and philosophy。 To me this particular session has strayed away from my original purpose that got me to the book。 But it's not bad and overall， the book is wonderful。 Highly recommended！ 。。。more
Adam Norton
，
Every part of this book was eye-opening and entertaining。 I have shared concepts from this book with more people than I have from any other book because Ellenberg does a fantastic job at explaining the concepts in exciting and understandable ways。
Stefan Bruun
，
The first half of the book is quite interesting。 Part psychology and part mathematics。 That part works quite well。 The last half is mostly math - which is fine for a math book。 The challenge is that the computations don't really help you "not to be wrong"。 They aren't ways of reasoning that can be applied in your daily life and seem to be unrelated to the theme of the book。The final chapter on thinking in probabilities does however fit quite nicely to the book and rounds things up， but could jus The first half of the book is quite interesting。 Part psychology and part mathematics。 That part works quite well。 The last half is mostly math - which is fine for a math book。 The challenge is that the computations don't really help you "not to be wrong"。 They aren't ways of reasoning that can be applied in your daily life and seem to be unrelated to the theme of the book。The final chapter on thinking in probabilities does however fit quite nicely to the book and rounds things up， but could just have been moved up。 Very similar to the book "Thinking in Bets" 。。。more
Darren Maguire
，
I think the title should just be "Fun Case Studies: Mathematical Thinking in Everyday Life。" It was very math heavy but an informative， insightful read。 I think the title should just be "Fun Case Studies: Mathematical Thinking in Everyday Life。" It was very math heavy but an informative， insightful read。 。。。more
Ole
，
Great principles explained simply。 Yet the author overstresses his points making the book longer than it should be。
Yan Cao
，
I enjoyed reading the first 3/4 of the book -- good math concepts that everyone should know， explained in simple but interesting ways！
Maurice
，
The book is primarily about statistical intuition （but also introduces a few other themes such as non-linearity）。 I'm not sure the author or editors had a clue who they were writing this book for。 If written for people unfamiliar with statistics， to introduce "statistical thinking" to them， the concepts are interesting， but the book never explains them properly。 The author goes on many tangents that often obscure concepts more than clarify them， many fluffy stories about "wrong" statistics in re The book is primarily about statistical intuition （but also introduces a few other themes such as non-linearity）。 I'm not sure the author or editors had a clue who they were writing this book for。 If written for people unfamiliar with statistics， to introduce "statistical thinking" to them， the concepts are interesting， but the book never explains them properly。 The author goes on many tangents that often obscure concepts more than clarify them， many fluffy stories about "wrong" statistics in relation to US politics & sports & tobacco。 If we assume the author wants to warn users of statistics for common mistakes， then the same argument of fluffy prose and totally unnecessary tangents apply。 。。。more
Meems
，
Loved the humor in this book。 Some of it was over my head in terms of the mathematics involved， but most of it was very accessible even to the non-mathematicians！
Nathanael Winslow
，
Should be titled "Why Nobody Can Be Sure They're Not Wrong: The Uncertainty of Mathematical Thinking"。 I don't know how this was a New York Times bestseller。 I'm interested in math。 I even have an engineering degree， so I've done my share of math， and I'm not averse to difficult to follow ideas。 But I just didn't enjoy reading this。 It was a hybrid of math history， some explanation of various theories， with some relatively related examples。 Granted， he tries HARD to be funny。 But I went in and o Should be titled "Why Nobody Can Be Sure They're Not Wrong: The Uncertainty of Mathematical Thinking"。 I don't know how this was a New York Times bestseller。 I'm interested in math。 I even have an engineering degree， so I've done my share of math， and I'm not averse to difficult to follow ideas。 But I just didn't enjoy reading this。 It was a hybrid of math history， some explanation of various theories， with some relatively related examples。 Granted， he tries HARD to be funny。 But I went in and out of understanding what on earth he was saying。。。several times I reread whole sections in an attempt to get the point。 I have to conclude that the book just is not structured well because I do feel like what he was saying was good stuff at times， but usually I had a really hard time grasping the big picture。 I guess he just didn't connect the dots well， in my opinion。 One reason for this is that I started the book expecting him to teach me "how not to be wrong" with "the power of mathematical thinking。" Can't imagine why I'd think that。。。 Instead， it was like "this is how these guys used this mathematical principle to make a decision and this is why it actually doesn't tell us anything！" Here， I'll tell you everything you need to know and you won't even have to read the book （spoiler alert）: You do math subconsciously every day every time you make a decision。 Formal math is like a framework that helps you make better decisions and strengthen your intuition。 You're welcome。 。。。more
Mariano Baraldi
，
Muy buen libro sobre anécdotas y usos cotidianos de la matemática y estadística
parastimo
，
This was a handy volume filled with simple， yet useful， ideas。 I think I learned something today and that is all thanks to this。
Nancy
，
Fun read about a variety of mathematical insights all explained in an easy and fun style
Eda Kaja
，
Fun， easy to read。 As a mathematician， I enjoyed learning about different approaches to thinking about problems as well as the introduction to many areas of math。
Thomas
，
Deep book， lots of math， but even with my cursory understanding of math a good read。 The main focus was logic and how we look at the world。 Too often we miss the obvious because we limit our view。
S。
，
Interesting， but just like any other maths or so book， it gets quite incomprehensible， and therefore， quite irrefutable to the layman。
Phonso Balagtas
，
I thought the book was really interesting。 It did a good job of pointing out how mathematics （not just computations） is used in everyday life。 It gave me a better understanding of certain complex mathematical ideas。 I still found the book to be somewhat difficult to understand at certain points though， especially when ideas would get very abstract。
Demi Fang
，
read across an embarrassingly long period of time because i lost the original gifted copy while moving and started back up on a new copy a few years later。 statistics is the least recent field of math that i've taken （since high school？） so it was both a little painful and a little refreshing to get through this book。 Ellenberg's tone is very friendly; his humor only gets a little annoying when i'm in a bad mood。 but he covers a lot of very practical situations and breaks down the statistical th read across an embarrassingly long period of time because i lost the original gifted copy while moving and started back up on a new copy a few years later。 statistics is the least recent field of math that i've taken （since high school？） so it was both a little painful and a little refreshing to get through this book。 Ellenberg's tone is very friendly; his humor only gets a little annoying when i'm in a bad mood。 but he covers a lot of very practical situations and breaks down the statistical theory and its history for each。 he also just has some really great literary references and pieces of wisdom sprinkled throughout。 i can't say i'll understand or remember all the details， but that's my fault for not reading with great care！ 。。。more
Jim Kerr
，
Pretty math-heavy book about taking a mathematical approach to daily life。 It goes through the development of many theories and ideas， which was very interesting。 The world is full of uncertainty， and that should factor in when you make decisions。
Molly Graham
，
Flipping fantastic book。 I read it six or seven years ago and I still think about it and revisit parts regularly。 This book made me get my undergraduate degree in math。 Can't wait to read Shape！ Flipping fantastic book。 I read it six or seven years ago and I still think about it and revisit parts regularly。 This book made me get my undergraduate degree in math。 Can't wait to read Shape！ 。。。more
Aloke
，
I would reread it just for its explanation of Bayes Law。But on top of that Ellenberg is a good synthesizer。 You get lots of entertaining anecdotes but they are in service of a higher point。 It may take a while to get there but feels worth the wait。 I also like that he tries to debunk the “cult of the genius” and its corollary “the tortured genius”。 （Ellenberg probably isn’t a fan of A Beautiful Mind and he tweeted shade at The Queen’s Gambit）
Libri
，
Làm sao để luôn đúng？ Hmmm， khó đấy， vậy ít sai hơn thì sao？Chuyện kể rằng khi chiến tranh thế giới thứ 2 leo thang， các chiến đấu cơ của Mỹ te tua trở về với hàng tá vết đạn trên mình。 Vị trí của các lỗ đạn chủ yếu là trên động cơ， thân， hệ thống nhiên liệu và các phần khác với số lượng trên 1 feet vuông như sau:Động cơ: 1。1 lỗ/ 1 feet vuông。Thân: 1。73 lỗ/ 1 feet vuông。Hệ thống nhiên liệu: 1。55 lỗ/ 1 feet vuông。Các phần còn lại: 1。8 lỗ/ 1 feet vuông。Vậy cần gia cố phần nào của chiến đấu cơ để t Làm sao để luôn đúng？ Hmmm， khó đấy， vậy ít sai hơn thì sao？Chuyện kể rằng khi chiến tranh thế giới thứ 2 leo thang， các chiến đấu cơ của Mỹ te tua trở về với hàng tá vết đạn trên mình。 Vị trí của các lỗ đạn chủ yếu là trên động cơ， thân， hệ thống nhiên liệu và các phần khác với số lượng trên 1 feet vuông như sau:Động cơ: 1。1 lỗ/ 1 feet vuông。Thân: 1。73 lỗ/ 1 feet vuông。Hệ thống nhiên liệu: 1。55 lỗ/ 1 feet vuông。Các phần còn lại: 1。8 lỗ/ 1 feet vuông。Vậy cần gia cố phần nào của chiến đấu cơ để tăng tỷ lệ sống sót trở về？ Phải chăng là phần ăn nhiều đạn nhất？ SAI！Vấn đề nằm ở chỗ， chỉ những chiếc chiến đấu cơ không thể trở về mới có câu trả lời chính xác nhất。 Dữ liệu về chúng đã thành tro bụi？ KHÔNG！Những kẻ sống sót trở về mặc dù đã ăn chi chít đạn là bởi vì chúng ít bị tấn công vào Động cơ - chính là phần cần phải gia cố。 Những phần khác: ăn đạn thoải mái vẫn còn có thể lết về nguyên vẹn。Và bạn đoán đúng rồi đấy， sau khi gia cố phần động cơ thì tỷ lệ máy bay trở về đã tăng lên。Làm sao để thấu hiểu ý nghĩa đằng sau những con số khô khan？ Phải chăng môn xác suất thống kê sinh ra chỉ là để "tiêu diệt" sinh viên đại học？ Còn bao nhiêu ví dụ trong cuộc sống có thể giải quyết bằng tư duy toán học？Đọc xong quyển sách này， bạn sẽ thay đổi hoàn toàn cái nhìn về toán học và đời sống。Đúng nhiều hơn？ Hmmmm， sai ít hơn cũng đủ tốt rồi mà？"How not to be wrong" - mượn ngay tại Libri: https://www。librireading。com/product-。。。 。。。more
Mostafa
，
"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。"I liked this book alot， I liked it more when I refreshed my statisical knowledge before reading it。 The book addresses very interesting topics with an easy and funny style。 I didn't like some redundant proofs of some topics， some of political reference I didn't get， and I think that religious proofs was incoherent with the book。The book won't teach you a magical way not t "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。"I liked this book alot， I liked it more when I refreshed my statisical knowledge before reading it。 The book addresses very interesting topics with an easy and funny style。 I didn't like some redundant proofs of some topics， some of political reference I didn't get， and I think that religious proofs was incoherent with the book。The book won't teach you a magical way not to be wrong but it's not always wrong to be wrong。 。。。more
Sushilg
，
Very great insight into how probability plays important role into our decisions。I would say the narrative wonders around the subject for a long before diving into the core。Again， it takes detour quite a few times before reaching to the core idea。。。by the time I lost the focus or interest。One of my friend did a excellent job in translating this in straight， no-nonsense way。I would still call it as a good read！
Kyle Steinicke
，
An interesting read， there were times where I got lost in his long-winded explanations。 Some of the analogies that Ellenberg used just confused me when I already had a decent understanding of the concept。 There was some interesting history and I learned some new things which is all you can ask for at the end of the day。 A well deserved four stars。
Ben
，
Great book that keeps a mix of practical examples and abstract。 There's a bit in there about politics and things like "x% believe that benefits should be cut" that is really apt for the last few years。 Especially when within that percent， everyone disagrees _which_ benefits should be cut （basically， the ones they don't personally use）。 Great book that keeps a mix of practical examples and abstract。 There's a bit in there about politics and things like "x% believe that benefits should be cut" that is really apt for the last few years。 Especially when within that percent， everyone disagrees _which_ benefits should be cut （basically， the ones they don't personally use）。 。。。more
Brian Weisz
，