How Not to Be Wrong: The Power of Mathematical Thinking
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- Create Date：2021-04-19 11:55:27
- Update Date：2025-09-06
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- Author：Jordan Ellenberg
- ISBN：1594205221
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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
Maya
，
The book does a good job explaining mathematical concepts in an easy to understand and tangible ways， using examples from real life that the reader can relate to。 He covers stories such as probability， hypothesis testing， p-values and p-hacking， expectation， regression， correlation vs causation and others。 He also covers a lot of mathematicians and their lives/stories， which I enjoyed。There were some chapters that I personally did not find interesting。 But overall I think the book would be very The book does a good job explaining mathematical concepts in an easy to understand and tangible ways， using examples from real life that the reader can relate to。 He covers stories such as probability， hypothesis testing， p-values and p-hacking， expectation， regression， correlation vs causation and others。 He also covers a lot of mathematicians and their lives/stories， which I enjoyed。There were some chapters that I personally did not find interesting。 But overall I think the book would be very helpful for mathematicians looking for good ways to explain math， and non-mathematicians looking to understand where and how math is used around them all the time。 。。。more
Marta P。
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“Mathematics is pretty much the same。 You may not be aiming for a mathematically oriented career。 That’s fine—most people aren’t。 But you can still do math。 You probably already are doing math， even if you don’t call it that。 Math is woven into the way we reason。 And math makes you better at things。 Knowing mathematics is like wearing a pair of X-ray specs that reveal hidden structures underneath the messy and chaotic surface of the world。 Math is a science of not being wrong about things， its t “Mathematics is pretty much the same。 You may not be aiming for a mathematically oriented career。 That’s fine—most people aren’t。 But you can still do math。 You probably already are doing math， even if you don’t call it that。 Math is woven into the way we reason。 And math makes you better at things。 Knowing mathematics is like wearing a pair of X-ray specs that reveal hidden structures underneath the messy and chaotic surface of the world。 Math is a science of not being wrong about things， its techniques and habits hammered out by centuries of hard work and argument。 With the tools of mathematics in hand， you can understand the world in a deeper， sounder， and more meaningful way。 All you need is a coach， or even just a book， to teach you the rules and some basic tactics。 I will be your coach。 I will show you how。”It's funny to think that I discovered the book named "How not to be wrong" by mistake - I was searching for a book with a very similar title， and didn't realise that the authors were different。 I'm very happy I did！ :）I was one of those students who were alright at Maths， but knew that they were going to do something different in their life （not so much in my case， since I ended up studying Computer Science。。。） and at the same time were intrigued by the facets of the subject， including those topics that are often not covered in the programme due to lack of time。 This book is a valuable summary of many of such facets， from the history and ancient discoveries to concrete applications in the modern world， like the stats of the elections or the maths behind lotteries。 I'm certainly going to recommend this to the students I know。 。。。more
Steve
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Interesting overview of the history of math even though much of the mechanics is not for me。
Preston
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Interesting book about mathematics， Sometimes it was a little hard to follow in audiobook format and I had to re-listen to sections to follow along。
Tim Moore
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While providing historical context of interesting selected math concepts， I found the book boring and too wordy at times while still managing to lack critical details for understanding some concepts。
Anupreet Choudhary
，
Some beautiful concepts are explained。 Good for people with a quantitative mindset。
Valerie Ciraulo
，
Disclaimer: From a science major with a fairly solid mathematical background。It's nice when a book written by a mathematician can be engaging and occasionally funny。The book crosses some very important points when it comes to using mathematics in everyday life。 I feel this book has two flaws。 First， sometimes the prose is a bit stunted and meandering。 Second， the intended audience for this book seems to vary rather widely。 Overall a good read。The most important point that comes across from this Disclaimer: From a science major with a fairly solid mathematical background。It's nice when a book written by a mathematician can be engaging and occasionally funny。The book crosses some very important points when it comes to using mathematics in everyday life。 I feel this book has two flaws。 First， sometimes the prose is a bit stunted and meandering。 Second， the intended audience for this book seems to vary rather widely。 Overall a good read。The most important point that comes across from this book is that in order to not be wrong， we must be willing to admit that we make mistakes and we do not always know the answer。We can make educated and thoughtfull guesses， sure， be we need to remain cognizant that our educated guesses are just that - guesses。This is something I wish a lot more people understood about and within the science field。 。。。more
Christopher
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It was okay。 A bit much text for not that much information。 Mathematics？ Close to none， but some history about mathematics which was nice。 If anyone wonders the “level” of maths in this book。 It explained that 5^3 = 5*5*5
Sean
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I read this whole thing， and I have no idea what it's supposed to be about。 Its title has nothing to do with it。 I guess I'd describe it as "math teacher who's really into math tells you about all the math going on the world at excrutiating length。" How what he tells you is supposed to be applicable to how one functions in the world is sketchy at best。 It's like if some math nerd tells you "Did you know every time you play catch， you're doing calculus？" Interesting， maybe， yet you still don't ne I read this whole thing， and I have no idea what it's supposed to be about。 Its title has nothing to do with it。 I guess I'd describe it as "math teacher who's really into math tells you about all the math going on the world at excrutiating length。" How what he tells you is supposed to be applicable to how one functions in the world is sketchy at best。 It's like if some math nerd tells you "Did you know every time you play catch， you're doing calculus？" Interesting， maybe， yet you still don't need to know a damn thing about calculus to throw and catch a ball。 。。。more
Filip Poposki
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One of my all time favourites。
Francisco
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Literally took me more than a month to finish this，in short this is not how you make math interesting to non-mathematicians。
Jakub Kopka
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This book is just。。。 Wow。
Frank Lindt
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Tough material which requires the reader with less of a mathematical background to reread some of the paragraphs， which makes the read not extremely fluent。 Once you get through those bits， the book is a worthwhile addition to any private library with its bits of math knowledge and supplementary historic overview of mathematical thinking。
Trương Tín
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Simple and profound。
Max
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It taught me a LOT！ Especially chapter 17 was very useful
Gaurav Sharma
，
It's a wonderful book。 There are lots of eyeopeners regarding statistics of daily life。Examples from real events that will tell you the importance of mathematics。But one star taken aback， it's not for layman。 I understand the basic principles used in this book， but had to read twice to understand the applied part。So if one is in the field of statistics， statistical experimentation， they will understand it much better。 It's a wonderful book。 There are lots of eyeopeners regarding statistics of daily life。Examples from real events that will tell you the importance of mathematics。But one star taken aback， it's not for layman。 I understand the basic principles used in this book， but had to read twice to understand the applied part。So if one is in the field of statistics， statistical experimentation， they will understand it much better。 。。。more
Hannah
，
S1V1L1
Rahul Chodankar
，
Requires a good understanding of freshman mathematics to thoroughly enjoy。
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
，