How Not to Be Wrong: The Power of Mathematical Thinking by Jordan Ellenberg (PDF)

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“Witty, compelling, and just plain fun to read . . .” —Evelyn Lamb, Scientific AmericanThe 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.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐Ellenberg brings an interesting but very relevant background to this book – he is a math professor with a PhD in mathematics from Harvard and also has an MFA in creative writing. This combination of skills works well in a book that attempts to illustrate how mathematical thinking can be applied to everyday matters. He does this in an entertaining and pragmatic manner that makes it easy to digest some of the underlying principles.One of the underlying themes throughout the various examples/case studies that Ellenberg discusses is the importance of asking the right questions and not accepting things at face value. In an increasingly binary world (left/right, good/bad etc), he shows the importance of exploring the nuances of a problem (understanding uncertainty) and asking the right questions to get to the heart of the matter (something the media could do a better job of). The math starts off fairly easy but soon gets out of my comfort zone but that does not diminish the objective of the example under discussion.Not only is Ellenberg an engaging writer he is also somewhat prophetic. When he asks the question “Does someone have the movie rights to the story of a couple of teams beating the Massachusetts Cash Winfall lottery?, he did not foresee the movie “Jerry & Marge Go Large” coming out in 2022 (I think) — but it is a movie worth watching about a guy from Michigan and a bunch of kids from MIT beating the lottery system (side note: Ellenberg does a better job of explaining how they did it).I am convinced I am always right – at least that’s what I tell my daughter – and I made the right decision to read this book (another shout-out to Bill Gates!).

⭐A good balance between theory and practice. Just enough theory to support the conclusions. Wonderful examples of how to use/judge statistical information presented in the press or elsewhere. Good practical examples of decision making in high impact, low probability situations. I really liked it. Recommended to my by my professional elementary education daughter.

⭐You’ll start reading this book thinking there will be a lot of juicy math on odds vs. utility functions in decision theory, then toss it out in disgust when you find you’re reading a snail-paced “lives of the Saints in Probability…”BUT IF you toss it, you’d be WRONG just like the book’s title! Ok, I’m with George Box that all models are wrong but some are useful, so in all humility, even if our thinking is n-dimensional and nonlinear, our headlights still don’t go out centuries, and the law of unintended consequences will inevitably rear it’s fearsome head. So yes, I know I’m gunna be wrong more than right even reading this gem of a book.It gets FUN! As you read on, Jord gets into deeper and deeper math, and most significantly, starts to COMBINE stats, geometry, differential equations, etc. in eclectic, multi-disciplinary fields, which are much more like real life than academic exercises. It is not only math that has a new twist every hour these days, it is the combinations of fields (as in vocations and disciplines, not quantum fields) that is making math more and more relevant.I’m not one to discount the gut, heart, tradition or even intuition, but it really is enlightening to take a little more quant view at our normal evaluations of everyday spin. Yes, the author does have a bit of a left bent, but heck, those are just examples, and you’d have to be pretty emotion driven not to see how easily his logic applies to ANY “position.” I see a LOT of tongue in cheek in this book and a LOT of both wonder and just plain great story telling– please don’t pass on this book if you’re bright but not necessarily a policy wonk!I’ve been in school board meetings where one group or another wants to add social justice at the expense of STEM and math, and I just scratch my head. I’ve seen left proposals to take out intelligent design while adding Islam (??) and right proposals to remove Islam, Darwin and Linear Algebra to add family social values. Hmmm. The folks that criticize this author for being a little too green might consider that he is clearly for adding back a LOT more math in the curricula! Hey, I’m a geek, and only anti-geeks can argue with that! I guarantee that even if you are way right, but smart, you’ll thoroughly enjoy this book, and it applies just as clearly to one cause or position as another, and tries to avoid being “dumb” about ANY linear thinking.I’m more into enjoying what you buy here than getting into politics, but because of some of Jordan’s controversy, just thought I’d add my 2c that this is well worth reading regardless of your politics, as it is fun and smart. Just give it a chance, it gets better and better faster and faster– second derivative + — jounce, jolt, surge etc. stuff.;=) Enjoy…

⭐This is a book about mathematics but there is really very little mathematics in it. It is not about the history of mathematics either, though Dr. Ellenberg reaches throughout the book for some of the names and doings of that history to illustrate his themes. The theme is really the world, especially the social world, and how so much of what we experience is expressible mathematically, even if that expression comes not to a definite answer, but only a maybe or other equivocation. This is a book about getting us to think about the world’s regularities and the claims of people in terms of the mathematics that can represent them. It turns out if you understand even the broad outlines of the mathematics you are in a much better position to analyze the claim or make the bet even if you do not (or cannot) actually DO the mathematics involved.A simple example tells the tale. We have all heard claims of the following sort: “the majority of Americans do not support X” (where X of course is just about anything at all of a social or political nature). Now it turns out that if you ask a whole lot of Americans three questions, questions about X, Y, and Z, and if roughly a third of the people asked are positive on one of the three and negative on the other two, it will turn out you can say with a straight face that a majority of Americans do not support X, Y, or Z, your choice, and you would be right! It is this sort of thing that “How Not to be Wrong” is really about. It is well written, not dry, enlightening (you will come away with a greater appreciation for mis-directed claims), and addresses much if not all of the social world we navigate daily.Enjoy

⭐These were the key points for me in this book:1. Survivorship bias – average return on investment funds for example – omits the funds that were so unsuccessful that they were closed – so that only survivors data is analyzed resulting in a false impression;2. Sometimes a line is actually a curve or a parabole. About the risks of linear regression (continuous increase of population is not a straight line but a curve so that the expected rate of growth will be reduced);3. A small selection will produce more unexpected results – for example smaller population states have the most extreme ratios for cancer – both low and high – but this is just another result of randomness and does not give any important insights;4. Law of large numbers revisited from several angles;5. Don’t talk about percentages of numbers when the numbers can be negative. The example is job growth by sectors – lets say retail sector adds 10 jobs, construction loses 10 jobs and IT adds 2 jobs. The total job adds are 2 people. So if you would want to manipulate the data you could say that all the jobs were created in the IT sector, because the total job growth is the same as the IT sector growth;6. There was another warning about getting fooled by randomness: a stockbroker sends different stock tips to a large number of recipients and does this over and over. There will be a few recipients who will get stock tips that were right again and again. So the stockbroker can seem genius because no-one will be able to know about all the wrong suggestions;7. Bayesian inference. A fancy name in order to impress at smalltalk but basically means a statistical test which is done on the same data but after some new input has emerged;8. p-values. How to test the reliability of scientific statistical studies. Turns out that there still are many unreliable studies published;9. There was also a big discussion on the election systems in different countries. Basically the paragraph showed how in many cases the system modifies the initial process in such a way that the most popular candidate may not win.A few general comments:1. It is mostly a very boring book and although it contains lots of important intelligence then because of the books marketing I was hoping for much more entertaining read;2. I made lots of notes in the book but there was a big gap from about page 189 to 272 when it just got too theoretical.3. Although the book should show us the maths in everyday life it seems to be mostly intended for math scientists in order to show to their kids that their work has some real life connection instead of showing to the rest of us to apply math concepts in real life. Do not get me wrong, it has this value also, but there is just too much of theoretical math.

⭐I bought this book because I saw a post on LinkedIn which talked about how mathematics had contributed to the decision in WW2 to add extra armour to fighter planes in places where the returning planes did not have bullet holes (because the planes which didn’t return had been shot-down due to being hit in different places to those which had made it back, and shots in those places were more dangerous). I thought that was a great example of how maths and logical thinking could help with better decision making and a more intelligent thought process. I had hoped for a book full of similar examples.Unfortunately, this was the most interesting example in the book. The book has other examples, for sure, and, as you would expect, it also highlights other areas where our intuition or “logic” is wrong. But, these examples, at least for me, were much less interesting. The US elections are one area it talks about in more detail.If I’m honest, this book reminds me why I had to drop A Level maths after 3 months i.e. because I wasn’t very good at it, didn’t enjoy it, and found it to be “too much hard work”. Perhaps that’s not the best approach to difficult things, and maybe I wish I had persevered with the A Level, but I did find this book to be quite hard work. As the author claims at the start, it isn’t packed full of equations, but it does get into some detail around things like probability, which I have twice studied at university (BSc and MBA), but still found difficult to follow. I think part of the challenge is that, for me at least, this book needed to be “studied” rather than just “read”, and I didn’t want to study it. If you’re more literate in Maths, that may not apply to you, and it may be an easier read.Parts of it were certainly interesting, and I read the whole 430+ pages because I know that there are important ideas / lessons here, even if I’m not smart enough to fully understand all of them (or not motivated enough – probably both).I wouldn’t recommend against the book, I’m just trying to give you a better sense of what to expect. If I’d known what it contained, I probably wouldn’t have bought it, to be honest, and I certainly wouldn’t have chosen it for my Xmas holidays “easy reading” (it wasn’t), but I am also sure I’ve learned something from it.My final comment is that I think it’s unnecessarily long. The author is clearly 100 times smarter than me, probably more, but I do think he could have made this shorter and still made the same points.So, overall, I’m a bit disappointed, but perhaps more with myself than with the book. If you’re ok with the Maths, give it a go. It’s well researched, well thought through and, in places, very funny.

⭐I am enjoying this book, as it explains things clearly and the mathematics is made easy to follow.However, my criticism is aimed at the publishers, not the author. The text is a bit small (I’m in my 40s, and the text is only just about legible), and the asterisks (used for the footnotes) are microscopic. Frequently I would get to the bottom of the page and discover that the author had written a footnote. I would then spend a good minute or two trying to discover where the asterisk was in the text, and then have to do some re-reading to remind myself of the context of what the footnote was for, then finally read the footnote. By which point I had lost the thread of the rest of the page, and would need to re-read that before I could progress.So rather than be a nice little aside (like you would experience when reading a Terry Pratchett novel), each footnote added about 3 or 4 minutes of discontinuity to the reading.

⭐The author clearly knows and loves maths and, to a large extent, that’s infectious. Unfortunately there are too many digressions, inside jokes and [US] sports references that – for me, at least – are quite excluding. I suspect you’ll get more from this book if you’re not coming to the terms and concepts for the very first time. Hans Rosling’s book ‘Factfulness’ is much more aimed at true beginners, and shows how maths and reasoning are relevant in the real world.

⭐I’m struggling with this tbh. I’ve read other ‘maths of day to day life’ type books and found them really interesting and entertaining. But with this one I keep losing interest. Some insightful bits which are good. I’m no professor but have an interest in reading maths books, maybe the topics covered just don’t interest me. I’d still say give it a go, its maybe just me.

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