The Power of Mathematical Thinking - How Not to Be Wrong

I had a relationship with this book. I glanced at her at the bookstore and passed her by twice. Gave her the eye and read her back side. I opened her up and read a few pages. I wrote down her title and found her on kindle because she was cheaper there. I started slowly and read the first few chapters. She remained hidden in my kindle for a few weeks. Boredom. I remembered she still existed and resumed reading. We took a walk through history and she explained all these wonderful things. She told me about common fallacies, and great decision making. She shed light on things I learned a decade ago at eight am in a college class. She made me think about the conundrums of our politics and public opinion. She made me think about how bad all my past (math) relationships really were. The beauty in our unique ability to exercise cognitive dissonance. I read the second to the last page not knowing it was almost over and I fell asleep. I woke up and turned the page and it said 'Acknowledgements'. How could I not know it was over in that final paragraph? She left me. With bewildered curiosity and hope. She changed me. Now I see things differently. Now I am different.

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...

I loved the book. But I loved reading the reviews, afterward, more. While I do have a minor in math from one of the best technical colleges, nothing in this book was beyond my pre-calc high school education (circa 1977). Rather it was fascination that some readers did not have sufficient high school math skills to appreciate or understand. I also found no political bias in his writing. Frankly I was expecting it, and looking for it. Rather his observations were grounded in mathematical analysis. Just because a conclusion, arrived at though mathematical analysis, differs from your world view, does not make it biased. This was a fun read, and I did learn (or was forced to remember) some math principles. At its core the author confirmed a saying I use often: "That is the beautify of math. Even if you don't believe it, it is still true."

This is a tremendous book. I had to put it down and walk away because I knew if I kept reading it would eventually end, and I did not want it to end. Best book I've ever seen in the area of 'layman's mathematics'.

I thought that this was going to be a book about basic mathematical literacy. It was much more and much better. It delves into the whole area of inference - the dreaded "p-value", regression, and Bayesian methods. The final verdict is that it is an amazingly thought-provoking work.

Charlie Brown asks Linus, "I see you're reading 'The Brothers Karamazov.' Don't you have problems with the Russian names?" To which Linus says, "If I come to a name I can't pronounce, I just 'beep' right over it."

'How Not to Be Wrong' had Malcolm Gladwell possibilities, but failed and miserably. Like every mathematician, Mr. Ellenberg thinks that the proof is worth so much more than the end concept. His anecdotes are truly interesting, but Ellenberg spends needless and countless pages trying to confuse the reader with proofs, proof minutia, and proofs of proofs when simpler explanations would suffice and be appreciated. I found myself 'beeping' over the proofs to try to find the good stuff. It was there, but so, so hard to find. I am a recovering Mechanical Engineer, so I can appreciate the math. HOWEVER, if your book touts that I can use math NOT to be wrong, then PLEASE give me something I can actually use. Present it to me clearly and say, "Here, use this! Don't be wrong!"

Other things I was able to dig out of this book:

-- This book should have been edited with the proofs and the proofs of proofs buried in the appendix
-- Whoever edited this book should be fired, and whoever published this book, edited as it was, should be fired
-- Mathematicians DO have a critical place in society, but maybe authoring non-text books is NOT their place
-- If this book was used as the text for an advanced college course, the drop rate would be well over 50%
-- If your politics can be classified as far-left or extremely far-left, you damage yourself by trying to use math to disprove historical facts
-- People still have not gotten over the fact that Bush beat Gore in Florida

'How Not to Be Wrong?' One way is to never ever suggest a friend read this 'beeping' book.

For all those who love Mathematics, Statistics, Probability and Reading of Data in Day to day life. this is a must read. if you like the freakonomics series and Tim harford's economical evaluations, this too will go along in your shelves. neatly written, neat descriptions, less of mathematical over load and lots of common sense. Nice Work By Jordan Ellenberg.

Too much emphasis on statistics. If you didn't know better you might think that statistic is the only area in mathematics. Statistics is the most incorrectly used field of mathematics in media, business and politics that is why he can find many examples but just doing statistics right does not mean you will never be wrong. The books promise is not "how to get statistics right", it is about power of mathematical thinking. And there is certainly more to that power than statistics.

I bought this book after reading the New Scientist review, and expected more applications of mathematical thinking in daily life. Unfortunately I was disappointed.
We live in a sea of mathematics, and Ellenberg clearly wants to help us navigate this ocean, but he gets bogged down in deep historical episodes and tangents that I found myself skimming these passages looking for better material. The examples he does provide are great, but they are few and far between.
Other commenters have noted his liberal bias. As a libertarian (which today places me on the right wing of the spectrum even though at the time of my birth in the mid 1960s we were ensconced on the left wing) I found his bias to be a bit grating at times, likely due to the fact that while conservatives think liberals are stupid, liberals see conservatives as evil. I had a bigger problem with when his style betrayed his age. It struck me as a bit too flippant and borderline "cutesy" and likely won't age well. Perhaps it was simply the choice of his editor. I don't know; I don't read his Slate column.
Overall I'm giving this book a mediocre rating because I do think it has some sections that are worth reading. The introduction is fantastic, tightly written and well thought out. If only the rest of the book had been.

Great insights into the power of math to reveal relationships that can lead to predictions that are far more likely to be correct than what intuition or "common sense" may lead you to believe. Well written and easy to understand.

In the begging book is very interesting and gives insight about wrong conclusion from data. But chapters very often got into so much mathematical details, that makes book sometimes but difficult to read. I should say that I found many interesting stories about important mathematical theorems and their consequences.

I've already been recommending this book to family and friends, so I thought I'd take a few moments to recommend it to strangers on the internet, too.

This book, as anyone who is familiar with Jordan Ellenberg's writing (or speaking!) would expect, is written in an entertaining, witty, and engaging style. Each chapter of the book is framed by one or two major, motivating questions, such as:

- What parts of military aircraft should get the most armor?
- Is it ever a good idea to play the lottery?
- How should votes be counted in a democracy?

The answers that mathematical thinking asks you to accept are often surprising and unintuitive, but Jordan guides the reader through the fog of potentially-complicated arguments with a conversational style rife with clear, succinct examples and amusing historical anecdotes. In the hands of other writers, the mathematics in this book may be dull, or technical and complicated, or all of these things; but with How Not To Be Wrong, Jordan has instead created a book that you will eagerly and (mostly) effortlessly consume.

To put it another way: Steven Pinker said that "assumption of equality between writer and reader makes the reader feel like a genius, [while] bad writing makes the reader feel like a dunce." Jordan Ellenberg makes the reader feel like a genius.

Finally, regarding another reviewer's comments about the author's "liberal bias", I'd like to point out that I had the exact opposite impression while reading this book. Whenever politics were considered, I thought Jordan was even-handed and stuck to the mathematics at hand without wading into any political commentary. While I have liberal political ideals, and I avoid talking about politics with the more conservative members of my family, I would not feel uncomfortable recommending or gifting this book to any of them. This simply is not a book about politics, and I'm surprised that anyone would would have their political feathers ruffled when reading it.

Enough already with injecting political bias into an otherwise interesting book. Was it really necessary to extol the virtues of the Swedish social model in order to make a point about linearity? Give me a break.

This is a remarkable accomplishment: to present substantial ideas about mathematics and statistics to a general audience without either oversimplifying the content or overwhelming the reader with difficult details. The writing style is lively and entertaining. The wide interests of the author allow him to illustrate the abstract ideas in a variety of clever ways. This is a book that could do a lot to improve the public's understanding of what the mathematical sciences really have to offer.

The author presents several situations where some basic mathematical principles have been both used and misused. However the author frequently veers away from mathematical reasoning to go on anecdotal political rants. Perhaps the most glaring example of this is his insistence on defending the Washington Post for reporting that a statistic put out by the 2012 Romney campaign was "true but false" (the Washington Post was widely criticized for this).

To say that something is both true and false is perhaps the simplest example of a logical contradiction, and something that should make any true mathematician shudder. Yet the the author goes on for several pages trying to defend it, despite it clearly being untenable. Most of his arguments here begin to be based on politics rather than mathematics. His reasoning seems to be that the statistic in question was true but misleading (which would have been a perfectly acceptable wording), so somehow this justifies a newspaper making a logically inconsistent statement.

The book had NO purpose or message for the non-mathematician. As a layman in math, I couldn't find the message. For me, the book's title did not have relevance to the content. I would NOT recommend this book to anyone. Unfortunately, that was $27.00 wasted. "Some days your the pigeon and some days your the statue"

It's just okay. I have a degree in mathematics and a masters in the education of mathematics and I didn't see a lot lf exciting content in the book. The author, while very well educated, didn't really tell a good story. He was also very political which I find to be the worst offense in mathematal writing. Borrow the book from a friend. It's not worth purchasing.

This was a very enjoyable book – not something the average reader will say about the average math book! But this one wasn’t average.

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 fighter plane to put armor, the infamous Laffer curve and its various applications (such as charting “Swedishness” versus “Libertopia”), what stockbrokers have in common with the Bible, the tricky give and take between causation and correlation, the lottery and how to game it, the problem with voting systems, and even Florentine artists and the theory of modern perspective. There is nothing abstract about this book.

Secondly, we don’t just learn about math, we learn about the history of math, who discovered what, not necessarily in any chronological order, and we learn about people we – or, at least I – haven’t heard about, like an obscure Frenchman who wanted to figure out the odds of a simple coin toss game and defined the rules of probability in the process. Every once in a while Ellenberg stops to dispense some nuggets of his own philosophy that make you want to rip out the page and post it over your desk, they are so well-said. Like this one: “Math gives us a way of being unsure in a principled way: not just throwing up our hands and saying ‘huh,’ but rather making a firm assertion: “I’m not sure, this is why I’m not sure, and this is roughly how not-sure I am.”

Thirdly, Ellenberg is not only a brilliant mathematician but also a brilliant writer. What are the chances to get such a combination (which I’m sure an expected value could be arrived at mathematically)? He has such a wonderful way with words that not only do you find yourself understanding and even caring for more complex mathematical scenarios than you most likely bargained for, you also find yourself greatly entertained in the process. Especially his prolific footnotes (and hand-drawn sketches) had me laughing out loud in many instances. He reminds me of Bill Bryson in that way – another writer who combines science and history in a hugely entertaining way. Here are but a few examples:

“I once had an uneasy moment with a colleague in an airport when he made the remark, unexceptional in a mathematical context, that it might be necessary to blow up the plane at one point.” (About mathematical terminology.)

“And you can’t deny that there are aspects of the natural world – I’m thinking pandas here – that seem more likely to have resulted from grudging bureaucratic compromise than from the mind of an all-knowing deity with total creative control.” (On the calculation of the likelihood of there being a God.)

“Now imagine you’re Filippo Brunelleschi standing out on the flat prairie, the canvas on an easel in front of you, painting the train tracks – anachronistic, okay, but just go with it.” (On how parallel lines are not parallel in plane geometry.)

"Sometimes scientists discover the theory and leave it to mathematicians to figure out why it's elegant, and other times mathematicians develop an elegant theory and leave it to scientists to figure out what it's good for. (On mathematical elegance and its practical utility.)

“After two thousand years of scrubbing, the stain was still there.” (On Euclid’s fifth axiom, likening it to a stain in the corner of the floor that one wants to scrub to make the surface nice and clean.)

What makes this book such a good read is Ellenberg’s passion for his subject. “The sensation of mathematical understanding – of suddenly knowing what’s going on, with total certainty, all the way to the bottom – is a special thing, attainable in few if any other places in life. You feel you’ve reached into the universe’s guts and put your hand on the wire. It’s hard to describe to people who haven’t experienced it.”

I don’t know about you, but that right there – the image of the universe’s guts and me reaching right in there – is enough to make me want to start over and study mathematics as well.

Useful
I am an aging 61 year old guy who was one of the worst in math at school half a century ago.
I also have to stay up to date in an increasingly math and statistically oriented world.
this is how the book helped me:
Reduces "Just world bias" Makes you more more comfortable that there are just patterns of randomness.
Reduces generation bias.The person who made something is right and then tortures the facts until they confess.
Reduces "sunk cost bias"(i have lost $200 to the slot machines I will keep on playing because I want it back.)
Reduces confirmation bias(this proves Jesus loves me.)
Exaggerated expectations(I have the smartest kids)
the list goes on.

Minus:The author is like one of those professor types who wants to give a great show in the university courseroom instead of giving a great show.
I got more from Anti Fragile,Tipping point,Freaconomics and Super Freakonomics all 5 star for me.In fairness these other books are more accesible and do not have you standing on your toes at all times to follow the authors thoughts that are sometimes voiced to sound cute.Like in some Manhattan literary circle.Still I am proud of myself that I could finish it to the end and I will sound a lot smarter the next time I meet a New York academic literary type.Unfortunately the statistical chance of this happening is negligable.

The author is a very smart guy and a very good mathematician (who I know personally and like), so I really, really wanted to like this book. But I just could not bring myself to do it. The introduction to the book (with the Abraham Wald airplane armoring observation) is by far the most interesting part, in the rest the author falls into the Taleb trap of trying to write about mathematics while not requiring any thinking of the reader. This way lie the demons of rambling and boredom, and these ultimately devour the book. The book actually succeeds in making things seem much more complicated than they really are (I doubt that this was the author's goal, and yet...) In addition, the individual chapters are quite disconnected from one another, and so the book reads like an incoherent collection of semi-coherent columns or blog posts.

In addition, as others have pointed out, the book has a very strong socio-political agenda, which seems inspired by the author's domicile in Madison, WI - the hotbed of mainstream academic liberalism. This would not be such a problem if it were clearly acknowledged (after all, we all have our hobby horses), but it is not, so it reads in many parts like poorly disguised propaganda, which, in addition, is somewhat half-hearted (the author is too smart to actually inhale deeply into his lungs). In particular, the objections (due to McKay at al) he outlines to the Rips et al work on the Bible Codes are completely negated by the comment he makes near the end of the relevant chapter where he says that the authors picked the names of the rabbis BEFORE doing the study (since I know some of the authors as well, I can vouch for their complete honesty, whatever the intellectual merit of that particular piece of work). The result leaves this reader scratching his head.

Three chapters are devoted to the Bush-Gore electoral debacle. That is three chapters too many. The Florida election was a tie, and the Supreme Court discredited itself by adjudicating it. Flipping a coin would have made mathematical sense; nothing else did (yes, flipping a coin might not have been politically feasible, but this is not a book on politics). There ARE better voting schemes than the simple yes/no voting we practice (google "range voting"), and describing them clearly, together with the paradoxes they avoid would be quite interesting. This book does not do this, and politicizing the issue does no one any favors.

So, regretfully, my advice is to avoid this book, and to spend the time rereading Freakonomics, which did what this book failed - it showed how insight backed up by logic helps us understand the world around us.

Part of the daily life as an investor is about making choices between alternatives. Is this stock at a more attractive valuation than that? Shall I buy, shall I sell or do nothing? A famous quote is: "investment is an art not a science", which doesn't mean that math is not needed, but instead that it's unlikely for anyone to become a successful investor by just looking at the numbers. Finance professor and value investor Aswath Damodaran describes people as either number crunchers or storytellers but insists that you need to tackle both to become a good investor. The book How Not To Be Wrong is focused on math but it's also likely to help you improve your storytelling capabilities.

The author, Jordan Ellenberg, is an American mathematician and writer. He has competed in the International Mathematical Olympiad three times, winning two gold medals and one silver medal. He has been writing about math for a general audience for the past fifteen years and he has penned pieces for many of the largest newspapers in the US. Ellenberg has also published two books where The Grasshopper King was his first.

How Not To Be Wrong is structured in five chapters describing linearity, inference, expectation, regression and existence. There are further sub-chapters where different real-world situations are described to clarify the subjects.

Some of the nuggets from the book are the description of a lottery called Cash WinFall which at some points had a positive expected value for the buyers. Some mathematically minded people noticed this and took advantage of the favorable odds in the game. As the author writes: "If gambling is exciting you are doing it wrong" - but in this specific example the opposite was true. Another gem is the story about the mathematician Abraham Wald who during World War II got the question from the US military on where the amount of armor on the air fighters should be strengthened. He was widely expected to answer to strengthen them where the bullet holes of the surviving planes were, but instead answered that the armor should be placed on the parts which were not hit on the surviving planes arguing that the destroyed planes were likely hit on those places, namely the engines. This is an example of survivorship bias. It is also an example of inversion where thinking like a mathematician, to prove something by showing that what can't be true, often gives us the right answer. The author brings up a profound quote from Sherlock Holmes on the topic: "It is an old maxim of mine that when you have excluded the impossible, whatever remains, however improbable, must be the truth".

In science, statistical significance is a method used to distinguish if a hypothesis is true or false. It may be hard for the scientist to accept that a hypothesis failed and that the result was negative, wasting years of scientific work as the scientist is not rewarded for unsuccessful studies. This is an example of bad incentives. Similarly, it's hard for the investor who has put a lot of work into analyzing a stock, to accept that the numbers don't add up and move on to the next opportunity. By tweaking some numbers in the excel spreadsheet it may look like a compelling opportunity after all - confirmation bias at work. The author also brings up a study of the rate of return of 5 000 funds where the return was 20% higher if the dead funds were excluded which is another example of where it's possible to use statistics to suit the purpose.

For the most part, it’s easy to follow the reasoning in the book without knowing much math but in some parts, especially in the later parts of the book, it is a bit more difficult. The examples brought up throughout the book span across a wide spectrum of subjects and in a few examples I thought the point made by the author was a bit incomplete. However, I don't think of this as a great disturbance as the point is brought home anyway.

How Not To Be Wrong is another great example of a book that, while not focused on finance, nevertheless is a great source of knowledge for the investor.

This is a review by investingbythebooks.com

Great title. It speaks to me. And within the confines of rigorous and mathematical inquiry Ellenberg delivers on that promise. This book does not require a degree in Math to understand, and it is not technical. But you do have to commit to working through things from a logical point of view and you have to stay with some of the sections until it clears up. That is not a criticism, it just is the way it is. to be right requires a certain amount of work, no freebies here. But the rewards are greater than the effort you put in to it, there is a lot here to make you a wiser person.

I recommend this book for those that wish to get better (not perfect, just better) at not being fooled by fools, which is a pretty prevalent occurrence in today's world.

I do think however that Mr Ellenberg, like anyone, can fall prey to the sins of misplaced assumptions. so this is not a perfect read, and that is okay. You get a lot from it just by its pointing in the right directions. in fact, to find the places where he goes wrong is part of the process by which one can hopefully get most things right. so maybe it should have been titled " How to mostly be close" But that wouldn't have sold as many copies I guess.

My review title says it all. Highly recommended!

p.s. Below please find a few favorable passages of mine for your reference.
Mathematics is not just a sequence of computations to be carried out by rote until your patience or stamina runs out – although it might seem that way from what you’ve been taught in courses called mathematics. Those integrals are to mathematics as weight training and calisthenics. If you want to play soccer at a competitive level, you’ve got to do a lot of boring, repetitive, apparently pointless drills. Pg2
A mathematician is always asking, “What assumptions are you making? And are they justified?” pg7
In order to give a sensible answer, you need to know more about just numbers....Dividing one number by another is mere computation; figuring out what you should divide by what is mathematics.pg85
In a 2012 study, scientists at Amgen set out to replicate some of the most famous experimental results in the biology of cancer, 53 studies in all. In their independent trials, there were able to reproduce only six. pg150

This book is fun and entertaining. The author challenges some deep rooted misconceptions, he puts you on guard; see for instance the section on the stock broker.
Although no math is involved some sections require attentive reading. Very humorous but often well disguised. You may appreciate the humor more if you are a bit more into history and math reading.
The book has a wealth of excellent references. For instance the part where the author talks about nonstandard analysis has incited me to look deeper into this topic. Thought provoking.
The book resonates well with some of the ideas that I teach my continuous improvement students. For instance, 'given enough data anything can be proven to be statistically significant.' What is statistically significant may have no practical significance (the effect of your test was proven but has no real value). What can not be proved to be statistically significant can still have practical significance (your test did not have enough power to prove it). These are important and basic concepts that statistical textbooks often fail to mention. This book has put some of these gaps in clear evidence which every practitioner of statistics may appreciate
I have enjoyed reading this book and have bought a few copies for close friends.
I highly recommend this book to broaden your perspective on every day life aspects and to review your concepts of 'common sense.' You will be surprised how your deep-ingrained conceptions may not be as solid as you think they are.
I would recommend this book also for junior and senior high students, it will help them not only to be more critical about the news that they consume but also to appreciate the value of the universal language of mathematics that forms the basis for news reporting. Elementary concepts such as calculating ratios for unemployment are enlightening; these are the basics required to consume information critically in a time where we tend to depend on pre-digested and often erroneous representation of facts.

Now it is time to read a book about mathematics. That sentence in itself may have put you off. Mathematics for many of us is something we endured in school, and since we can calculate a tip or balance a checkbook, we just don’t need much more. Mathematicians, we think, are engaged in their own world, building proofs upon proofs that do not have much to do with the way the rest of the world works. Jordan Ellenberg is mathematician. His work is in research into number theory, the beautiful and arcane behavior of those mysterious entities, the whole numbers 1, 2, 3, and so on. Number theory has proved surprisingly practical in encryption, but that’s not the sort of message Ellenberg wants to get across in _How Not to Be Wrong: The Power of Mathematical Thinking_ (The Penguin Press). Mathematics is not an esoteric language that happens to be useful when experts apply it. Ellenberg explains that he and his mathematician buddies do spend most of their time in the profound and complicated areas of mathematics. “That’s where the celebrity theorems and conjectures live: The Riemann Hypothesis, Fermat’s Last Theorem, the Poincaré Conjecture, P vs. NP, Gödel’s theorem…” There are books that try to explain each of these to the non-mathematician, but Ellenberg is more interested in showing that profundities do not have to be complicated and that looking at things in a mathematical way makes them more meaningful. “Knowing mathematics is like wearing a pair of X-ray specs that reveal hidden structures underneath the messy and chaotic surface of the world… With the tools of mathematics in hand, you can understand the world in a deeper, sounder, and more meaningful way.” The chapters here all show the beauty of attempts to understand how mathematics bears on the everyday, and Ellenberg is a great explainer, with good examples and good humor. It isn’t always easy; there are pages where you cannot just let the words sink in but have to think hard about some of the computations. The enjoyment of sharing Ellenberg’s appreciation for his subject, though, is well worth the effort.

Here is one example from the book. Abraham Wald was a mathematician faced with the problem of designing more robust airplanes during WWII. You can coat an airplane in armor, but it costs money to do so, and makes the airplane heavier and less useful. So the idea is to put the armor only where it is going to do the most good. Officers documented that planes returning from missions had more bullet holes in such places as the wings and the fuselage, and not so much on the engine. With more bullets hitting the wings and fuselage, they thought that those were the areas that needed the extra armor. Wald was consulted, and thought about the problem in a different way. The way Ellenberg tells the story, it sounds like common sense, but he includes a page of Wald’s actual calculations to make his re-thinking of the problem rigorous (amusingly, in the included page, Wald has admitted, “The exact calculation is tedious…”). What Wald demonstrated is that bullets would be hitting the airplane all over, randomly distributed; there was no reason to think that wings were particularly liable to take a hit other than that they had a big area to be hit. And Wald’s insight was that the returning planes had more bullet holes in the fuselage and wings because they were able to return with hits to those areas. The sample of planes returning did not include those planes that had been shot down, and those were the ones that weren’t taking the superficial wing or fuselage hits, but hits to the engines. Any armor that needed to be applied, then, ought to protect the engines.

Ellenberg’s book is divided into five different, overlapping sections: Linearity, Inference, Expectation, Regression, and Existence. To illustrate the array of subjects, and the humorous tone, here is what is included in the Regression section: “Hereditary Genius, the curse of the Home Run Derby, arranging elephants in rows and columns, Bertillonage, the invention of the scatterplot, Galton’s ellipse, rich states vote for Democrats but rich people vote for Republicans, ‘Is it possible, then, that lung cancer is one of the causes of smoking cigarettes?,’ why handsome men are such jerks.” It’s a useful tour of a lot of a lot of material we non-mathematicians do not think about very often, and a reminder of the sway mathematical patterns have over broad aspects of our existence.

Spectacularly well written and dense with insight.

Many of the ideas in higher mathematics are extremely difficult for most of us to comprehend but Ellenberg does an amazing job of unraveling the complexity and using common language to make the important ideas in mathematics accessible to all of us.

Parts of the book are difficult to read simply because the concepts are so difficult to understand but those parts are where you will ultimately gain the most insight because the ideas are new to you and stretch your mind. Fortunately, the book has an excellent flow to it so your momentum from the easier sections helps you through the difficult parts.

Ellenberg's vast knowledge is apparent without being at all pretentious. His intent is clearly to teach and through gentle repetition give each reader the best possible opportunity to understand new concepts. You won't recall everything interesting that you read in the book, and that's a shame, but you will retain the approach of looking at many issues from various perspectives in order to gain a deeper understanding of many subjects.

I found myself laughing out loud (at math stories!) and then being quietly terrified by some of the most important concepts. As a longtime risk management professional I am all too aware of uncertainty, false truths and the dangers of selective emphasis. Ellenberg gives structure to a lot of those issues and is section on medical research does nothing to dampen my concerns about the rush to prove things that may not be true.

My copy of the book is massively dogeared to highlight particularly insightful sections and exceptionally good turns of phrase. Some of my favorites:

"We've (mathematicians) managed to stay just ahead of the ever-increasing sphere of computer dominance, like action heroes outracing a fireball."

"Mathematics is a way not to be wrong, but it isn't a a way not to be wrong about everything"

"If you never give advice until you're sure it's right, you're not giving enough advice."

"When you reason correctly...you find that you always think you're right, but you don't think you're always right."

This is the most entertaining book on the practical application of mathematical thinking I have ever picked up. It manages to be informative, dare I say educational, while being extremely well and clearly written in a conversational tone. Dr. Ellenberg is a true polymath (pun intended), obviously passionate about his chosen field of concentration but equally comfortable with quoting contemporary fiction (Pynchon, D.F. Wallace), relating historical oddities, and using sports analogies.
There have been complaints, amongst the reviews, that there is a political bias in the writing. Dr. Ellenberg is hardly reticent to present his beliefs, but he is fair, open minded, willing to express the limitations of his thinking; and, as far as I can determine, using sound logic when making his points. Please reject all the negative comments that dismiss his arguments on the basis of his politics as opposed to his mathematics. These specious views only demonstrate that people that don't like the message often resort to attacking the messenger.
The material presented is by necessity challenging; but can be appreciated through casual reading, or, better still, through careful examination. The footnotes add to the pleasure.
There are frequent diversions that serve to clarify possible confusion, or purely to amuse, that are invariably absorbing. A reader cannot fail to feel the pleasure Dr. Ellenberg is so eager to share with his readers.
If the books only lesson was to recommend self analysis. it would be of limited use. We need to have our assumptions and errors in thinking pointed out. I found myself repeatedly examining preconceived notions, the sort of factoids that passes as truth on the nightly news, that are all to easy to fall into.
A recognition of the beauty of mathematical proofs and respect for the discipline of mind that writes them would certainly help, but is not essential to love this book. I highly recommend it to anyone who has ever loved a math class, or who, up to this point, has failed to understand why anyone might.

I am very bad at math. Any book that tries to show me how math can be applied in every day life is worth reading. I learned that quadratic equations can be used to calculate when something is going to land. It is my understanding that quadratic equations can be used when an object does follow a straight line. This is due to something like gravity that pulls something an object off the original course. There are no quadratic equations in this book to solve, but Jordan Ellenberg makes this algebra topic interesting to me. I also like the statistics subject called regression to the mean. I like sports, so figuring out how many home runs a player will likely hit or how many three point shots a basketball player can likely shoot over the course of a season is exciting. It is especially interesting when an athlete is on a hot streak. Regression implies that a player is not likely to maintain a high level of performance all season, but it is possible to calculate how productive that player can be. I am also interested about learning the different curves in geometry.There are curves called parabolas. There is another curve called an ellipse and another called a hyperbola. I want to learn how these concepts can be applied in real life Jordan Ellenberg mentions that three novels by Thomas Pynchon are about the kinds of curves. I am never read anything by this writer before, but I am motivated to read him now because of Jordan Ellenberg. This book is a reminder that sharpening my math skills is a worthy endeavor.

This is a thought-provoking and intermittently entertaining book about the powers of mathematics, how people use maths more than they realise and how some people have used advanced maths to make a lot of money. Unfortunately, you need to have considerable maths skills to make the best of this work. Ellenberg teaches math and for page after page he descends into complex algebra and equations which will lose you unless you did advanced calculus and so on. So while I liked the premise of this book and liked what I understood, there was an awful lot that I did not understand.

A collection of contemporary anecdotes illustrating some basic statistics concepts, things you'll find in a good intro stat textbook like Freedman Pisani Purves but presented with some lively, if not overly clever, prose. My main complaint is the false advertising of the title and repeatedly calling all this "pure math"; not sure why the author is so determined to sell all this as math and hesitant to call it what it is -- statistics. (I heard his parents are statisticians so maybe that has something to do with it...)

We hear figures and statistics in the news all the time, and use our mathematical abilities to process them. We do not always interpret them correctly, though, and this leads to incorrect beliefs about the world. Author and mathematician Jordan Ellenberg knows the importance of using math correctly--he states that knowing math "is like wearing a pair of X-ray specs that reveal hidden structures underneath the messy and chaotic surface of the world." In "How Not To Be Wrong," Ellenberg shows us how to avoid misinterpreting the math in our lives and coming to wrong conclusions.

In this wide-ranging, erudite book, Ellenberg examines areas in math such as linearity, regression, the Law of Large Numbers, probability, randomness, prime numbers, geometry, and correlation, providing examples in such areas as economics, war, religion, medicine, terrorism, sports, politics, and state lotteries to help the reader avoid making common mathematical errors. The author includes scatter plots, graphs, tables, and charts to illustrate the concepts he discusses. "How Not To Be Wrong" is a great pop math book, and a really fun read for those who like books of the type.

The author tries too hard to be funny, and he's probably also trying to show how cool a mathematician can *actually* be. The book is filled with wannabe-shocking associations such as: "I just told you the story of this guy in college who had hundreds of identical T-shirts and was wearing a different one every day. This brings us back to the beginning of the universe." Or wanna-sound-cool titles such as "Reductio ad unlikely", "Miss more planes" or "Are you there god? It's me, Bayesian inference". I love math and I expected a book where I can enjoy both the writing style, as well as discover some math intuitions or perspectives I wasn't aware of. Unfortunately, this bestseller-style book is trying too hard to be "the Freakonomics of math", so it was not the one for me. I'll keep looking.
(I'm giving it 2 stars though for the introduction chapter, which was well written and described how we should understand math through intuitions and real examples rather than through dry formulas.)

While this book was very interesting and I did learn a lot of interesting points about things like how lotteries work, etc. I did find this book extremely technical. I had to listen really hard in many areas to wrap my brain cells around the concepts.

If you want to give this book a try, thinks twice before beginning. If you are mathematically inclined, then go for it as it is really well written and has many interesting points to consider; however, if math is not your thing - walk away....

Enjoy and happy reading!

If you have kept up with recent trends, you probably already have read or heard about books on how irrational our thinking is and what we can do about it. I believe it's a move in the right direction. We really are biased and not as rational as we think we are and being aware of it will serve us well in the long run.

Almost all those books have been written by social scientists, psychologists, economists, journalists etc and after reading a few of them, they tend to get repetitive. That's why I loved this book so much, because this book is written by a mathematician and it shows. Sure, there are a couple of topics that are common with the other books. Say for example, regression to mediocrity and the law of small / large numbers were covered in Thinking Fast and Slow by Daniel Kahneman. But this book looks at each of those topics from a different perspective and, although I already knew them, I have started looking at them in a different way.

At the same time there were many things that hasn't been covered in any of the other books I have read and I learned quite a few things. For example, how it is possible for a group to be irrational even if every single individual in that group is rational. (To be completely honest, I had already learned it in the course Model Thinking by Prof Scott E. Page on Coursera, but I didn't read it any of the pop science or pop psychology books).

My only criticism is that there were parts where the author kind of dived a bit too deep and got a little too mathematical for my taste. For example, the part about the power ball and the lottery could have been shortened a bit.

My final verdict - even though I have read many of those other books by social scientist and other writers, I still learned many new things from this book and gained fresh perspective on things I already knew. There are two books that I consider a must read for everyone - this book (How Not to Be Wrong by Jordan Ellenberg) and Thinking Fast and Slow by Daniel Kahneman.

A few months ago when my subscription to the Wall Street Journal expired, I didn't renew it. Not that it stopped being a great paper, but that I was losing an hour a day to it.

Maybe also that Nassim N Taleb, a thinker I respect, wrote that he never reads the daily paper. He prefers the classics, which is a step too far for me, but his point about not getting wrapped up in the day's events seems to have some merit I wanted to try.

Anyway, with a lot more time for books, I'm often reading three or four at a time.

None recently has been as much fun as "How Not to Be Wrong."

I never expected a book on math to be so enjoyable. The author has a great sense of wit. And for a young man, is remarkably wise about more than just numbers.

Yes, a few pages were more abstract than I had patience for. But pragmatism is MY personal problem, and it was easy to skim ahead, getting out of the brambles back to a clear path.

The most fascinating pages for me were the ones on elections, particularly in using math to determine the winner in elections with three candidates. One can't help wondering how different the world would now be if Gore had been elected in 2000. (Less important, but also different if Perot had not kept Bush Sr from getting elected in 1992.) This is an area where math could be seen to have some practical application. Though maybe not, as the discussion of another 3-candidate race in Burlington, VT makes clear the difficulties.

I think you'll like this book even if you weren't a math major. Maybe especially if you weren't a math major. Real math majors would find the book simplistic. I found it just about always on target.

If it helps gauge this review, I loved algebra and geometry in high school. Trig seemed a waste of time (even more so when cheap calculators were invented). I never took calculus but what I know of it makes me wonder why we teach such an arcane, difficult subject to so many who won't ever use it. We could do a lot better with the limited school time of our children.

And that's exactly among the many topics the author addresses.

Delightful book.

Despite being a grad student in math, I couldn't bear with it till the end. His inconsistent writing and flaws in explanation complicated concepts are well noticeable. He usually went off tangent and interrupted the main theme of each chapter by spending a good amount of time with some side stories. This frustrated me a lot. I pushed myself several times to read it through. I made some progress but finally I couldn't stand his bad writing style. So I decided to stop reading at about the first third of the book. Wish I didn't pay for this book. I could've saved my money and rather spent on a better one.

Some popular math novels that touch advanced topics than this book could do much better at telling stories. So I don't think the knowledge of readers is an issue to enjoy the book. It's the author's writing style prevents the joy.

Read it at your own risk.

Jordan Ellenberg's book is a fairly entertaining popular history of mathematics, written with an eye towards exploring the modes of thinking that are likely to be useful to people in their daily lives. It does suffer from having a sensational title, and from not living up to it. The subjects that are covered I think are mostly useful to the lay reader, but the book is nothing like as relentlessly utilitarian (or as enjoyable) as Huff's "How to Lie With Statistics", and certainly not as tightly written. Not a fair comparison, to be sure, but the title invites it. I would categorize this book more as a collection of descriptions of mathematical and statistical concepts, accounts of historical events of mathematical relevance, brief biographies of mathematical figures, all written for a lay audience, and bound together by the thread of having some applicability to the average reader's way of thinking in daily life. There's little here that hasn't been covered in other books, but it's told in a mostly entertaining, easy-going style. I will say that I'm not at all a mathematician, but I found relatively few things here that I hadn't been exposed to elsewhere, and I suspect that most people who are at least somewhat well read will find themselves in a similar situation. However, there are some well-written accounts here of important lessons for those who haven't seen them before, and entertaining even when familiar. I'm thinking of Abraham Wald's insight into airplane armor, the Baltimore stockbroker, the descriptions of some of the flawed lotteries, and what I thought (as someone with the barest of understanding of them myself) was a very good plain-language description of non-Euclidean geometries.

There are a few sour notes and missed opportunities. The description of Bayesian statistics falls prey to what so many such descriptions do: it convinces you of the importance of priors, but then skates around the fact that you often don't have any useful way of defining, much less quantifying, your priors. I also think the way the author deals with Galton's eugenics is profoundly weak. It literally follows up a Galton quote ending in "degenerate stock" with "Mathematics is a way not to be wrong, but it isn't a way not to be wrong about everything."--just an awful copout. It's clear the author didn't want to deal with the subject, but felt he had to hat tip it--I don't think eugenics is something you can just hat tip. I think the biggest weakness of the book, though, is in many of its examples. Some of the criticism of the book, that the book's conclusions are incorrect because of the author's (obvious) politics, or that the book is entirely a liberal screed, are overblown (the title doesn't help with this, though). However, the politics is, frankly, tiresome. The author's politics are pretty well to the left and it shows (an example about how the Romney campaign got something wrong, another that Obama got right, Reagonomics is wrong, Florida was stolen from Gore, etc, etc). It shouldn't be difficult for any reasonably intelligent person, regardless of their politics, to read around this stuff and still get everything useful the book has to offer, but it does detract from the experience. I think even if one's politics align perfectly with the author's, one will find one's eyes rolling as the political trivialities pile up. The worst is how poorly this book will age because of it. Even now, just two years later, much of the text reads as very stale because the examples given aren't great examples, but obviously selected because they were current at the time and fit with the author's worldview. I can understand the argument that using current, relevant examples can help to engage the reader, but I don't think it works here. It's not a damning criticism of the book, but an unnecessary flaw.

Bottom line, check it out from the library (you'll not be going back to it), ignore the title (and the chapter titles), skim the chapters that cover things you already know, read the rest to get a decent summary of some things you might have missed, and just step over the politics as though you were walking through a pasture.

Ellenberg has written an intriguing book. He does a great job laying out some important mathematical thinking and applying it to some common issues of our time. I do have a strong math background (engineering), but I found some parts too deep to understand without resorting to heavy research. There is also a lot of rambling; some witty and playful, some more of a drone. I’m sure the next version will be more user friendly, I think he just tried too hard. You can tell that he put a lot of painstaking work into this book.

Well, I read the book a few weeks ago. I think the book is a very interesting one, written by a number theorist in a very entertaining way and accessible to the whole public. Ellenberg's purpose is to present the kind of reasoning one person has to bear in mind in order to better make decisions based on mathematical heuristics. I found it myself pretty deep, yet not technical at all. It is an awesome book that surely will help anyone to enhance its decision making reasoning. Read it twice!

I've read many of the other comments. Yes; there is a visible political agenda here at some points. But as long as you can filter this and use the mathematical thinking BEHIND the political talk, this shouldn't be an issue.

Otherwise, this book is phenomenal. If you love math as much as I do, you will see the value in the many points that Ellenburg makes in her book. But I think the most value lesson I took from this book is to think for yourself. She often calls into question the many practices statisticians use to manipulate numbers in order to support their argument. After reading this, you will see examples of this everywhere. Politicians do it. Health care institutions do it. Hell, almost everyone does it. But this book will make you more aware of how the information you are fed on a daily basis is being filtered before your very eyes. If you get anything from this book, it will be the ability to listen to a number of logical and statistical arguments and say, "Wow, that's great, great argument..... But let me see the raw data and facts and I will decide for myself."

You don't need to be a math-minded person to gain value from this book. I think everyone in this day and age can gain from the sort of thinking that questions the information you're being fed.

Not many examples in the book that I hadn't read before, or heard about on YouTube. Plus, his political leanings are painfully obvious. All his examples that involve government or politicians are absurdly partisan. Also, he has TONS of asterisks (*). There are so many that it gets distracting - many are irrelevant. It's not terrible, but I would not recommend this book.

1) The book covers several basic ideas (mainly statistical), 2) which have been covered before in many other much better books, and 3) does so in a long-winded chatty style.

I also wonder how much experience the author (a mathematician) has in conducting empirical research. For example, he notes the relatively large number of published studies with p-values slightly less than 0.05 and attributes it to "under-handed" p-hacking. While p-hacking undoubtedly goes on, a more benign explanation is this: researchers conduct a pretest study to get estimates for parameters such as variance, and then they perform power analysis to set sample sizes for the major study. That's not p-hacking, that's accepted research practice.

Ellenberg does an impressive job of connecting centuries-old mathematics concepts to model historical and modern events (wars, elections, lotteries, etc.). What's more impressive is that even if you don't understand every piece of mathematical nuance, you can still follow along and be entertained. The title might be misleading If you're looking for a book that explicitly lists actionable advice on "How not to be wrong" using math. Perhaps a more correct title would be "How mathematics can been used to understand real-world events."

It's really hard to write a book that communicates interesting mathematical concepts in a way that's readable for laymen, but this book is one of the few that succeeds. After a shaky and slightly condescending start, this book gets better and better as it goes on. It succeeds in piling up concepts without overwhelming the reader, so that by the end, you're dealing in deep subject matter. Interesting, multidisciplinary, rewarding. My one quibble is that too much of this book is about statistics, which is disappointing considering that Ellenberg's field of research is geometry, a (IMHO) much more elegant part of math.

"When am I ever going to use this?"

Except for the very few who really love math, every students asks this. And teachers don't know but they have to give an answer so they come up with lines like "You need it if you want to become an engineer".

To which students reply "But I don't want to become an engineer! And even if I did, I'll have the answers I need from the computer!".

And the teacher finally snaps and gives the real answer: "You need it to get your diploma!"

The answer is real enough except that it is wrong and with "How Not To Be Wrong" Jordan Ellenberg gives us the correct answer: math is to thinking what training is to sports. It may be true that once you've graduated high school you'll never have to solve a quadratic equation, just as you'll never see a football player curl barbells in the middle of a game. But just as having curled barbells countless times in the gym will help football players throw further and tackle harder, having done the algebra will train your mind to concentrate and to think outside the box.

But this is not a book about doing algebra or calculus. This is a book the results that come from knowing algebra and calculus. The theme running through HN2BW is that lots of things are counterintuitive. Here are a few.

In World War II, the air force wanted to know where to put armor on planes. Armor is heavy and putting it everywhere would make the plane too heavy to fly. They looked at the damage on their planes and realized the area with the most bullet holes was the fuselage, while the area with the fewest bullet holes was the engine. The answer is obvious: put the armor on the fuselage rather. But the military men knew enough to ask professional mathematicians and they had a statistical analysis department.

"Where did you get the data from?" asked the statisticians.
"From our planes, after they came back from a mission."
Obviously not before, or there would have been no bullet holes at all.
"Very good, that is important data to have. But what about the holes in the planes that didn't come back?"

And that is the correct question to ask. It's reasonable to assume that bullets fall on the plane more or less evenly but if planes come back with bullet holes in the fuselage, it means that bullets don't damage the plane much when they hit the fuselage. If few planes come back with holes in the engine area, that means that a hit to the engine will down the plane, so that it where the armor should go.

Apart from such counterintuitive insights, Ellenberg also teaches us a few things we really ought to know. Every thinking person understands that correlation doesn't imply causation. And everybody knows that if two things are equal to a third then they are equal to each other (ie if Jack and Jill are as old as James, then Jack and Jill are the same age).

But that doesn't apply to correlations: a stock portfolio made up of automobile manufacturers and software developers will correlate with a portfolio made up exclusively of automobile manufacturers and with a portfolio made up of exclusively of software developers but fluctuations in the automobile portfolio won't have anything to do with fluctuations in the software portfolio. Equality is a transitive relation but correlation is not transitive.

This isn't a book about beautiful mathematical results: you won't find Euler's jaw dropping identity here. Ellenberg explains statistics, those lies even more damnable than just plain damn lies but he shows us how mathematical thinking helps us to better understand data.

Vincent Poirier, Montreal

Comprehensively covers the "math issues" on the publics' radar in a way all the public needs clarified -- plus several other lesser known yet more erudite and stimulating topics. Never have profound mathematical concepts been so fluid, fun, and accessible.

Eric Siegel, Ph.D.
Founder, Predictive Analytics World
Author, Predictive Analytics: The Power to Predict Who Will Click, Buy, Lie, or Die

In this tome, which has over 430 pages of main text, the author discusses mathematical thought processes which are often applied in everyday life. It would be a lengthy exercise to list all of the topics that are touched upon here, but the overall theme is the use of mathematical ways of thinking in order to understand various observations in the world around us. The book includes several useful figures and tables but very few formulas, the emphasis being on the thought process rather than the blind application of formulas to observed phenomena.

I found the author’s writing style to be very lively, friendly, authoritative, often witty and quite captivating. The text is also generally accessible, although I had to re-read some passages a few times to allow certain explanations to eventually sink in.

I believe that this book can be enjoyed by a very broad readership. Although math/science enthusiasts may relish this book more than the average general reader, I do believe that everyone, even those who are math-phobic, stand to learn much from this work about the true nature of mathematics.

As a final note, I agree with a prior reviewer who pointed out that, although the book’s title is quite catchy, a more appropriate one would have actually been its subtitle.

for becoming less "interesting" as it proceeds. This is counter to the reality: in actuality the book becomes *more* interesting as it proceeds, just that it perhaps demands slightly greater commitment. (It can't all be as fun as Abraham Wald, who I will point out that prior to this, most people never heard of!) The point is the author has something to say and he says it well, in an interesting and engaging manner.

As a layperson who has recently had to delve into academic research papers on subjects such as Combinatorial Game Theory, Quantum Game Theory, Complexity Theory, and Mutually Orthogonal Latin Squares, I can tell you that Dr. Ellenberg is a top notch communicator of deceptively complex ideas.

Not surprising when you combine the chops of a literary novelist and mathematician. This is my favorite non-fiction book of 2014! (Strangely, my favorite fiction book of the year is The Causal Angel, also by mathematician. Just another bit of evidences against all appearance that the world is in fact moving in the right direction;)

I hate the title (are you kidding??) and the subtitle "The Power of Mathematical Thinking" should have been the actual title. Regardless that doesn't change the content and if you stick with this book you are going to enjoy it. It does move a little slowly at times and I read it in fairly small segments. I wish authors would stop using political examples and they simply alienate people who might otherwise benefit but like the title you can simply ignore the political potshots taken and enjoy the idea of mathematical thinking. We need more mathematical thinking because so much of our intuitive thinking is simply wrong.

This is not a great book but it is still quite good. You don't have to be great at math to get something out of this book but I think you need to at least not fear it. Recommended.

I really enjoyed this book! I'd assumed that any book on mathematics would be difficult to read, but this one kept my attention all the way through with interesting insights of how a mathematician views the world.

I'd borrowed this from the library, but I liked it so well, I'm considering buying my own copy.

Rated 4 stars only because of some slower sections, particularly the one discussing Euclid's Axioms, where it wasn't evident how the discussion fit the greater context.

The author starts out great, but then gets into his bad habit of constantly digressing; or to use one of his math terms, contantly going into
"tangents." If the author found a good editor and cut out much of the superfluous stuff, he might come out with a fairly good book with some key ideas that he is desparetly trying to get out -- but simply has not succedd, in my opinion!

He is young enough that i feel he can make his next book a better one that the public can enjoy reading and not losee interest after a few chapters with this present book.

[email protected]

A great book about mathematics and it's application to normal life. Jordan Ellenberg shows that the belief that people have with maths is often incorrect, some areas of math are devoted to randomness, and that's where things get very chaotic. I bought this book thinking I would get a formula to win every argument, but that is not what I got. Enjoyable read, not what I expected.

I love Mathematics. The author describes some very common errors that can be avoided with some basic math, but the most interesting parts for me are some stories about the evolution of Math over time, mainly the paradoxes and the logical deduction process. Highly recommended if you like math.

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 upper left "Libertopia" to lower right "Black Pit of Socialism". Along this line is shown a dot for USA toward the top and a dot for Sweden toward the bottom.Then the author introduces the idea that the curve is should not be a straight line, it should be an inverted parabola with the USA market on the left side approaching the peak which represents and optimum combination of benefits and costs and the Swedes having passed that point and needing to back up. An entirely different message all together! He moves into the famous mainstay of Reagan Republicans (and the Ferris Buhler's Day Off movie as a soul crushing lecture) known as the Laffer curve which compares revenues vs. tax rates. And we're off! And the first part of the book held my interest and moved right along.

While the second half got into some interesting topics like the role of adding a third choice to a race between two candidates and the resulting fiascoes versus the "true will of the people" a la Ralph Nader and Ross Porot and some discussion of correlation and regression to the mean, the author begins to digress into the history of mathematics and becomes quite wearisome and plodding. So, some highs, some lows, pretty much an average read in my opinion.

Fine entry in the pop math literature. More so the pop stats/probability lit, actually. Ellenberg writes well and entertainingly. He chooses interesting cases to illustrate the points he's making. And the points are all highly germane. Books like these don't solve the problem of wrong thinking, but they do raise one's awareness of some of the perils and pitfalls of an uncritical world view. Ellenberg does a very nice of job of drawing the link between mathematics and critical thinking. A very good read.

I may have never known this book existed until striking through the library one day, searching for an introductory text in basic computer programming, I noticed this book, mostly for its strange and comic title, as a "featured" book posted on the ends of reach library stack.

Combining a tremendously witty writing style and a penchant for explaining complex concepts "like I'm five" while retaining essential nuance, Ellenberg writes one of the most captivating, insightful, and engaging books I have ever read. Many times throughout reading I put the book down in a sudden fit of laughter.

Sections of the book may be conceptually dense where one could greatly augment comprehension by working out the problem on paper as the author suggests. Actually, this is what I plan to do, is to revisit some of the content in an active manner. Before reading this book I didn't consider myself much at all interested in math; yet now I have found an entirely new interest.

Cannot recommend this book enough, and I already have, many times.

I got a lot of great insights from this book. Yes, I did think that there was too much bias in the book when mathematical errors abound on both sides of the aisle, and I didn't care for the frequent negative comments about belief in God, but I could look past that. I loved the puzzles such as where to add armor to airplanes and so forth. I was able to share insights from the book with my kids and I really value that.

One of the best popular math/stat books I've read. What sets this book apart from many other good books in this genre is its emphases on the "simple and profound" -- the mathematical facts that seem simple but have wide application and deep implication in the real world. The author dose this in a very accessable and enjoyable way. There're so many interesting and insightful ideas in this book, I'm going to read it again.

A bunch of good "ah ha" moments coming out of this book. For example, "Oh, you're right, journalists and pundits do love to extrapolate non-linear trends as if they are linear." and "Oh, you're right, journalists and pundits love to use percentages even when aggregating positive and negative numbers."

I read this book while taking statistics in college at an Ivy League institution. In addition to other things, it provided the most interesting and enriching enriching descriptions of statistical principals I have ever found. It shows how things you see all the time, can be looked at from a mathematical or statistical point of view. It also just makes you care, kind of like Bill Bryson, but more specific and technical but conceptually, almost never are there equations, though maybe the occasional drawing. I highly recommend this to the casual reader, but even more so to math students in high school and in early college.

Way too technical for the casual reader. I work with numbers all day, every day but reading this book after work was just exhausting. Quit reading half way through. I have my copy on sale on the store if you want it for cheap!!

I have always thought that mathematicians are very smart people and that's the reason I didn't chose to become a mathematician while I was young. After reading this book, I regret very much. I want to understand math, to feel the connection with the universe but I think it's kind of late.

As an English teacher, I very much enjoyed this look into the other side. I thought the book would give me tricks into how to approach probabilistic situations better, but instead it was about the mathematical foundations that should help me understand things better. Hopefully I can approach situations better now too.

I was able to calibrate and disregard a lot of Ellenberg's snide, left-wing bias and enjoyed much of this book. However, in the end, it left me depressed. How are we supposed to make wise decisions when the data is uncertain? The idea that contradictory answers can be equally correct does not sit comfortably with me, but that's life, I suppose. It's a thought-provoking book and has merit in illuminating statistical-math history.

I enjoyed Part 1 but not Parts 2 - 5. Since I only skimmed Parts 3-5, I'm giving the book an extra star as 'benefit of the doubt'.

The book is titled, 'How Not To Be Wrong' and yet fails to clearly distinguish two major types of errors: empirical and deductive. I was annoyed that the author failed to identify exactly how he was helping the reader to be 'not wrong'. In this book, the author appears to be mainly concerned with empirical (modeling) errors. Some mathematicians will probably dislike the author's applications-oriented slant with an overemphasis on probability / statistics.

Would have given 5 stars, if the author had not advertised his political opinions throughout the book. Does not mean I agree or disagree, I just feel it has no place in a book of this format/topic.

On the infinitesimally small chance that the author ever reads my review:
If you are ever going to publish an updated edition, please leave out your airport anecdote about blowing up a plane. It never happened, and would not be funny even if it did.

Wonderful book. It is written in accessible prose, and it makes mathematical thinking tangible, fun and worthwhile. Although I am 60, this book would have been a useful read when I was 20 - it frames a good way to think about all kinds of complex, intractable and difficult-to-quantify problems without the mumbo jumbo that isolates too much of math and stat.

I very much enjoyed this book, it read very similarly to a "Short History of Nearly Everything" by Bill Bryson, or a "Freakonomics". The information in the book was educational and thought-provoking, while maintaining a humorous and easy-to-read format. I wish he would write another similar book, but I was disappointed to see that this was his only non-fiction.

Ellenberg is a professor of math, but there is surprisingly little rigor here. The book isn't really about mathematical thinking, but a subset, namely statistical thinking. A much better book, more tightly reasoned and by an actual participant in the research that Ellenberg discusses, is Gerd Gigerenzer's Risk Savvy. Risk Savvy explains key concepts (especially Bayes' Theorem) more clearly, and gives you probably more useful advice. The audio version of this book is read by the author. Most authors, Ellenberg included, are not good narrators. He does a good job for an amateur, but a professional would have been better.

Odd that there is no mention of the works of John Allen Paulos......he seems to be plowing the same fields but without as much rigor as Paulos.

Glad that I checked this out from the library first.

He also is an author who must have been paid by the word.....never seems to let an opportunity pass to use ten words where one would do.

Solid book about things in math that get mixed up or distorted by the average Joe. The author states at the beginning that there will not be too much math involved but I think he's probably wrong on that one. It gets deep at times and the average person will get lost. Most people never make it past algebra and geometry. He definitely goes past that.

He mentions Nate Silver at the end and that is a great book as well. "The Signal and the Noise" Excellent book there. This one is a bit deep at times but the examples for the most part are easy to understand and current. Well written.

I just listened to the audiobook for the second time and learned more the second time. It kept my attention the whole way. The book indeed shows the power of mathematical thinking. I especially like Jordan's point about the value of grit and hard work in learning and using math. My second favorite math writer, behind only John Allen Paulos

How Not to Be Wrong has a good beginning--any time the sloppy reasoning of political ideologues is exposed it's enjoyable for me. But his style--constantly trying to be amusing (not always succeeding)-- got tedious after a while. My advice is to read it, but be prepared to skip through parts of it.

The principles and ideas the author puts forth are engaging and thought provoking. He does a good job explaining most of what he covers, although once in a while I felt the urge to challenge his reasoning; but, we are not in a classroom, so I'll have to keep my thoughts to myself. HOWEVER, I was really disappointed by the all too frequent examples that are political. Whether you are a conservative or liberal, it makes no difference - there was no need for this. There are plenty of examples, cases, circumstances and the like that he could have used to illustrate his points without resorting to politically biased examples. Yes, I believe he is definitely pushing his agenda and his bias, but I will keep to myself my opinion of what I think he is, because what he is is not the point; my point, you see, is that there was no need for politics one way or the other, and having it spoils his otherwise OK book.

The promise of this book is that it would take math concepts and re-purpose them for use in everyday life. Evaluating the book by that criteria, it is a failure. While Eilenberg has some writing chops and can explain math problems and concepts, he struggles to make the connection to real-world application. There is nothing in this book you wouldn't learn in a college statistics class. I was excited to read this, but there's just no pay-off. Eilenberg would be better served to write something like a History of Math for People Who Don't Like Math. He has the ability to do that as that's essentially what this book is.

This book is awesome as it takes on the emotional world of decision making that takes the country in many wrong directions. This book remind me of the book American Séance and the work of Jacque Fresco a couple of decades ago where you use basic reasoning and probability to solve problems versus speculation and emotion. Great book.

Interesting book which central idea is that mathematics is a science of uncertainty and certainty, a science that can be wrong. The author presents good ideas however excessive use of digressions makes it hard to follow and enjoy.

Broad survey of mathematics and its applications to every day decision-making, written with flair and in a style that is accessible to many readers--not only those with advanced mathematical training.

This is a vastly overrated book that provides few examples of how mathematics can illuminate everyday probelms as it promises. It limits itself lazily to few examples, long before debated and discussed, such as the relationship between tobacco and cancer, political polls, old hat, in which the bias is clearly liberal-naive, and affords few enlightening examples of how math or statistics shed light on everyday pursuits. Quickly written, I assume, not profound, boring in fact. Overconfident writer and slack reviewers. The thesis of the book is excellent, but execution poor. Tougher editor needed.

This book is very good for being aware of the misuse of statistics. Good even for people who use and produce statistical information. In fact it explains very well "how not to be wrong". One should not understand that this means "how to be right' in the sense mathematicians think and develop their ideas. That is another matter.

Appealed more and more as I read on. I was pretty grumpy about immersing in statistician vignettes as the book commences but it broadens in scope as it proceeds in a rambling, enjoyable way. To my surprise, this morning it provided insight into the analytical shortcoming of an op-ed piece concerning crumbling infrastructure, based on a WW II analysis by Abraham Wald of where armor should be added to fighter planes. Ellenberg makes his insights appetizing and enjoyable.

Fascinating, entertaining and enlightening. Jordan Ellenberg shows you that "math" is just a way of expressing lines of reasoning and posing questions as concisely yet expressively possible. In fact it's actually inspired me to investigate math classes at my local community college so I can become more fluent in this language of exploration.

I picked this book up after I read some of the excerpts on Slate. I am not a particularly math focused person and tend to gravitate towards fiction, but this book was great! A well-written, entertaining read. And it delivers on its title - I already feel like I am living a better life with the knowledge gained.

Professor Ellenberg shows us how we can use math to understand the world around us and consequently make better decisions. He tells us fascinating stories about mathematicians, how their work changed the world we live in today while underlining the importance of keeping mathematics close to its empirical source and practical applications. If you are considering moving to another state for example and understanding the numbers related to health care or education for that matter, check out the chapter on linearity. The clear and effective explanation on taxation and how it impacts how much we would work in different scenarios is very interesting and equips us to better understand policies and in the end to be informed voters. I always wanted to better understand the monthly job reports issued by the Department of Labor or the states and the book gave me a good perspective on this too. Linear regression and the law of big numbers help me with better understanding college options for our son. Great book, an effective tool in our decision making toolbox - very well written with the non specialist in mind. Highly recommended!

Jordan Ellenberg's book is accessible for anyone who wishes to understand our world in a more thoughtful and logical way. The book is well researched, engaging, and endearing. If your math skills are rusty or you never studied some of the topics Dr. Ellenberg addresses, you can nevertheless get the essence of his arguments as you read his coherent and frequently humorous prose. We so often make crucial decisions in our lives based on faulty information, on intuition, or on limited understanding. Reading this book can help us make wiser choices for ourselves and for our society as a whole.

I have a very math-oriented mind but I found this book very difficult to get through. There are some very interesting ideas, but most of them are not presented very clearly. The author gets into some pretty difficult concepts for a book that is supposed to be directed at a lower level. I started skimming a lot of it because I was bored with his historical excursions that didn't add to the concepts he was trying to explain. He also seemed to be unable to explain one idea from start to finish without getting sidetracked multiple times, which makes the book flow very poorly. I was very disappointed.

Disappointing...thought I would learn some practical applications of math and connections to the real world...gave up after fifty pages, author didn't explain much...for example, he states that calculus "works", and doesn't define what it is (math of change) or how it relates to our lives....had high hopes but believe I wasted my money.

This book is most notable for its irony. The idea of using mathematics to objectively analyze every-day issues has promise. But the author's inability to bridle his own bias and his willingness to manipulate the math to reach his desired conclusions undermines the notion that math can be used as an objective tool of analysis, which I thought was his theme. One reviewer argues that while the politics are unnecessary and tiresome, it would be an exaggeration to dismiss the book entirely as a liberal screed. Perhaps--but not much of an exaggeration!

I greatly enjoyed reading this book and was sad when I got to the end. Its a light and often funny read that is hard to put down. The topics covered are wide and varied. While the title is a bit misleading (you aren't going to be taught how to think mathematically), you will better understand how much math governs your daily life and better recognize how it can lead, or mislead, you into making decisions. I fully recommend this book.

You guys are in for a treat. In fact I’m jealous of you.

You see, I had a little secret about my survival in grad school at Harvard, and that secret has a name, and that name is Jordan Ellenberg. We used to meet every Tuesday and Thursday to study schemes at the CallaLily Cafe a few blocks from the Science Center on Kirkland Street, and even though that sounds kind of dull, it was a blast. It was what kept me sane at Harvard.

You see, Jordan has an infectious positivity about him, which balances my rather intense suspicions, and moreover he’s hilariously funny. He’s really somewhere between a mathematician and a stand-up comedian, and to be honest I don’t know which one he’s better at, although he is a deeply talented mathematician.

The reason I’m telling you this is that he’s written a book, called How Not To Be Wrong, and available for purchase starting today, which is a delight to read and which will make you understand why I survived graduate school. In fact nobody will ever let me complain again once they’ve read this book, because it reads just like Jordan talks. In reading it, I felt like I was right back at CallaLily, singing Prince’s “Sexy MF” and watching Jordan flirt with the cashier lady again. Aaaah memories.

So what’s in the book? Well, he talks a lot about math, and about mathematicians, and the lottery, and in fact he has this long riff which starts out with lottery math, then goes to error-correcting codes and then to made-up languages and then to sphere packing and then arrives again at lotteries. And it’s brilliant and true and beautiful and also funny.

I have a theory about this book that you could essentially open it up to any page and begin to enjoy it, since it is thoroughly enjoyable and the math is cumulative but everywhere so well explained that it wouldn’t take long to follow along, and pretty soon you’d be giggling along with Jordan at every ridiculous footnote he’s inserted into his narrative.

In other words, every page is a standalone positive and ontological examination of the beauty and surprise of mathematical discovery. And so, if you are someone who shares with Jordan a love for mathematics, you will have a consistently great time with this book. In fact I’m imagining that you have an uncle or a mom who loves math or science, in which case this would be a seriously perfect gift to them, but of course you could also give that gift to yourself. I mean, this is a guy who can make nazi jokes funny, and he does.

Having said that, the magic of the book is that it’s not just a collection of wonderful mathy tidbits. Jordan also has a point about the act of scrutinizing something in a logical and mathematical fashion. That act itself is courageous and should be appreciated, and he explains why, and he tells us how much we’ve already benefited from people in the past who have had the bravery to do so. He appreciates them and we should too.

And yet, he also sends the important message that it’s not an elitist crew of the usual genius suspects, that in fact we can all do this in our own capacity. It’s a great message and, if it ends up allowing people to re-examine their need for certainty in an uncertain world, then Jordan will really end up doing good. Fingers crossed.

That’s not to say it’s a perfect book, and I wanted to argue with points on basically every other page, but mostly in a good, friendly, over-drinks kind of way, which is provocative but not annoying. One exception I might make came on page 256: no, Jordan, municipal bonds do not always get paid back, and no, stocks do not always go up, not even in expectation. In fact to the extent that both of those statements seem true to many people is the result of many cynical political acts and is damaging, mostly to people like retired civil servants. Don’t go there!

Another quibble: Jordan talks about how public policy makers make proclamations in the face of uncertainty, and he has a lot of sympathy and seems to think the should keep doing this. I’m on the other side on this one. Telling people to avoid certain foods and then changing stances seems more damaging than helpful and it happens constantly. And it’s often tied to industry and money, which also doesn’t impress.

Even so, even when I strongly disagree with Jordan, I always want to have the conversation. He forces that on the reader because he’s so darn positive and open-minded.

A few more goodies that I wanted to adore without giving too much away. Jordan does a great job with something he calls “The Great Square of Men” and Berkson’s Fallacy: it will explain to many many women why they are not finding the man they’re looking for. He also throws out a bone to nerds like me when he almost proves that every pig is yellow, and he absolutely kills it, stand-up comedian style, when comparing Ross Perot to a small dark pile of oats. Holy crap he was on a roll there.

So here’s one thing I’ve started doing since reading the book. When I give my 5-year-old son his dessert, it’s in the form of Hershey Drops, which are kind of like fat M&M’s. I give him 15 and I ask him to count them to make sure I got it right. Sometimes I give him 14 to make sure he’s paying attention. But that’s not the new part. The new part is something I stole from Jordan’s book.

The new part is that some days I ask him, “do you want me to give you 3 rows of 5 drops?” And I wait for him to figure out that’s enough and say “yes!” And the other days I ask him “do you want me to give you 5 rows of 3 drops?” and I again wait. And in either case I put the drops out in a rectangle.

And last night, for the first time, he explained to me in a slightly patronizing voice that it doesn’t matter which way I do it because it ends up being the same, because of the rectangle formation and how you look at it. And just to check I asked him which would be more, 10 rows of 7 drops or 7 rows of 10 drops, and he told me, “duh, it would be the same because it couldn’t be any different.”

And that, my friends, is how not to be wrong.

Well, this book is an excellent introduction to some of mathematicians' most useful spells when it comes to interpreting news stories, reasoning about uncertain things, and recognizing valid patterns while tossing out the random noise. Also, it's wonderfully written, lighthearted and colloquial; I was quoting it out loud to my housemates every ten minutes the whole time I was reading it. You should check it out!

This reads a lot like Predictably Irrational or Freakonomics. There are numerous examples of how people can be misled when they don't fully understand the meaning of mathematical statements. I wish there were a CD version in addition the the Audible so that I could send it to my granddad for father's day.

Lots of Words and anecdotes. Not much maths. I did not finish the book. It did not appear to be going anywhere and I was hoping to learn some maths. Some of the anecdotes were entertaining. I agree with the critics that say it was biased and failed to justify the opinions that were presented. A Glossary and some mathematical appendices would help.

It began OK, then degenerated into "p" values and other esoteric stuff that 80% of readers will not read and will cause them to go back to watching cartoons or the fishing channel. I can summarize this book in two words, "be skeptical". Those who need to read some of it will not and will remain gullible. Those who already know that much of what we hear/read is foma do not need to read it. That leaves...who (or whom)? I intend to finish it so as to see who done it and, maybe, improve my mind. I don't want to meet Jordan.

Almost comical. A professor from one of the most left wing universities in the country, who uses all manner of assumptions to prove why Gore should've won Florida, writing a book about How not to be Wrong. You can't make this stuff up. There ARE a few pieces of meaty interesting topics in here, but most of them are drowned out for you by either math you already learned, or math you never wanted to learn, depending who you are.

The book is wonderful, well-written and witty. That is, until the last thirty pages or so until the author's attitude, that's the only word I can use to describe it, comes through. Don't read to the end. There might be better books that won't leave a bad taste in your mouth. It was liking having a great meal only to find a cockroach leg on your plate.

I confess having a soft spot for popular science and mathematics' book, but this one crossed the line. As I say in the title, shallow, uninformative, and with a political agenda - manifested on the author's choices of themes. Although a waste of time for me, it may be useful for someone in need of an example of how to turn the most beautiful of subjects into pure doctrination.
There are far better choices out there.

The first indication I had that this isn't a book about how to analyze things objectively through mathematics was when I read the inside flap and it raised the question about who really won Florida in the 2000 election. I skipped ahead to that part of the book, hoping to see a sterile mathematical analysis. But there wasn't one.

There was a lot of totally subjective talk about why Scalia and the other justices ruled the way they did in Bush vs. Gore, with thinly veiled criticism of Scalia. This included the suggestion that Scalia doesn't care about finding the truth in a murder case, based on the author's superficial, sound-bite reference to a case that Scalia once ruled on.

Then he said that the overall count would have been more accurate if the court had allowed a recount in the counties that Gore asked for. This is totally false. The overall count would not have been more accurate if the recount - which could result in more votes being tallied - was only in counties deliberately chosen because they were likely to have more votes for one particular candidate. If you chose a few counties at random for a more thorough recount it would theoretically make the overall count more accurate, but not when you add the bias of choosing counties favorable to one candidate. A math expert should know this.

And, astonishingly, he disregarded the post-election recount sponsored by the New York Times and other media outlets. How can one do a mathematical analysis of the election without using this recount?

Well, he didn't do a mathematical analysis. He just concluded with conjecture about why he thinks the justices ruled the way they did - something that he has no way of knowing, and that isn't a mathematical analysis - with the implication that the result of the election would have been different had they not ruled that way. And, again, he gave NO math no support this.

From what I could see, the rest of the book wasn't any better. It's a political book, not a math book. Math can be a powerful tool to challenge conventional wisdom when used with an open mind. But this guy starts with the wisdom, conventional in academia, and works backwards in a lame attempt to prove it.

He's just another sniveling, politically oriented academic. And he tries to make his political points under the pretense of being an objective mathematician, applying his trade in a non-partisan way. It's phony and it doesn't work. I returned it. First thing I ever returned on the store.

This is an unsatisfactory book, because the author and/or his publisher could not decide what the book was supposed to be about and who were its intended readers. This is made clear by the difference between the front covers of the British and American editions of the book.

The front page of my copy, bought in the UK, reads in part: “HOW NOT TO BE WRONG ….. THE HIDDEN MATHS OF EVERYDAY LIFE”. The corresponding text on the USA cover (at least as shown on the the store-USA advertisement) reads: “HOW NOT TO BE WRONG: THE POWER OF MATHEMATICAL THINKING”. There is a clear distinction here, which runs right through the book and is never sorted out. The UK edition sub-title hints that the book is meant for the man-in-the-street who only knows elementary maths (arithmetic) and who is to be helped by this arithmetic in his day-to-day activity, while the US subtitle seems to aim the book at the mathematically skilled (such as statisticians). In fact the book is written continuously, and only, at the second (statistical expert) level.

This is curious, because the simplistic-sounding declaration of the UK edition is backed up by several of the review excerpts printed in the US edition, which say that the book shows how the use of simple mathematical thinking helps to ‘be right’ in dealing with ‘everyday’, ‘commonplace’, ‘street-smart’ situations. But in fact in the book’s 440 pages there is not a single example of how elementary mathematical thinking will help anyone ‘not to be wrong’ in the ordinary experiences of daily living. In other words, the author NEVER gets down to discussing ‘THE HIDDEN MATHS OF EVERYDAY LIFE’.

This is the fundamental flaw in the book. The situations which the author deals with are all of very great mathematical complexity which the ordinary person has very little chance of influencing (or indeed of understanding), and which do not make up the everyday life of the vast majority of people. The author discusses how many parallel lines will be cut when Buffon randomly drops a needle among them, or what kind of curve you get if you plot the current year’s temperatures against the temperatures ten years ago in the same (or perhaps in different) cities in the USA; what mathematical statistics go into playing the lottery, or betting on the performance of baseball and basketball players, or predicting who will win in local or national elections in the next poll, or who will be obese or taller or shorter or will contract cancer or be more successful in business, or whatever it may be, in the next twenty years. But in what way will ‘the hidden maths of everyday life’ help the ordinary person in any of these areas? The book never really tells us.

Again, Ellenberg highlights the statistical investigations of Francis Galton (Charles Darwin’s first cousin, as it happens) in two whole chapters, with huge emphasis on ‘regression to the mean’ (look it up) in family height, eugenics, family intelligence, business success, writing another acclaimed novel, etc. etc.). On page 309 Ellenberg makes the astonishing summary: “Biologists are eager to think regression stems from biology, management theorists like Secrist want it to come from competition, literary critics ascribe it to creative exhaustion - but it is none of these. It is mathematics”. This will not do. Ellenberg only shows that mathematics can draw graphs to illustrate the regression which has been observed. He certainly does not even begin to prove that regression stems from or is provable by mathematics. Astonishingly, he seems to attribute regressing upwards to the mean from a lower position to good luck, and regressing downwards to the mean from a superior position to mere bad luck.

To work out the probabilities of future results and the best pathways to follow in the difficult cases which the author discusses, requires qualified professional statistical mathematicians, not the ordinary maths of the man-in-the-street. The author shows that he believes (correctly) this to be the case, because he introduces and discusses every famous mathematical scholar from the sixteenth century to the present day. But what he is proving is not that ordinary ‘mathematical thinking’ helps to simplify and solve our day-to-day lives, but only that if we want ‘NOT TO BE WRONG’ in these out-of-the-way issues we would need to be more clever than all the great statisticians whom he discusses. May I invite the reader to look up, for example, Bayes’s Theorem (much referred to by the author) in Wikipedia, to see the kind of mathematical complexity that professional statisticians have to handle. Has the author enabled us to understand and apply Bayes’s theorem? He has not.

When trying to prove a point, the author usually spends page after page multiplying small decimal quantities or percentages, and writing minuscule values in sections of his boxes, and drawing complicated graphs, all of which require a degree of concentrated re-reading and re-thinking which are really beyond what can be expected of the ordinary reader.
It seems to me that (for those who have had the patience and the sufficient mathematical and general knowledge to read the book through to the end), the main reason for the popularity of the book must be that even when Ellenberg’s reasoning seems to be hard to follow, he often concludes with an eminently common-sense opinion. Examples are:

1. Don’t play the lottery - unless you enjoy it as a bit of a game.
2. However, the highly improbable still happens quite often.
3. Always initially treat polling statistics with suspicion, since there are so many factors which might or might not have been taken into account and which influence the figures of a poll - age? religion? ethnicity? educational level? salary? the weather on voting day? Democrat or Republican? .
4. Consider if a difference must be made in a ‘daily living decision’ where morality comes into it.
5. Remember that for every research report from a manufacturer of medicines which recommends the use of such-and-such a drug to the medical profession, there may be several (unpublished!) research reports claiming that this drug had no observable positive health effect.
6. Develop the strong points of your opinions every day, but every night see if there are weaknesses in them which can be attacked.
7. Accept the surprising fact that if an election is between two candidates only, then clearly the one with the most votes is the winner; but if there are three or more candidates, the voting system used can mean that the one who emerges with the most votes may not be the one whom most of the voters prefer.
8. Regression to the mean is a fact.

And so on…..

For me, the author’s book could usefully be replaced by a short pamphlet listing words of wisdom such as those above, with a few words of logical introduction to each item. I just don’t see how the mathematical thinking described in chapter after chapter of this book helps the common man or woman ‘to become better thinkers’, as the back cover claims it will.

And I dare to add: The book’s title is simply not justified. For rational humankind, ‘How Not To Be Wrong’ is not a search for mathematics alone to decide, but, more importantly, it is the proper field of enquiry for philosophy and religion.

The back cover of my edition asks, “Can maths … Prove the existence of God?” Our author does deal at some length with the (to me) unlikely ‘bible code’ belief that the names of prophets and rabbis and modern-day presidents of Israel were deliberately (by divine inspiration) encoded in the text of the Hebrew bible two or three thousand years ago, as will be discovered if you string together every fiftieth letter of the text from some starting-point! And he also brings up (in chapter 10) the question, which he handles very weakly, of how to relate the existence (or non-existence) of ourselves to the existence (or non-existence) of God. He satisfies himself with the (to me) untenable solution not only that we don’t know, but that more likely scenarios are that “we are actually not physical beings at all, but residents of a computer simulation being carried out by humans with unthinkably advanced technology”, or “created by a community of gods, something like those worshipped by the ancient Greeks” (p. 190).

In other words, our author will prefer any fantasy, provided that it excludes the overwhelming evidence for the existence of the unique Creator-God accepted both by the pagan Greeks (Aristotle) and by Judeo-Christians, sourced in the Bible and further studied by St Thomas Aquinas and Christian philosophers and theologians in general. Ellenberg is out of his depth here (as are the cosmologist Stephen Hawking in his book ‘The Grand Design - New Answers to the Ultimate Questions of Life’, and the biologist Richard Dawkins in ‘The God Delusion’), when they step outside of their materialistic scientific field into the over-arching fields of philosophy and theology. In defence of the view that there must be a unique pre-existing Creator-God to explain the existence of the universe and of rational mankind,,see for example Antony Flew’s book, ‘There is a God - How the world’s most notorious atheist changed his mind’. Flew sums up his opinion (on page 92), referring also to the work of another philosopher, Conway: “As Conway sees it, then, the God of the monotheistic religions has the same attributes as the God of Aristotle*, which Conway identifies as "immutability, immaterriality, omnipotence, omniscience, oneness or individuality, perfect goodness and necessary existence". There is of course a vast scholarly literature in support of this position, which flatly contradicts Ellenberg’s naive denial of the creation of the world by one Creator-God:

Finally, I refer to a contribution which I have just come across on the store. Type in "Has Science Discovered God? - Y-Jesus.com" and you will get seven pages of strictly scientific confirmation (by very modern scientists!) that the existence of a Creator God is necessary, to explain the existence of the material universe in which we live, and of rational mankind. This is followed by ten pages establishing that the Resurrection of Christ was a true, literal bodily Resurrection.

The book is generally interesting, but Mr. Ellenberg's liberal bias grates on me at times. Reagan is a pathetic dumb cowboy actor, Paul Krugman is a saint, Scott Walker a manipulative governor, blah, blah, blah. Had I known the Slate connection, I probably wouldn't have purchased the book in the first place. Having said that, he does have some interesting analyses of lotteries, probability theory, expected value and information theory (he even weaves in Shannon).For another view that is consistent with my criticism of the book, see: Linear Thinking and the Rahn Curve: Responding to a Critic by Daniel J. Mitchell

The author begins the book stating that good mathematicians always check the assumptions being made. From the first chapter he ignores his own advice and constructs an argument against those who are in favor of lower taxes and less government by stating his own opinion and disguising it as a “mathematical truth.” The author thinks that libertarians and conservatives are using “linear arguments.” He does not show or prove how this is so, but rather gives them this label and shows how such thinking is erroneous.

Frankly, his arguments are simply pathetic. He draws false conclusions from his own biased and subjective beliefs without even trying to prove what he says. I am surprised this book got past an editor and publisher. This book is more about trying to “prove” a liberal agenda than mathematics. It fails miserably on both objectives.

Mr Ellenberg seems like he knows his math, but he's so entrenched in liberal academia that it probably never dawned on him that others might have different views. I only got to chapter six. When he started in on yet another example of statistical abuse, this time defending President Obama from his detractors, I just couldn't stick it any more.

I don't demand that an author agree with me politically. I'm perfectly aware (as Mr Ellenberg seems not to be) that thoughtful people can disagree. There was just no reason for every second or third example chosen by Mr Ellenberg to illustrate his ideas to be political and absolutely no reason at all for all of them to lean one way. Both parties commit egregious violations of mathematical principles every day, why go out of your way to alienate half of your audience? I'm surprised that the editor at Penguin let this pass.

I just might have been able to put up with all of this if the math had been more interesting. By chapter six, however, I was expecting to be deeply into it, maybe delving into Bayes Theorem or techniques for holding certain parameters invariant in a regression analysis or something. Instead, he was still pounding on about those evil opponents of President Obama and their abuses of percentages.

Boring.

This volume is basically just a repackaging of popular economics topics that have been written about ad nauseam. Vaguely entertaining, but the research is very shallow, and the writing is amateurish.

Ultra Liberal Apologist and Revisionist. I bought this book to gain a greater understanding between mathematics and world events. What I got was a cheerleading book representing every liberal idea's wonderfulness and why every conservative idea is wrong, cruel, irrelevant or elitist. I don't need to be reminded how wonderful Obama is and how he is actually G-d in the flesh. This book should have been titled "Why Any Idea That Isn't Liberal Is Wrong".

I rarely ever do not finish a book, but this one did it. Had some interesting stuff at first then it kind of turned into a political commentary. I don't do politics. I do like math though and this kind of veered off course. I would had to think i had to sit through
a semester with this guy.

If you were thinking about buying this book on the basis of it being anything like Freakonomics, don't. You don't get two sentences with in the first chapter without a blatantly partisan political attack followed by weak logic supporting a single minded world view. This is much less a math book and more so a political and social rant.

If MSNBC is your thing and you enjoy reading things that reinforce your beliefs then this book is for you. If you want a data-driven book like Freakonomics, I suggest you look elsewhere.