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How Not to Be Wrong: The Power of…

How Not to Be Wrong: The Power of Mathematical Thinking (2014)

by Jordan Ellenberg

Other authors: Elise Craig (Fact checker)

Other authors: See the other authors section.

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Showing 1-5 of 14 (next | show all)
Really really good. That's why I took so long to read it. I had to make myself slow down. He does get caught up in chasing some geometric proofs which were less than interesting but overall a really strong argument for learning math in its totality. Probably should be used as a hs text in an ambitious academically rigorous school. ( )
  kallai7 | Mar 23, 2017 |
Obnoxious title aside, I found this informative and enjoyable. Ellenberg gets a little lost in the weeds deriving a few things where a two-sentence summary would do, but hey - his book, his call. Most of the content here was common sense - not all curves are linear, correlation doesn't imply causation, improbable things happen all the time, small sample sizes skew results, and so on - but common sense isn't really all that common, and it's important to keep these fundamentals in mind when you use numbers and patterns and trends to try to understand the world around you. My takeaway, at least. ( )
  steve520 | Dec 10, 2016 |
In order to pick up this book, I guess you have to have at least a faint interest in mathematics. Otherwise, the word 'mathematical' in the title will probably scare you off. However, not being wrong anymore sounds like a good enough prospect to make up for all the maths in the book, right? How Not to Be Wrong: The Power of Mathematical Thinking starts out by giving a reason why mathematical thinking can be a helpful skill in everyone's life and what math can reveal about improving your chances to win the lottery, understanding different systems to elect a president, and many more. The titles of chapters such as "Everyone is obese", "How much is that in dead Americans?" or "Miss more planes!" show first, that math can be fun, and second, that the intended audience of the book are not math professors but rather everyone.

Anticipating readers' feeling towards mathematics, Jordan Ellenberg attempts to answer the most-asked question in math classes first: "So, when am I going to use this?" Ellenberg encourages people to look deeper into things and discover the math in our everyday lives. However, he is very straightforward and also admits that there are aspects of your mathematical education that you might not specifically need anymore. But why should you still learn maths? Ellenberg argues that there is so much more to maths than just adding and subtracting numbers or doing fractions. Math classes improve your way of thinking about many aspects in your life - or at least, math classes should do that. This issue is still debated among math teachers. There are still the ones who prefer the traditional approach of having students practice doing fractions and solving yet another sometimes often slightly math-related problem until they finally discover an algorithm that they can use for a very limited range of problems 'normal' people don't have, anyway. And then there is the more modern approach to teach students the meaning behind what they are doing and to promote critical thinking before mindlessly applying algorithms to problems. This is not to say that students should not learn algorithms anymore. They still should, to my (and Ellenberg's) mind. However, this is just the foundation of what maths is all about. The following quotation sums up Ellenberg's view quite nicely and I couldn't agree more.

"Working an integral or performing linear regression is something that a computer can do quite effectively. Understanding whether the result makes sense - or deciding whether the method is the right one to use in the first place - requires a guiding human hand. When we teach mathematics we are supposed to be explaning how to be that guide. A math course that fails to do so is essentially training the student to be a very slow, buggy version of Microsoft Excel. And let's be frank: that really is what many of our math courses are doing."

At the same time, Ellenberg admits that not everything can be solved with one hundred percent certainty, even though this is often expected of mathematicians. Sometimes, for example when asked to predict which presidential candidate is going to win a certain state, mathematicians can provide a probability, but not rule out uncertainty entirely. However:

"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, and this is roughly how not-sure I am.' Or even more: 'I'm unsure, and you should be too.'"

The book also touches upon a topic many of us discuss around here. Are pop fiction and classic literature - literature with a capital 'L', if you may - mutually exclusive? Or framed differently: Is reading pop fiction a waste of time, and is classic literature always worth the time and effort you put in reading? Ellenberg compares this to the phenomenon of how the guys (or women, for that matter) you meet are either handsome and mean or nice and ugly, but never nice and handsome. He says that we do not even look at the mean and ugly ones so they are ruled out anyway. The triangle of acceptable men, then, which he defines as either nice or handsome is naturally only a small portion of all the men you can meet. And the nice and handsome men are an even smaller part of all the men available. Therefore, the chance of meeting a nice and handsome man has to be quite small logically. If you substitute the two axes from 'ugly' to 'handsome' and 'mean' to 'nice' with 'bad' to 'good' and 'classic' to 'popular', you end up with a similar situation for literary works. If you want to look up the whole reasoning, either read the book or look up Berkson's fallacy. Here goes Ellenberg and his answer seems quite intelligent to me:

"Literary snobbery works the same way. You know how popular novels are terrible? It's because the masses don't appreciate quality. It's because the Great Sphere of Novels, and the only novels you ever hear about are the ones in the Acceptable Triangle, which are either popular or good."

To sum up, I enjoyed reading How Not to Be Wrong: The Power of Mathematical Thinking a lot, not only because I agree with what Ellenberg writes to a large extent. No matter if you are interested in mathematics or not, you will probably find this book quite interesting and will probably (not certainly, of course!) not be sorry about picking it up. 4 stars. ( )
1 vote OscarWilde87 | Sep 5, 2016 |
Just one of those books that I saw whilst browsing in my local bookshop, and bought (almost) on impulse
  corracreigh | Jan 4, 2016 |
Undoubtedly interesting and great to visit, but I didn't find that this book distinguished itself from others of it's ilk. At times it fell deep into explanations that lost the attention of one particular reader. ( )
  LaPhenix | Nov 22, 2015 |
Showing 1-5 of 14 (next | show all)
Mr. Ellenberg's key point: Mathematics is not some strange language used by a few single-minded experts. Rather, it is a powerful extension of our common sense, one that anyone can employ to tackle real-life problems.
Ellenberg’s talent for finding real-life situations that enshrine mathematical principles would be the envy of any math teacher. He presents these in fluid succession, like courses in a fine restaurant, taking care to make each insight shine through, unencumbered by jargon or notation. Part of the sheer intellectual joy of the book is watching the author leap nimbly from topic to topic, comparing slime molds to the Bush-Gore Florida vote, criminology to Beethoven’s Ninth Symphony. The final effect is of one enormous mosaic unified by mathematics.

» Add other authors (1 possible)

Author nameRoleType of authorWork?Status
Jordan Ellenbergprimary authorall editionscalculated
Craig, EliseFact checkersecondary authorall editionsconfirmed
Dewey, AmandaDesignersecondary authorsome editionsconfirmed
Elewa, AdlyCover designersecondary authorsome editionsconfirmed
Villepique, GregCopy editorsecondary authorsome editionsconfirmed
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"What is best in mathematics deserves not merely to be learnt as a task, but to be assimilated as a part of daily thought, and brought again and again before the mind with ever-renewed encouragement."

Bertrand Russell, "The Study of Mathematics" (1902)
for Tanya
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Right now, in a classroom somewhere in the world, a student is mouthing off to her math teacher. - When Am I Going To Use This?
A few years ago, in the heat of the battle over the Affordable Care Act, Daniel J. Mitchell of the libertarian Cato Institute posted a blog entry with the provocative title: "Why Is Obama Trying to Make America More Like Sweden when Swedes Are Trying to Be Less Like Swedenborg?" - Chapter
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"Using the mathematician's method of analyzing life and exposing the hard-won insights of the academic community to the layman, minus the jargon ... Ellenberg pulls from history as well as from the latest theoretical developments to provide those not trained in math with the knowledge they need"--… (more)

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