Ellenberg has successfully showed how Math is convoluted into all kinds of sciences through this incredible work. I particularly enjoyed the development of such-and-such theories throughout the history. The stories, dramas, and discussions are amazingly detailed, with cited speeches and writings from the involved mathematicians and scientists. Despite Ellenberg’s intention to bring Math closer to general public via this book, which I wholly support, I believe it can only be fully enjoyed by readers who were/are used to doing Math. Against the stereotype of a mathematician, his writing is very appealing and humbly witty. However, his tendency to detour from the main subject can make it exhausting to follow. There are some parts of the book where numbers and tables should have been utilized instead of wordy descriptions. The book still did a great job in educating the readers to pay attention to common situations in which we’re more likely to make mistakes. Definitely recommend this book to those who love Math, all the more so to analysts and researchers.

Personal notes: Doing Math and problem solving was my leisure activity back in middle/high school, I attended several competitions and brought home some prizes, but everything stopped when I started university. I did some small Math projects after that, but could not feel Math like the way I had. Perhaps I missed the feeling of learning Math, the clicking moment when everything started to make sense; and when I read this book, I felt like I became a student again, seeing the examples leading to a new knowledge, and that knowledge links to another, making a huge system of reasoning, making Math the science of all sciences.

A readable, engaging and nontechnical exploration of the value of mathematics. One of the best books I've read this year.

I don't remember why I put this on the Big List, or when, but I'm glad it came up. And then I was even more glad when the introduction read a little like Bill Bryson and promised to make math accessible and answer the question, "When will I ever use this in real life?" Ellenberg can turn a phrase, for sure, and assured me I would need to know nothing but basic arithmetic to understand what he was going to do. Sign! Me! Up! And then I did a little dance, despite being tucked nicely into bed in my bookfort, with heating pad.

And that lasted through the first chapter. I hung in for a good long while because of clever illustrations and again, a great turn of phrase and the absolutely injudicious use of footnotes to make dorky jokes. But it turns out I also needed to remember geometry, which is fine. I'm okay at that. And then have an understanding of calculus, which is less fine because my understanding of it is limited to what's been dramatized by Neal Stephenson. So I powered for a few additional chapters and gained a learning or two, but hit a wall when it was time for the chapter on P-value.

The book fronts like a Bryson-esque explanation of math qua math but it's really a book on statistics and probability. Those things are cool, too, but I wish either he or his publishers or both had just been honest about it. I wanted the Whole Big Math Picture Written Especially for People Who Were Freakishly Good at the Verbal Parts of Standardized Tests. I ran into several chapters that all merged to take me back to Math 660, which I only took like 18 months ago, except not as friendly as my professor was. No mention of a quincunx or the Guiness factory. I already knew P-value. I never did know how to find alphas in a z-table and I still don't know. I know upper and lower control limits and special cause variation, but Ellenberg didn't really mention those. Mostly because you don't argue with standard deviation-- which, now that I think about it, he went out of his way not to talk about. Hey!

So, yeah. How Not to Be Wrong is not about how to build/grow a more mathematical mindset or see the flourishing logical beauty in the world around you. It's about how to make sure your efforts in statistics and probability support the case you're trying to make, whatever that might be. And, of course, the converse of that.

Being a great lover of Mathematics, I enjoyed this book immensely. More importantly, I learned very much from it. I learned purely numeric things, like Bayesian methods, and expected value. I also learned how many Mathematical ideas can be used not only to do Mathematics, but also to think Mathematically. How not to be Wrong installed an update to the software in my brain that included many new features and incredibly useful tools. This book, more than most other things, enhanced my logical thinking, helped make better decisions, made even more of a scientist, and added to the depth of my thought, in general.

How not to be Wrong seems to be an exaggeration of what this book can teach you. Believe me, it is not.

3.5 star rating.

Great book overrall, with invaluable nuggets of mathematical thinking. Ellenberg does a valiant job of explaining, using real-life examples, of mathematical concepts of linearity, inference, expectation & probability, regression, and existence.

Nonetheless, the biggest shortcoming of the book is that its title is a misnomer. For every one page of signal, How Not To Be Wrong has two pages of noise. Ellenberg inundates the reader with a lot of abstract information that serve no other purpose other than making the book a tard too hard to follow. One starts the book with the expectation of applied and recreational mathematics, but in many sections of the book the author makes an excursion into pure mathematics. The effect is that there's frustratingly only a sporadic flow of the book. At many sections of the book the reader feels as if Ellenberg is soliloquising yet hoping that you are following his esoteric line of thinking. Brevity would do a great deal of justice to the title of the book.
Additionally, Ellenberg writes on the assumption that the reader has prior knowledge of some of the mathematical concepts. For instance, the book started talking about p-values without any explanation of how they are derived from samples. At times, I felt like I was reading a maths textbook rather than a nonfiction book. I was lucky to have read Charles Wheelan's Naked Statistics prior, which does a stupendous job of explaining concepts which Ellenberg overlooked.

In all, I was satisfied that the book canvassed various disciplines in explaining the concepts, from economics to finance, warfare, politics, scientific research, law, and philosophy. Save for my reservations about the book, it is a worthy read.