I only read about half and skimmed the rest, so I will still be wrong at least 50% of the time.

I found this to be brilliant in spots, but there was quite a bit of “math word play” that I didn’t invest the time/attention to completely follow the logic. Ellenberg does a great job of simplifying complex topics that have evolved over centuries and provides thought provoking tools on how to apply those theories to real world issues. Things like the inverted u shaped Laffer curve to tell if more of a will increase or decrease b, the 2x2 matrix to scatterplot results to see whether there is causation or correlation, etc. are valuable. But he also devoted quite a bit of time to wordy math issues that were difficult to follow (political race outcomes, lotto roll down results). On balance, I am glad that I read this book but also glad that it ended.

From the AI:

"How Not to Be Wrong: The Power of Mathematical Thinking" is an ambitious exploration of the applications of mathematical thinking in various aspects of our lives. While the book tackles complex topics with enthusiasm, it occasionally suffers from an overabundance of technical detail that might overwhelm readers without a strong mathematical background.

The author, Jordan Ellenberg, has a knack for explaining intricate mathematical concepts, but at times, the explanations can become convoluted, making it challenging for readers to grasp the core ideas. Additionally, some sections of the book feel overly lengthy, causing the pacing to drag.

However, where the book shines is in its real-world examples and anecdotes, which help illustrate the practicality of mathematical thinking. These stories provide valuable insights into how mathematical principles can be applied to everyday situations, making the content more relatable.

In summary, "How Not to Be Wrong" is a mixed bag. It offers valuable insights into the power of mathematical thinking but may require readers to have a certain level of mathematical proficiency to fully appreciate its content. If you're willing to wade through the technical aspects, you'll find nuggets of wisdom that can genuinely enhance your analytical skills and perspective on the world

Would have been better to read this before spending $120k on grad school

Jumbled writing with too much filler. Billed at Amazon as "The Freakonomics of math," which I would say is accurate, and that's not a compliment. You could more efficiently learn about not being wrong by reading the Wikipedia entry on inductive logic, because this book is essentially about the limits of induction.

Probably one of the longest I’ve read a book, this one was a great book. I enjoyed the narration and the problems picked and the obvious brilliance of the author. But truth be told, so many of the concepts in this book flew over my head though the writing is simple enough. I’d recommend this book to a data nerd or anyone with love for mathematics and wants to apply simple math to real life.

The first chapter was super fascinating, but as the book went on, I found it less and less accessible to me. I got lost in all the math explanations and could no longer keep up after a while. Maybe I'm not mathematically-inclined enough to understand. The analogies the author chooses to use are also kind of boring. If you have a good understanding of math, this book might be interesting to you.

ei olnud halb raamat, aga ei olnud minu meelest ka see, mis lubati. matemaatikaosad (mida tegelikult ootasin) olid keerulisemad ja igavamad kui... paremates matemaatikaraamatutes (no vabandust, aga minu latt on ikkagi Hajameelse magistri raamatute juures). need osad, kus seletati lahti inimaju probleeme (me ei ole kõverate või eksponentsiaalse kasvu ettekujutamises kuigi head) või majandusstatistika või loteriide või hääletussüsteemide tausta... neid ma juba teadsin, sest ma olen lugenud raamatuid ajust ja majandusest ja poliitikast jne.

ei saa ka öelda, et poleks lugemist väärt olnud, sest igast peatükist ma umbes ühe uue asja ikkagi teada sain ja need olid teadmist väärt ka. näiteks et irratsionaalarv on arv, mis ei ole kahe täisarvu suhe (ratio) - jessas, ma olen kuuendast eluaastast saadik pead murdnud, kust see nimi tuleb; MIKS keegi mulle enne ei öelnud?! ja et korrelatsioon ei ole transitiivne (duh). ja kui ma peaks kunagi tahtma lotosündikaadi asutada, siis selle jaoks sai ka päris häid näpunäiteid.

kõige toredamad ja südamlikumad olid üldse need osad, kus autor lihtsalt filosofeerib matemaatika mõtte ja olemuse üle ja räägib sellest, kuidas on olla matemaatik.

***
A basic rule of mathematical life: if the universe hands you a hard problem, try to solve an easier one instead, and hope the simple version is close enough to the original problem that the universe doesn't object.

Ignore the title. This is no self help book but a valuable book concerning probability, hypothesis, proof and logic, which has become more valuable in an America in which the majority of the populace puts more trust in those who speak in absolute terms and speak of absolute solutions than those who admit uncertainty or acknowledge systemic complexity.

I wasn't going to write a review really but the majority of the other reviews seemed to be old men and I figured it wouldn't hurt for a younger, female voice to be added into the mix.
I went to a tour event for this book when it first came out, so I was 12. He read the first portion of the book and I was hooked. I subsequently started to read it many times of the years, but it was still too complicated for me. I started it again last year and got a good portion of the way through it, but put it aside when I got sucked into other, (let's be real, fast paced fiction) books. However, I'm really okay with that because I think that now, having just completed my first year as a math student, was the perfect time to read it.
It's a very insightful book about how to use logical, mathematical thinking, and when we shouldn't. It's about how numbers can be deceiving, and how to correctly interpret data. It discusses not just mathematical concepts, but also mathematical philosophy.
It was a deeply interesting read, that skillfully utilized storytelling to keep readers engaged. It probes you to think about deeper questions, including the role that math plays in your life. (And also tells you the best way to play the lottery which like, is cool).

If you are unconvinced of how maths might be relevant to the world around you, this is the book for you. Jordan Ellenberg takes the reader gently through a ream of mathematical topics - such as linearity, inference and so on - and (this isn't a textbook remember) puts these potentially horrible notions into concrete, intelligible terms.

The opening chapter is emblematic of the work as a whole. Ellenberg introduces the Laffer curve - which is just a line starting at zero at 0%, rising to some peak and then dropping to zero again at 100%. What does the graph show? It is a qualitative illustration of the fact that raising taxes from 0% generates some government income; you can keep raising taxes for a while, but eventually you hit a tipping point where additional taxes will actually reduce government revenue. Why? Because, in the limit of 100% taxation, no one would work at all. This graph, supposedly drawn by economist Arthur Laffer at a dinner with Dick Cheney and Donald Rumsfeld among others, is demonstrative of the non-linearity of the relationship between government revenue and income tax rates. Yes, raising rates below some threshold can raise revenues, but only to a point.

Why does the reader care? Because ignoring non-linearity leads to an awful lot of mistakes (the book is called 'How Not to be Wrong' keep in mind). Taking just one example, Ellenburg notes media headlines reporting that Sweden was reducing its taxes. If soak and spend Sweden is doing this, then what a great advert for reducing taxes in America too. This, implicitly to be sure, makes the assumption that the relationship between taxes and government revenues is linear. If revenues go up when Sweden lowers its taxes then so too in the US (a negative linear relation). But this is entirely false: the US is possibly to the left of the Laffer Curve's hump, while Sweden might be to the right. As such, Sweden may well lower its taxes and see a rise in government takings, but the US might see the opposite. Linearity cannot be assumed (and indeed is demonstrably false in this case, as Laffer showed). .

From here the author works his way into discussions of inference, or the art of understanding statistical significance; expectation, giving the wonderful example of a lottery that could be gamed under certain conditions, a fact exploited by some students who actually calculated the 'expected value' of their takings; regression, in particular focussing on the incredibly important notion of regression to the mean; and existence, or the nature of mathematical objects (formalism and that kind of thing).

If that all sounds forbiddingly difficult it, for the most part, is anything but. Ellenberg admirably explains difficult ideas in simple terms. The Law of Large Numbers, for instance, is just one such 'very formal sounding thing' (technical term). But in this author's hands, it is brilliantly (er) handled. First we are told about a highly counterintuitive finding: that North Dakota has the lowest rates of brain cancer in the US while South Dakota has one of the highest. This is explained first by pointing to the Law of Large Numbers - which says (in Wikipedia's terms) that "the average of the results obtained from a large number of trials should be close to the expected value and will tend to become closer to the expected value as more trials are performed".

This is hopelessly abstract. Instead, Ellenburg makes the point that small states like North or South Dakota will only have a few instances of a rare condition like brain cancer. Therefore, a few more cases in South Dakota can swing the proportion of cases in that state from the bottom to the top of the rankings (and vice versa for the North). By contrast, there are so many people in Texas or California that a few cases more or less will barely move the needle. This is the Law in action. With lots of people come more cases; small fluctuations are cancelled out and you're left with the number of cases you'd expect. As Ellenburg puts it: "smaller populations are inherently more variable". Intuitive result but spun out of what appears to be a bizarre finding.

Far from a series of disconnected examples, the author impressively manages to weave these illustrations of his subject together. Indeed, a key takeaway is how mathematics - the study of structures in some sense - is almost designed to provide transferable insight from one area to another. A real tour de force is found in the latter part of the book. The discussion initially is on expectation values. The application is to the lottery example mentioned above and why, under certain circumstances, it is actually worth playing: the expected value of a ticket exceeds its price, so just play a lot of tickets and you are highly likely to win overall.

There is a question remaining about what numbers should be chosen. Random choices works pretty well given the scheme the students have going on, but specific numbers are, it turns, out even better. Yet after a big discussion of expectation values, we take up a seemingly irrelevant issue, that of projective geometry. This leads to unusual geometries, including the seven-point Fano plane. This, it is shown, actually has precisely the property one would want when choosing numbers for a 3 pick, 7 ball lottery (out of nowhere - it really comes as a surprise when you return to the lottery example).

Though the expected value of using Fano plane numbers is equal to just randomly choosing your 3 picks, there is a lot less variance in the Fano approach. In other words, you won't win as big but you also are much less likely not to win much. The description of variance in the middle of all this is superb. The author then steps beyond 7-ball lotteries by describing how Fano's plane furnished an IBM researcher with an idea for error correcting an early computer. Finally (after some information theory) we return to larger error correcting codes that can furnish us with sets of tickets with just the properties you want for the particular lottery strategy the student's were employing.

It really is astonishing how long the lottery example is threaded through the overall account, cropping up in the context of multiple different mathematical stories and concepts. This is characteristic of the book as a whole. The author, whose passion for the subject veritably leaps off the page, paints an inspiring picture of an intertwined subject full of amazing results and surprising linkages. I defy anyone not to be a little excited by the maths on display.

The book is a little long; it also tails off somewhat. The author's attempts to bring to life some of the more abstruse arguments around the reality of mathematics, by going into the details of mathematics' turn to formalism in the twentieth century is a bit of a slog. I'm also not convinced it matches the style of the rest of the book - stepping as it does away from the pleasingly graspable examples (such as lotteries or Swedish taxes). There is also some overwrought discussion of elections and polls. In particular, the incredibly number-heavy discussion of different electoral schemes was mind-numbing and difficult to follow.

Aside from a few less than stellar sections and a bit of an unwelcome turn towards philosophy in the final pages of the book, this work is exceptionally well worth reading. For those who have scarcely thought of maths since school I think this is a must read, albeit a potentially challenging one in places. For those, like me, with an applied maths background, this book will likely be an easier read but, I still think, a very worthwhile one. I loved the recaps of (say) Bayes' theorem and all that though it wasn't anything new. But what really pulled me in were the discussions of the linkages and the connectedness of the subject as a whole. In short, I relished reading an expert's take on the field, particularly his comments on current maths and the future of the subject. In fact, I would welcome an entire Ellenberg book on modern mathematics as, in the hands of this author, I feel I might just about follow (some of) it.