Is Math Real?: How Simple Questions Lead Us to Mathematics' Deepest Truths

by Eugenia Cheng

One of the world’s most creative mathematicians offers a new way to look at math—focusing on questions, not answers   Where do we learn From rules in a textbook? From logic and deduction? Not really, according to mathematician Eugenia we learn it from human curiosity—most importantly, from asking questions. This may come as a surprise to those who think that math is about finding the one right answer, or those who were told that the “dumb” question they asked just proved they were bad at math. But Cheng shows why people who ask questions like “Why does 1 + 1 = 2?” are at the very heart of the search for mathematical truth.   Is Math Real? is a much-needed repudiation of the rigid ways we’re taught to do math, and a celebration of the true, curious spirit of the discipline. Written with intelligence and passion, Is Math Real? brings us math as we’ve never seen it before, revealing how profound insights can emerge from seemingly unlikely sources.   

Genres: Nonfiction, Science, Mathematics, Philosophy, Stem, Book Club, Science Nature

337 pages, Kindle Edition

Published August 15, 2023

About the author

Eugenia Cheng is a mathematician, pianist, and lecturer. She is passionate about ridding the world of math-phobia. Eugenia’s first book, How to Bake Pi, has been an international success. Molly’s Mathematical Adventure is her first children's book.

Reviews

[Brian Clegg · Rating 4 out of 5]

As soon as I saw this book, I knew I had to read it, if only because I wrote a book called Are Numbers Real?. The maths content of Eugenia Cheng's book is brilliant: where I was covering the history of mathematics, she focuses on what real, pure mathematicians do. (Funnily, I had called my book Is Maths Real?, but it was changed to the less accurate Are Numbers Real? so we wouldn't need different covers for the UK and US editions.)

The mathematical journey that Cheng takes us through is mesmerising. She starts by showing the power of abstraction - how by thinking about the nature of, say, something basic like addition or multiplication it is possible to extend the concept into something other than numbers. We also discover that, in some ways, the answer '2' is the least interesting response to 'What is 1 + 1?' - real maths isn't about the answer per se, but about digging into the processes, mechanisms and definitions to get a deeper understanding of the underlying logic.

From these simple beginnings, we are then helped to get over what has proved a stumbling block for many: the abstraction of what we'd call variables in computing. Using an x (say) instead of a specific number. I loved algebra at school, because it felt like code breaking, but I absolutely understand why this step is one that defeats many young people in their exposure to mathematics. We then get on to formulae and their relationship to other mathematical structures like geometric ones, and different visual representations. And this was all a delight.

I wouldn't entirely agree with Cheng on why so many people aren't interested in, or openly dislike, maths. I suspect a lot of it is about the very thing that makes it attractive to her - that abstraction. If we look at the rest of STEM, engineering and medicine give us practical things. Physics and chemistry tells us how the world works. Biology tells us about interesting animals and feeds into medicine. But most of maths is neither useful in ordinary life nor telling us anything about the world, because it exists within its own abstracted universe. This book makes clear how beautiful that can be - but it's a hard sell to teenagers.

Originally, I was going to give this book five stars, because the maths coverage is brilliant, but most of Cheng's books I've read have the flaw of containing (for me, at least) too much about her and her opinions. I want to read about maths, not Cheng's interest in food, her politics or her cultural inclinations. I do want to know about why mathematicians find maths interesting - but that’s a very different thing. This sort of personal content does appeal to some readers, just as, say, reading a magazine about celebrities is fascinating for some, but it puts me off.

Overall, then, do read it if you want to know more about the nature of pure mathematics and about being a mathematician - the mathematical content is great - but you may need to occasionally grit your teeth over the rest.

[Simon Tudge · Rating 3 out of 5]

Yes and no. Quite a lot to recommend in this book. I found parts of it quite fascinating. I'd certainly recommend this if you are a teacher, as much of it is about the pedogalogical aspect of mathematics.

I particularly like the "from this point of view this, but from this point of view this" kind of style. Especially the argument about how pi=4 from a certain perspective. That tickled me nicely just how I like it.

There are a few sections that simply start explaining certain sections of maths. This is a book that purports to be exploring the basis of maths, but there's a long section on trigonometry, that really is just a primer on trigonometry, and seems to serve no purpose to the overall argument. Could be useful if you wanted to learn trigonometry I guess.

Then there are the diversions into "politics". It really feels like these are being crowbared into book, and often feel a bit contrived and add very little to the argument.

"Not thinking that 'i' can be a number is like thinking that women can't be mathematicians."

"If you don't think that x can represent a number you're like someone who thinks that "they" can't represent a non binary individual.

"If you think that 3 is greater than 4 you're like someone who thinks that white people are greater than black people, because white people are not greater than black people and 3 is not greater than 4"

OK I made up one of those examples for comic affect. But the other two are real.

It's all very touching, but so contrived as to be distracting.

Then there's the section on decolonising maths. Where the idea that revelation from a Hindu godess is as valid as a formal proof is floated. This had me scratching my head a little.

There's actually quite a lot to recommend, all told. Some fascinating mathematics. And I love the emphasis on embracing uncertainty, and making maths more accessible. So kudos there. Certainly recommend for some, I think maybe I'm just not the target audience?

[Steve Kimmins]

A rare DNF that I’ll briefly comment on.
For me, it started well. An experienced and recognised academic in Mathematics tries to explain her subject from about the most fundamental starting points she can find. In particular, with her interest in STEM education, which interests me too, she often seemed to be orientating her explanations to those with no mathematical grounding at all.
For example, it might seem bizarre to discuss 1+1=2, its validity and occasions where you could expect a different result (a trivial example would be one pile of sand added to another pile still gives one pile of sand, albeit bigger). It was a tool for her to explain the basic need to define the basis of your maths if you expect to get something out of it; it’s as much a language of human invention as any other and definitions are critical.

However, I personally found the pace slow. When I abandoned at about 60% we’d just got onto algebra after some number theory. The author is also fairly verbose and brings in all sorts of analogies, and sometimes goes off at a tangent, often related to her interests in cooking and music. Although I’d like to think I’m on roughly the same page as her politically and her social concerns I rarely felt that their involvement to be of use to the mathematical core of the book.
So I just got rather bored..!

But I’d recommend it perhaps to students with an arts background, who may find maths rather confusing, as perhaps one entry route into understanding it without involving the traditional proofs and problem solving aspects you find at school. You could maybe see the point of it without starting to become a practitioner.

[Stefanie]

I am sad about it, but I have to move this book to my DNF shelf. This is a case of bad timing, and "it's me, not you." May 2024 was just not the month for me to take on books that required a lot of brainpower and focus to get through.

To be fair, in the 17% (89 pages) I read, Cheng was doing great at making math concepts approachable. And while it required some thinking on my part, I was enjoying it.

So while I'd like to think I'd come back and finish this, without a book club to push me through, I have to be real and say I probably will not. Too much else out there to read that qualifies as pure fun that I'll prioritize. But I hope this book finds appreciative readers, which it deserves.

[Derek · Rating 1 out of 5]

I had to abandon this book after 200 pages. I enjoyed the discussion of math, but got entirely fed up with the current-events asides. For example, on page 182 she repeats her claim that math is a white male domain, only two paragraphs after she informs the reader that Algebra comes from the arabic al-jabr and was developed by a Persian mathematician in the 9th century. She also conveniently never mentions that mathmatic scores in international comparisons (such as TIMSS and PISA) are dominated by Singapore, Hong Kong, Korea, and Japan. Although I'm sure her experience as an Asian Woman has been influenced by patriarchy, I am also sure that she's aware of the facts I've mentioned here; and it would make her a more responsible advocate if she acknolwedged them.
Also, I chose this book because I wanted to read about math, not about current events. As a teacher of students who don't look like me, I'm a huge advocate for equity in education. That's not what I was looking for in choosing this book, however.

[Gordon Campbell · Rating 2 out of 5]

Starts well then depends into esoteric drivel

There are some interesting views expressed by the author in the first half of the book, if you can get past her obsession with “Eurocentric white male mathematicians’ influence on modern maths”. She goes on a bit about it. Unnecessary and could just go in and tell us about the ancients and their maths, whether Greek, Egyptian or Neanderthal and not go on about how they may have discovered it first. I got to 80% of the book then gave up (very unusual for me, because I insist on finishing a book no matter how painful) because the author was using left and right handed hair braids to demonstrate a principle, which eluded me for the remaining 20%. Don’t waste your money.

[Laura · Rating 3 out of 5]

Eugenia Cheng is a very talented science/math communicator. I've discovered her through "x + y" a book I absolutely loved. "Is Math Real" didn't capture me quite as much as "x + y", but it still made me think about the world through different, rapidly changing lenses. The beginning and ending of the book are very strong in my opinion, but the middle sags. This is where we discuss calculus and graphing, where I found myself skimming because the explanations felt too simple for me, and I didn't discover anything I didn't already know or consider. The middle was also prone to changes of topic that weren't well channeled and prepared. Cheng's work touches on a lot of pressing social issues, but sometimes the way she brings those up feels a bit "out of the blue." And I'm saying this despite being in complete agreement with her statements. Take the example of discussing casting thin actors in movies in the chapter about graphing--it really had nothing to do with the chapter, and even the author admitted it wasn't fitting in by a simple "I digress." I also thought that the middle was a bit too focused on saying that people who take mathematical 'rules' (the ones taught in school) for granted might not be good at math after all. This felt like an oversimplification; I know in my case I felt the rules 'made sense' and I've always had an easy time performing certain mathematical abstractions and operations in my mind. This doesn't make me a mathematician, but doesn't make me a rule follower either. Her point was that mathematicians will dig deeper than that; agree, but some may still share that 'intuitive' feel with numbers. Since Cheng likes parallels with real life I'll use this example: my dad is super talented at painting and drawing; it's eerie how he intuitively knows how to draw. He was so good that in 4th grade he got in trouble with the art teacher who accused him of having an adult doing his homework--he painted a super realistic war scene. At age 10. His classmates had seen him paint incredibly accurate pictures before and they rose to defend him. At that point my dad did not yet know/understand perspective and colors the way an expert artist does, he learned some of that later in school. And he never persuaded an art degree (primarily because he wanted to have a salary). But does that mean that his intuitive painting makes him not an artist? How deep did he need to interrogate before we considered him an artist? Anyway, like the author, I'm digressing a bit. Toward the end the book was more moderate in its proclamations of what makes a mathematician, and the awe returned to the pages.
" As an abstract concept, it is real. This is the level at which math is real. We can’t touch it, but there are plenty of other real things that we can’t touch either. Sometimes it’s for logistical reasons, like the center of the earth or the inside of our own brains. But there are some real things we can’t touch because they’re abstract, like love, hunger, population density, greed, grief, kindness, joy."
Overall, an enjoyable thought-provoking read. For those who were 'good at math' in school, some parts may feel over-explained, but I think it's worth your time.

[Jose · Rating 5 out of 5]

In this book the author wants to let people know that if you hate math it's more likely because of the way you were taught. In fact, if there are things that don't make sense to you and you've asked "dumb questions" then you probably think more like professional mathematicians.

I found this book through to Ali Ward's Ologies podcast

Dr. Cheng talks about many mathematical concepts with an explanation of why and how mathematicians come up with concepts. I was blown away in the section "why is 1 + 1 = 2" because it turns the question on its head. We should think about "When does 1 + 1 not equal 2" for example, when you are painting, if you have one color, adding another color gives you a new combined color, not two colors, in this case 1 + 1 = 1. So then a good definition of *when* does 1 + 1 = 2 is in order.

I like that Dr. Cheng hates it when people try to use math to make themselves sound smarter as if knowing these things makes you a better, superior person somehow (it does not, it's your character)

I liked the little commentary on current events sprinkled here and there, I suppose that some people will balk at that, that's fine by me.

I didn't like that the material for me was introductory, I didn't walk about with new mathematical theory (well, at the end she goes into her category theory research) but it's an introductory book aimed at people who don't do math.

Overall, this is an excellent book. Highly recommend it. Math if for you and for all of us.

[فاروق الفرشيشي · Rating 2 out of 5]

After reading this book, I've learnt a lot of things. I've learnt that Eugenia Cheng doesn't like any kind of discrimination. She's a modern feminist. She's an LGBTQ ally. She holds all the values of a good Democrat. The Earth is not flat, the global warming is trivial, the immigration is human, etc. Before reading it, I used to know why Maths are useful. Now that all the new stuff I've learnt is just about Eugenia Cheng, I wonder where I'd use such information. Maybe to write a book called "Is Eugenia real?

[Claire · Rating 3 out of 5]

I listened to Eugenia Chang on Ologies and was inspired by her description of mathematics to pick up this book. I think her explanations translated better over an audio medium for me, and ultimately her description of math concepts didn't quite grab me. On the whole, I do wish her math pedagogy had been around when I was still in coursework. Had someone approached math from her gentle, curious, and inclusive perspective, I think my school experiences would have been drastically different.

[Jody Walsh · Rating 4 out of 5]

An interesting look at mathematics. She takes math beyond memorizing facts and formulas and helps the reader understand the meaning behind the facts and formulas. She includes real world problems, shows you the beauty of mathematics and understands that math can be intimidating. Of course I enjoyed the explanation of braiding. I learned some interesting new vocabulary and about new fields of mathematics!

[Jon Dale · Rating 4 out of 5]

I picked this book up in a book store and started reading and ended up buying it and finishing it in a week.

Starting with simple questions, why does 1+1=2, how many holes does a straw have, Cheng takes the reader on a journey into theoretical mathematics that is a surprisingly fun ride.

[Karen GoatKeeper · Rating 3 out of 5]

When does 1 + 1 not equal 2? Bend your mind around this as the answers are real, surprising and rather fun. Basic math gives the impression there is only one 'right' answer to a problem. That's true for practical everyday calculations (if it wasn't, our checkbooks would be unmanageable). But that often isn't true if the problem is looked at in another way.
A strong, basic understanding of math is essential for trying to follow the questions and answers in this book. The reason for calculus and what it does, different kinds of triangles, even genetics come into play on these pages. Some of the asides add to understanding the math questions. Others are only opinions of the author.
This book is not an easy read. Even with a good math background, some of it is not understandable. It does explain, sort of, what mathematicians do and how they approach their work.
The purpose of the book is to get past the rigid way math is normally viewed and this is done well. Some of the different ways of approaching a math question leave the impression it is all playing around with the question with no practical ends. Yet, some of this, as with calculus, ends up having major implications in the 'real' world most of us live in.

[Nebu Pookins · Rating 2 out of 5]

I wrote a full review at https://nebu.substack.com/p/book-revi... but the TL;DR is as follows:

- The book is very woke.
- The target audience is unclear. The author sometimes sounds like she's addressing young children, but she also uses technical jargon from category theory like "sylleptic monoidal 2-category".
- Many of the core claims of the book, such as "A lot of people have the wrong idea about what math is" and "A lot of math is taught incorrectly", are not particularly original or insightful, and have been better argued elsewhere.
- Her answer to "Is Math Real?" is "Yes", because (she argues) abstract concepts like "love" are real.
- As an aside in one of her chapters, she ponders an alternative version of mathematics that is not as proof-oriented as the one most mathematicians practice. I found this idea very interesting, but unfortunately she does not dive deeply into that topic. I would have preferred to have read a book by her that focused entirely on that topic.

[Phyllis · Rating 1 out of 5]

Ratings, being opinions, relate as much toward the person who rates as the book itself. This could be the book for you. It's not the book for me.

So, Eugenia Cheng has written a book that I think is somewhat aimed toward people who (1) hated math classes and, as a result, did badly in them and (2) others who just think it would be fun to see possible answers to questions like, "Why does 1+1=2?"

I'm not in the first group and Ms Cheng's mind and mine don't travel on the same highway so I was disappointed and occasionally confused by the way she went about demonstrating things.

[k.]

tries to take mathematical frustration towards curiosity and understanding, though i found i could not finish it. it doesn't pass muster for my non-fiction aesthetics, nor is its subject interesting enough for me to push past the obstacles it continually throws (cloying political correctness).

[Stephen · Rating 2 out of 5]

This book was a disappointment. Mathematics is a great subject, and if you think I am mad for saying so, this book should have been for you. A book that is not for mathematics geeks, but for those who have big questions about what it is, why we have it, and the weird assumptions it makes. It asks some very pertinent questions and challenges basic assumptions. 1+1=2, but why? And when doesn't it?

Good questions, and the promise of the book is that it will answer all the questions people think are too stupid to ask, and in the answering will show that they are not syupid questions at all. It promises to look at mathematics afresh and shake up how we teach it.

The promise is good. The execution less so. It is slow going, and at points it just descends into a mathematics primer. The 1+1 doesn't always =2 discussion was okay, but having thrown in some logic truth tables, it didn't really explain those. But the most irritating thing for me was all the political comment. I didn't necessarily disagree with the comment, and I am not sure that there is never a place for such comments in a work on another subject, but in this case we had a book that was trying to open up a subject to everyone, but was presumably just going to irritate some readers unnecessarily with its right-on and overt political messaging. It wasted space, and was a distraction that will alienate some of those for whom it might be a useful work.

I'll stick with Matt Parker as the go to for making mathematics accessible.

[Tobias Taylor · Rating 4 out of 5]

"...maths will be there, quietly waiting, for anyone who wants to go there, anyone who is curious, anyone who is imaginative, anyone who dreams, and anyone who asks questions."

I wish I'd learnt maths in this way—with wonder and curiosity. The author takes an approach that is both similar and somewhat of an opposite to Richard Feynman. She talks/writes a lot around an idea which is usually helpful, sometimes overworked, and other times still not clear. Feynman uses fewer works, with more clarity but sometimes you still don't understand and then you're really on your own because he's said barely anything about it to start with.

If you have never learnt maths OR you have any curiosity whatsoever about the subject then this is a fantastic book. I really value this approach to learning highly. It's the equivalent of making you desire to travel further than you can walk -> so you want to build some machine to help you get there faster -> so you need to learn what tools can help you do the job -> so you are interested to learn about a spanner. The alternative is trying to teach you why a spanner is relevant to your life before you have any use for it.

[Emerson Kellman]

could not get through this book. it was made for people who don’t love math and want to be convinced to love it, and this just wasn’t for me. she painted people who love math to be wrong for loving the black-and-white of it, and also was a major yapper who went into 5 tangents-per-page.

[Barbara McVeigh · Rating 3 out of 5]

I had hoped this book would turn me into a math person. I’m still not a math person, although it was an interesting read and I learned new things.

[Slater Shrieve · Rating 1 out of 5]

This book is insufferable

Sincerely,
a math major

[Jack · Rating 5 out of 5]

Very good book about the "goal" of maths by means of asking questions and a nice insight in category theory.

[Sara · Rating 4 out of 5]

As a maths student with an interest in education, I enjoyed this book. It often motivated me to study and rekindled my love for mathematics more than university does. It was an easy and fun read, but the title made me hope for a deeper ontological exploration of mathematics.

[Luke · Rating 4 out of 5]

Delightfully retracing basic math concepts to show mathematicians motivations and enthusiasm, emphasizing an openness to not assuming things are "obvious", an educator's deep interest in honest innocent questions that do not one correct answer, and the relevance of math's interest in contextual "why and when is such true?" in seeing similarities and differences in analogy to current political and cultural rifts.

[Ward Hills · Rating 2 out of 5]

The author presents a set of excellent and accessible descriptions and explanations of the ideas and meanings of mathematical argument. She takes the next step and shows how many mathematical approaches can be applied to areas in which you would not normally expect to find application. Demonstrates that maths is not only real but insightful.

In that way it is a very good work.

I stopped reading the half way through because I became annoyed to the point of distraction by the political and social agenda interlaced in the book.

By way of illustration, she spends several pages building a solid argument for rigour in mathematical statements. Her explanation is excellent and brings the reader along quite effortlessly to some fundamental insights with broad utility. She is an exceptional communicator. However, what follows is a few paragraphs of unsupported statements and ambiguous labeling of types of people. In this latter part, she is at best inconsistent in language and arbitrary in the labels she uses. This is in stark contrast to the earlier part of the chapter.

In another place she complains about students challenging her and makes a blanket statement about how student challenges are more common for her due to her gender and race. Others have experienced what she describes who did not have the same labels. The experience could be as due to being a young lecturer with unenthusiastic, or perhaps overly confident, audiences as it is about the particular lecturer.

In still another place she uses an an example set the types of privilege one racial group has. The internal logic of the arbitrary types is correct. The choice of the category types and the language used is from a specific social perspective and detracts from her good mathematical point.

If she wants to write a book about social issues she should do so. Given her ability to communicate about how to think well it might prove an insightful work. If she is going to insert a political argument into a book on maths my strong suggestion is to treat all her arguments with the same rigour.

[Carrie Rose · Rating 3 out of 5]

I really wanted to love this book and give it a great review, because there's so much in it to recommend. I have a degree in math and I work as a math tutor, and I got really excited when I read the introduction to the book, because it expressed a lot of how I feel about math. Unfortunately, the great material in the chapters kept getting interrupted by the author's political digressions and opinions.

The good: I have been telling people for years that I love how math is about making up worlds and that it's about so much more than following algorithms. Eugenia Cheng discusses this in a much more eloquent way than I can. I like her definition of math, and I appreciate that she discusses seemingly simple questions in great detail, illuminating the fact that they're actually important issues to consider. (I have always enjoyed number theory, which revisits a lot of the "facts" that we learned in childhood and asks, "But why is that true and what does it mean?") This book touches on a lot of very interesting mathematical topics and relates them to real life, and it also comes up with some excellent reasons why we don't always need to relate everything to real life every time we want to study math. It gives an excellent answer to questions I'm asked often by students: "Why do I have to study this? How will I use this in my life?"

The bad: Even when I agreed with the author's opinions, she drove me crazy by constantly jumping to stressful topics. If I wanted to read about systematic oppression or government or discrimination or heartbreak, I would have chosen a different book. One of the things I love about math is that a lot of those real-world troubles can be set aside. Cheng is very bothered by math being dominated by white men (in the last few hundred years, although a lot of the origins of math are from non-white cultures), and she brings this up a lot and gives examples. But (as a woman) I have never personally encountered this form of discrimination. Even though she talks about women being discriminated against, nobody has ever told me that my gender is a problem in the world of math. I have always felt that my work was being evaluated on its merits, and my demographics were irrelevant. I think that math does better than other subjects at disregarding demographics, because it's less subjective.

The chapter "What Makes Math Good" was particularly annoying to me. Cheng told the story of Srinivasa Ramanujan, a mathematician from India who didn't have formal mathematical training when he was young but had a brilliant mind. She emphasizes the oppression and tragedy in his story and suggests that the white Europeans were being unfair and discriminatory toward him. This may well be true, but that's not why I care about Ramanujan! In college, I wrote a paper based on his work because it was brilliant and it stood the test of time. I was a teenage girl studying the work of a poor Indian guy, and our demographics didn't matter, because it was just about the math. But Cheng was over-focused on demographics. Would Ramanujan want to be remembered as an oppressed, impoverished, non-white, non-European? Or would he rather be remembered as a brilliant mathematician who still inspires students with his ideas?

Cheng tried to use math to justify her controversial opinions. For example, she said that being intolerant of intolerant people is good, because intolerance of intolerance is the same as tolerance, just like -(-1)=1. This isn't something that can be simplified this much (for example, there's a difference between tolerating people and tolerating behavior), and I think she's misusing math by pretending that this is a reasonable application of it.

The confusing: I'm not sure who this book is written for. Someone like me might be the ideal reader (if you removed the political commentary), because I already like math enough to pick up a book about it. But she seemed to be addressing people who don't like math because they don't see the subject the way she does (and I do). I would like those people to read this book, or at least parts of it, so they can understand me better when I talk about the creative and exciting aspects of math. But I think maybe most of the examples aren't written in a way that that audience would appreciate. She encouraged readers to skim over things if it got too confusing, but if you have to skim over confusing stuff, I don't know whether that would feel intriguing or stressful. I understood almost all of the math in the book because of my math background, but there was some stuff at the end about braiding that I hadn't heard before, and I didn't enjoy the way it was covered. I would have liked it to either be more rigorous in its definitions (don't just say "sort-of-multiplication" - tell me what that means!) or to cover less material so I could remember what these vaguely defined terms meant. But maybe that's not how it felt to other readers, and maybe I wasn't the target audience of the book.

I would recommend parts of this book to people who want to know how I view math and what I think is appealing about it. But I don't know if I would recommend that people read the entire book. It starts out strong with a great introduction, but it starts going downhill with political asides in the first chapter. It also occasionally gets bogged down by overcomplicating mathematical ideas when I think Cheng is actually trying to present things simply, but that's a nitpicky complaint because I'm not sure what the right balance is (I suppose it depends on the audience). I would tell people who are curious about new ways of thinking about math to take the good in this book and skim over the annoying. And if the idea of reading a whole book about math sounds terrible (even though it's trying to help you see it in a creative, interesting way), I doubt you'll enjoy this book.

[Jim · Rating 1 out of 5]

Math content was enlightening…ruined by the strained political/social op-ed

[Maggie · Rating 1 out of 5]

dnf - couldn’t even get past the first chapter - the author is horribly wordy.

[Pavi · Rating 1 out of 5]

boring!!
she just yaps.

[Ashley Lambert-Maberly · Rating 4 out of 5]

Most science books follow a bit of a progression: they start with simple explanations, which I know already most likely, they move into more difficult concepts, which I follow with ease, they ramp up the complexity, which I follow with difficulty, and then at about the 80% mark they lose me and I no longer have any idea what they're talking about.

In this case I lasted until about 86% of the way through, but to be fair I also didn't understand the trigonometry chapter. Not her fault: despite being "good at math," in school, I never had, never will, understand or like trigonometry. I understand some of the beauty of math is abstract and you needn't always have practical applications to appreciate it, but the beauty of trigonometry escapes me.

As does category theory, which I ought to like, because it's the abstract qualities of math that appeal to me the most. I like principles (e.g. (a + b = b + a). I like talking about sets, and qualities, and I eagerly read her book on infinity. But category theory always starts like this: "you can write 30 as 5 x 6, and you can write 6 as 2 x 3, and of course it's all divisible by 1, and you can draw arrows between them, and you can arrange it all so it looks like a cube," and I think "yes, you can, but why on earth would you want to do that?" And I can never understand if you (a) have to do that to make something else work, or if (b) it's illuminating you can do that because it means something about 30 that's not true for other numbers, or (c) it's just one of many ways to illustrate 30-ness and it seems an easy one to start with (it's not), or (d) something else I don't understand. And then it moves on to abstraction very quickly, and instead of 30 -> 6 it's A -> B and I think I can draw a diagram of George Clooney -> velociraptor but I don't know that that makes it mean anything ...

However: for the first 80%ish, she's great. I especially appreciated understanding (for the first time, and it helps illuminate my difficulty with category theory) that math has increasingly difficult areas of abstraction, and most people will indeed be comfortable only up to a certain point. For some it's imaginary numbers, or irrational numbers, or negative numbers, but even simple numbers like 1, 2, 3 etc are abstractions, and I'd never thought about math like that before. It is, indeed, all abstract ways of representing things, even the humble and much used 1.

Like most readers, despite being largely liberal (I like being fiscally conservative, but that's about it) I wouldn't mind if she dialed back the frequent asides (or entire chapters) on subjects often dismissed as mere 'political correctness.' I agree with her, but they're raised too often in a book purportedly about maths. It's a bit like reading an Italian cookbook where the author keeps raising the political situation in the Gaza strip, it's out of place.

(Note: I'm a writer, so I suffer when I offer fewer than five stars. But these aren't ratings of quality, they're a subjective account of how much I liked the book: 5* = an unalloyed pleasure from start to finish, 4* = really enjoyed it, 3* = readable but not thrilling, 2* = disappointing, and 1* = hated it.)