Is Maths Real?: How Simple Questions Lead Us to Mathematics’ Deepest Truths

It's almost like reading two books in one. First you get the maths in an engaging way that makes you ask the questions and more importantly explains the answers that way your teachers never did. And it also shows you where maths overlaps with real and relevant areas of our lives where genuine impacts can be made by framing your maths. Great stuff, loved every minute of it.

Provides really nice, reader friendly, insights into the basics of maths, especially number theory. A bit too "me!, me!" for many tastes when it comes to telling us about personal likes and dislikes, plus she comes across as a grossly over-simplistic social historian. Nevertheless well worth reading for the mathematical insights provided, which are a lot deeper than may be thought at first sight.

Actually I cannot say because I could not go beyond the second page...

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.

This book does not contain insights on how to understand maths - which is what I was expecting. It is VERY verbose with little maths and a lot of psycho babble - a complete waste of money.

Precisely the opposite of its claim. I couldn't get past chapter1. One for the charity shop I'm afraid!

Used this book for general interest.

I picked up this book primarily for my son, who is currently navigating the labyrinthine world of school math. He's the kind of kid who needs a 'why' before he dives into the 'how,' and I thought this book might offer some insights into the practical applications of math. Little did I know that this book would turn out to be a captivating journey for both of us.Engaging and AddictiveThe first thing that struck me about this book was how engrossing it was. I found myself as glued to its pages as I was when reading science fiction classics like Isaac Asimov's "Foundation" series. The author has a knack for making complex mathematical concepts not just understandable but downright fascinating.Practical AdviceThe book is not just theoretical; it offers actionable advice for parents. It addresses the often monotonous and rote memorization part of math education and provides strategies to make the learning process more engaging and meaningful.Some Takeaways1. Math as Brain Exercise: The book likens doing math to exercising one's "brain muscle," a concept that resonated with my son. He enjoys physical exercises like pull-ups because he believes they make him better at his other interests like swimming and ninja activities. The book successfully draws a parallel here, making math more relatable for kids.2. Math as Accumulated Wisdom: The book underscores the idea that math is not just numbers and formulas; it's the accumulated knowledge passed down through generations of humans. Learning math is akin to standing on the shoulders of giants, benefiting from the discoveries and insights of those who came before us. This perspective adds a layer of profundity and significance to the subject, making it more appealing to learners.3. The Changing Landscape of Math: The book points out that the algorithmic or "vertical math" that was the focus when I was in school is not as relevant today. It emphasizes the importance of understanding the underlying principles rather than just memorizing formulas.4. Flexibility and Rigidity in Math: One of the most enlightening sections of the book discusses how math is both flexible and rigid. Kids are not born with the conventional wisdom of 1+1 always equaling 2 for good reason. Because in the real world in different contexts 1+1 do not equal to 2. It is important to encourage kids to think freely and understand why it equals 2 in the context of a math classroom.This book is a treasure trove of wisdom not just for children but also for adults. It has changed the way I look at math and given me valuable tools to help my son on his mathematical journey. Whether you're a parent, a teacher, or anyone interested in understanding the real-world applications of math, this book is a must-read.

A very welcome addition to efforts of Mathematicians / maths-likers to eliminate Maths Phobia across continents ! In Bharat, I have been advocating FOLK-CAP way of Enjoying Maths Problem Solving AT-NO-EXTRA-COST to Edu.dept and Parents Pocket.. viz Maths for Billions!. Prof.Eugenia Cheng book should be in personal library of all students and Teacher Educators. FOLK-CAP is an ACRONYM for Figure Out the Logic with Knowledge of Current And Previous. Uniformly solve problem all through 15yrs Schooling.

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.

“Is Math Real?” makes the case for the study of abstract math and demystifies it (as much as it can, anyway). It critiques the math education status quo and explicitly argues against the importance of real world applications as part of that process. The author argues for using math as a way to sharpen our intellectual “core muscles”; the point of learning trigonometry or algebra is not just to calculate angles and solve equations, but to build logical frameworks and work inside them. She laments a focus on producing correct answers quickly, at the expense of the open questioning process that is critical for mathematical research. She reinforces this by poking at declared truths, demonstrating situations where 1+1 doesn’t equal 2, or walking through the logic of why 1 is not a prime number. She points out the paradox of how an “obvious” truth often means something that is “so clearly true that I can’t explain it”. She discusses the value of rigorously proving something over merely observing a likely pattern.The author’s style relies heavily on digressions, making analogies to cooking, social behavior, and cultural forces. She explicitly calls out the gatekeeping of traditional white European male control of academic math, and the way that diminishes other cultures' mathematical traditions. These asides can be jarring; one page you are stepping through a logical derivation and the next you are considering the extent to which medieval African mathematicians were erased from history. I don’t have one single opinion on these. Sometimes I found them interesting, other times distracting. They varied in depth and sometimes felt incomplete.They serve to reinforce the idea that math is not monolithic, but I don’t think they were always effective. They do make the book feel very human.Math is not concrete, and “Is Math Real?” celebrates this as its great strength. I don’t know that this book will convince many math skeptics, but it may present a new perspective for them.3.5 stars