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Beyond Infinity: An expedition to the outer limits of the mathematical universe

3.78  ·  Rating details ·  323 ratings  ·  62 reviews
Even small children know there are infinitely many whole numbers - start counting and you'll never reach the end. But there are also infinitely many decimal numbers between zero and one. Are these two types of infinity the same? Are they larger or smaller than each other? Can we even talk about 'larger' and 'smaller' when we talk about infinity? In Beyond Infinity, interna ...more
Paperback, 304 pages
Published March 1st 2018 by Profile Books (first published March 9th 2017)
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3.78  · 
Rating details
 ·  323 ratings  ·  62 reviews

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Manuel Antão
Oct 27, 2017 rated it really liked it  ·  review of another edition
Shelves: 2017
If you're into stuff like this, you can read the full review.

Cantorian Sets: "Beyond Infinity - An expedition to the outer limits of the mathematical universe" by Eugenia Cheng

“If this be not that you look for, I have no more to say, but bid Bianca farewell for ever and a day.”
In “The Taming of the Shrew” by William Shakespeare (quoted by Cheng in the book)
Eugenia Cheng starts by saying right at the beginning of the book, "Infinity is not a number," and I think it really helps to get that mis
Jul 24, 2018 rated it it was amazing  ·  review of another edition
Maths As Art Form

If you find it hard to tell your reals from your naturals or can’t remember why infinitely repeating decimals aren’t irrational, then this may be the book for you. A charming sortie into the poetry of mathematics, a guided tour of what they didn’t teach you in school: how numbers work and what it means to say that there are an infinite number of them. Cheng knows how to make a narrative with a beginning, middle and end, and with just the right touch of humour. Beyond Infinity is
Brian Clegg
Mar 05, 2017 rated it really liked it  ·  review of another edition
Popular maths writers have it much harder than authors of popular science books. Pretty well everyone loves science at junior school, even if they're put off it in their teens, so for science writers, it's just a matter of recapturing that childhood delight in exploring how the world works. But, to be honest, maths is a relatively rare enthusiasm at any age, so the author of a popular maths book has to really work at his or her task - and this is something Eugenia Cheng certainly does, bubbling ...more
Jose Moa
Nov 23, 2017 rated it it was amazing  ·  review of another edition
Shelves: mathematics, science
There are to day a lot of good popular books about mathematics that those of some age and fond of maths would like have read when young,this one is one of theese books.
Here Eugenia Cheng explains in a masterful way for the layman concepts of advanced mathematics,as the infinite series of infinite cardinals and ordinals,the concept of infinite countable sets is to say those that one can put in a one to one correspondence with the natural numbers and the uncountable sets where one cant ,as for exa
Peter Mcloughlin
Most people are on bad terms with math and I understand why the subject doesn't get much love. This author wants to change that. She covers cool concepts in the mathematics of infinity which is really cool to think about and introduces it in a personal and gentle way that might bring back some love in the most anxiety prone math probe. Go on its okay, this book won't bite.
Corey Thibodeaux
Apr 01, 2019 rated it really liked it  ·  review of another edition
Shelves: non-fiction, numbers
I had nothing but the best intentions.

This book is the mathematical equivalent of asking a meteorologist why the sky is blue. When answered comprehensibly, the answer is much more than any simple patron would necessitate. Just say "because of tiny molecules in Earth's atmosphere," or something to that effect. Anything more would make me feel like a dummy.

So in my good intentions, I, a writer and wordsmith, wanted to broaden my mind by accessing the mathematical lobe left dormant after my freshm
Tadas Talaikis
OK, I have understood I'm not interested in abstractions that give me nothing reusable in real world problems, even though I deal with some every day. Also, probably not for audioformat, I can't immediately get the English terms for math symbols, probably would have been better in text.

On the other hand, algebra is a must in the world today, and sooner children get the concepts, the better.

"I was helping two six year olds to understand symmetry." That killed me, haha, now I can understand why so
There are some big numbers out there, footballers earn a jaw dropping amount per year, for what I am not entirely sure… The global economy is around US$107.5 trillion, there are approximately seven quintillion, five hundred quadrillion grains of sand on the earth and it is thought that there are 10 times as many stars as that. All of these numbers are frankly huge, enormous, gargantuan even, but compared to ∞ they are a mere drop in the ocean. In this book, Eugenia Cheng takes us on a journey to ...more
Jeremy S
Apr 11, 2017 rated it it was amazing  ·  review of another edition
Shelves: owned, big-thinking
This book was fascinating. I truly believe if I'd had a math teacher like Cheng I would have been fully engaged.

I loved algebra growing up, and I have fond memories of a friend of my mom who used to print off algebra equations for me to do while I was waiting for my mom to get off work. I'd anxiously look forward to them.

I look back at my time in school and wonder where the shift happened? It's frustrating for me as I am now so interested in physics, biology, and math, three things I avoided lik
Alex Schroeder
Oct 24, 2017 rated it it was amazing  ·  review of another edition
In Beyond Infinity, Eugenia Cheng does a great job explaining different aspects of infinity. From the infinitely large to the infinitesimally small, Cheng helps the reader comprehend a variety of concepts that otherwise may have been challenging to understand. Cheng starts introducing infinity by defining it. She explains why it is not a number and goes through the steps that led to that conclusion. She concludes part one by showing that different infinities are larger than others and differenti ...more
Eugenia Cheng likes to play with infinity. Among her favorite mind-boggling conundrums: If she were immortal, she could procrastinate forever.

But in a way, she writes, this book is not about infinity. It’s about a journey into the abstract unknown. This book tells how abstract thinking works and what it does for us. For Cheng, the usefulness of math is about mathematical thinking and how it sheds light on the thinking process.

“We use science to study the world abstractly,” writes Cheng. We use
This review has been hidden because it contains spoilers. To view it, click here.
Tom Hill
The premise of this book sounded interesting to me. Unfortunately the journey was not nearly as good as the promise. Eugenia Cheng obviously has a passion for mathematics but her enthusiasm cannot overcome the obstacles involved in making a complicated subject easy to follow. Ms Cheng seems to jump around quite a bit in trying to explain infinity and lost me several times. Your average layman would not find this an enjoyable read.
Carina Kaltenbach
I've always liked maths, and to be honest I really miss it in my current education. This book certainly doesn't reach the level that I have been used to think about concepts, but I loved it. Especially since infinity has always been a bit of an issue for me...
I loved Cheng's explanations and metaphors and talking about cake and cookies when actually conveying complex topics (even though sometimes I just wanted to tell her: "Stop calling yourself fat, your weight doesn't measure you"). I'm certa
Bob Small
Jul 15, 2018 rated it it was amazing  ·  review of another edition
Just brilliant...
Jul 02, 2018 rated it it was amazing  ·  review of another edition
I really enjoyed this book about infinity. Occasionally I enjoy reading a book about a science related subject as my educational background is in Mathematics however I am no professional in the subject. This was a refreshing read on a topic I have taken for granted, as many due. Infinity.

Most view infinity as simply a number so large it is like an endpoint. This book talks about how it is more than that and delves in to what infinity means. It also comes with refreshing reminders of basic mathem
Jun 18, 2018 rated it really liked it  ·  review of another edition
Shelves: 2018, math, calculus
This is a gentle introduction into calculus that is easy to follow and thought provoking. Infinity wants you to think. Infinity wants to challenge what you think you know about numbers-natural, real and imaginary. Eugenia Cheng's passion for the subject makes the complex accessible. Beyond Infinity is a good read.

"In life and in mathematics there is a trade-off between beauty and practicality, along with a contrast between dreams and reality, between the explicable and the inexplicable. Infinity
Stephen Rynkiewicz
Mathematics is much more fun without the calculating. Eugenia Cheng understands this; her math class at the School of the Art Institute is titled "The Elegance of Abstraction," which itself is a nice bit of generalization for the math averse. Cheng here plays mind games with infinity, where some things are more infinite than others.

Digressions on food, music and sports help her confront her task with rigor without seeming to go on forever. She fondly recalls the two-line programming loop she wr
Alex Telfar
May 10, 2017 rated it liked it  ·  review of another edition
Shelves: at_vic_lib
I liked it, but I wanted to it to go further into topology, real analysis, higher math ... The first half was good, and just skimmed the second half. It was an easy read, which given the potentially confusing nature of the topic seems impressive.

One of the things I have a new appreciation for is number theory. It does seem rather amazing that we can generate the natural numbers (0, +1), integers (-ve), or even the reals (a/b, irrationals), with a few rules, and given only these simple rules the
Ashley Lambert-Maberly
Infinity is a confusing topic, and I think Ms. Cheng did a brilliant job of delivering it in an interesting, fun, engaging way. Yes, at times I didn't quite understand, but given the topic that's acceptable--I certainly understood more than I expected to, and that's all on her.

At the very least, I'm glad I don't have to move people from a one floor hotel with an infinite number of rooms, to a two floor hotel, each of which has an infinite number of rooms, and that's something prior to reading th
Chris Jaffe
Two stars? This is a time when the rating tells you more about the reader than the book.

I thought I'd give a math book a try. I haven't done any math since high school. Let's see what happens if I go into it out of curiosity. The title sounds interesting.

Turns out I wasn't interested. I read really closely for the first several chapters, but had trouble giving a damn about any of it. There's a lot of talk about different infinities and trying to be precise about close differences between things
Paula Yerke
I feel like I should throw a party in celebration of getting through this book!! I found this book VERY challenging. I was always good at Math but this is like entering another dimension where everyone else thinks and speaks differently. It was also weirdly philosophical. I DID learn some things about infinity, but was it worth blowing my mind?? I think I will leave Cheng's other books to math brains who clearly think on another level than I do. My stretch book for the year!
Aug 09, 2017 rated it it was ok  ·  review of another edition
It seemed to me that a lot of time was dedicated explaining very simple notions like natural numbers, but more complicated areas were rushed through.
Also, some examples seem more convoluted than they need to be, like the one demonstrating why the real numbers are more infinite than the natural numbers. The style is right for a popular science book, but I feel the examples could have been picked a little better.
David Rubin
Apr 14, 2017 rated it really liked it  ·  review of another edition
Ms. Cheng does a great job of explaining difficult math ideas to the non-mathematician, or to someone, like me, who did not take much math in high school or college. Most of the book involved the question of whether some infinities are larger than others. Quite a trick!!

She keeps the subject of infinity interesting and almost fully comprehensible -- within my limited ability to comprehend. I may even read another math book!
J Henderson
Feb 27, 2018 rated it really liked it  ·  review of another edition
Interesting exploration of infinity as a mathematical concept and how it is present in many different ways within mathematics. Eugenia Chang explores Hilbert Hotels, Cantor's Continuum hypothesis, and shows why the concept of real numbers was not complete until a more focused study of irrational numbers in the late 1800's! Eugenia explores these concept in a very approachable way allowing people to explore ideas such as some infinities being larger than others.
Rayfes Mondal
It's hard to explain certain mathematical concepts and infinity can seem graspable but yet remain confusing, particularly when you compare the sizes of different infinities. The author does a good job in making progress here but this isn't a book I recommend for someone that isn't already enthusiastic about math. The purpose of the book is different (espousing on how to teach math) but A Mathematician's Lament is incredible. Also check out Letters to a Young Mathematician.
Better than her first book. Filled with charming metaphors and analogies to help explain the math. A good introduction to infinite cardinals and ordinals. But there are so many more things, both weird and fascinating, to say about infinity that wasn't said. The book barely scratched the surface. If your background is in mathematics, you will already have heard everything said in this book. If not, you may really enjoy it.
Peter Sidell
Jun 24, 2017 rated it it was amazing  ·  review of another edition
A lucid and stimulating demonstration of ways to think about infinity. Although perhaps too many of the authors examples have to do with food. I doubt this would work well as an audio book. The discussion of multidimensionality was most meaningful for me. It left me feeling that the multidimensionality of superstrings is rational and understandable.
Mar 26, 2018 marked it as to-read  ·  review of another edition
Heard the author on Innovation Hub:

(She wasn't there to promote this book, but I liked the conversation.)

Update 5/10/18: she popped up in another podcast today! This time, actually talking about infinity:
Ton van Gessel
Jul 07, 2017 rated it really liked it  ·  review of another edition
Shelves: math
I do like this book. It is quite easy to follow . It is written in informal style and includes some personal stories. Its the kind of book you read on holiday, in the park or as I did in your lunch break. Nice, not to demanding and informative.
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