Beyond Infinity: An Expedition to the Outer Limits of Mathematics by Eugenia Cheng (PDF)

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[Cheng] does a great service by showing us non-mathematician schlubs how real mathematical creativity works. — Wall Street Journal How big is the universe? How many numbers are there? And is infinity + 1 is the same as 1 + infinity? Such questions occur to young children and our greatest minds. And they are all the same question: What is infinity? In Beyond Infinity, Eugenia Cheng takes us on a staggering journey from elemental math to its loftiest abstractions. Along the way, she considers how to use a chessboard to plan a worldwide dinner party, how to make a chicken-sandwich sandwich, and how to create infinite cookies from a finite ball of dough. Beyond Infinity shows how one little symbol holds the biggest idea of all.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐Eugenia Cheng’s book on infinity is a delightful, deceptively sophisticated introduction to math’s most mind-bending topic. It covers ground that math lovers will find familiar (e.g., Zeno’s paradoxes, Cantor’s theory of transfinite numbers, diverging and converging series, Hilbert’s Hotel, Dedekind and Cantor’s constructions of real numbers). But its artful explanations are highly original—Cheng has a rare knack for translating challenging mathematical abstractions into easily-grasped terms through the use of concrete metaphors and down-to-earth analogies. In one of my favorite examples, she deftly elucidates the strange nature of infinite ordinal numbers by describing the key ideas involved in terms of the amount of hassle involved in accommodating extra guests at an infinitely large hotel. (The Hilbert.) I was also charmed by her explanations of exponential growth in terms of puff pastry (and I learned some interesting baking lore along the way), by her referring to the iPod Shuffle to explain factorial growth, and by her explanation of how to make an infinitely long line of cookies with a (weirdly) finite amount of dough. Superb analogies like these are invaluable for helping non-experts get their minds around math concepts, and dreaming them up requires a special talent for isolating the essence of abstract ideas and figuring out how to put them in familiar terms. (Which I know from personal experience is a lot harder than it looks.) Few writers on math I’ve run across are as good at this as Cheng. I found her book almost shockingly readable, and she engagingly conveys her sense of delight about the mathematical enterprise throughout—it’s baked with joy.

⭐The topics covered are some of the most fascinating in math (infinite sets, cardinality, etc.) Decent explanations, but struggling with focus and clarity at times. Ok writing, but lacking the spark and charm of other great pop math books – for ex. Infinite Powers by Steven Strogatz (awesome intuitive intro to key concepts in calculus).That said, decent reading – I would still recommend it if you’re interested in these topics. I really hope for a crisper, tighter 2nd edition. And maybe use the word “mathematicians” just a tad less often – we get it, very special group of people, but it gets repetitive very quickly.

⭐to expand my view of the infinity

⭐This book gets pretty abstract at times, and the examples that the author provides are not very good at providing clarity. (Maybe there is no way to make this topic clear though to non-mathematics folks). Having majored in mathematics in college, the book made sense to me and I understood most if not all. The Hilbert Hotel example which I have read about before was well described. However, the chapter on dimensions in mathematics was not very useful or interesting. Einstein has pretty much proven that the fourth dimension is time with his theory of relativity and the examples in this chapter were kind of lame. I would suggest that only those folks who have studied math and are interested in math should read this book.

⭐Perfect reading material for a visit to Hilbert’s Hotel (which has unlimited rooms and hence unlimited spaces in which to read), Eugenia Cheng’s new book is an absolute delight. Cheng explores the bizarre implications of the infinite, and shows how not all infinities are the same. Her sense of humor is extraordinary and the examples highly imaginative, making the book a pleasure to read. For example, she compares the power of mathematicians to that of a spoiled child who must face the consequences of asking for (and promptly being eaten by) a pet lion; be careful what you wish for is the valuable lesson. Cheng makes mathematics seem so fun, I can imagine the book inspiring many young readers to pursue careers in the field. All in all, a book as entertaining as the works of Lewis Carroll.-Paul Halpern, author of

⭐I’m not a math person, but my granddaughter just got her first teaching job as a math teacher so I got this for her college grad gift. Of course I read it first and found it to be such fun! And understandable, too.

⭐I seem to be badly out of step with the current trend in popular science books. The chatty style in this one, including anecdotes from the author’s personal life, did not grab me at all. I had the same feeling about a book on the fine structure constant, and my review on that has been poorly received. I have the same feeling about the two books: no worries at all about the expertise of the authors or the science contained in the books. Personally, though, I’d rather put the chat to one side and concentrate on the science. The other reviews of this book (and that) suggest that they are doing a good job in communicating science to the lay reader and I thoroughly approve of such an achievement. So, well done for that, and I’ll face up to being out of step.

⭐When I read in the introduction that the author works in the area of category theory, I got all excited thinking that the tale would eventually lead there. Nope, that is the last we hear about category theory. the rest of the book does not even cover what I heard about infinity during my first year of college. A few of Cheng’s metaphors are indeed useful for illustrating some aspects of the subject, but I was hoping to find out something new about infinity, and there I was left feeling short-changed.

⭐If this book was written for a non-mathematical reader, then it has missed it’s mark. The text is tedious and repetative and never seems to reach a conclusion. The author seems to assume that the reader is familiar with advanced mathematics because she uses examples of re-arranged formulae without explanation of how they work.

⭐I with there were more books like this. Dr Cheng has mastered the trick of writing both precisely and approachably. She leads the reader from idea to idea with deftness and zero condescension. I often found myself pondering “But wouldn’t that mean…?” to find my query answered on the next page.

⭐It took me a bit to get into, but was fascinating. There are some bits I would love to query and will look at how to discuss (there is bound to be a forum somewhere).

⭐was a gift for a maths studentshe enjoyed it

⭐good in parts

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