Beyond Infinity: An Expedition to the Outer Limits of Mathematics

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  The Quantum Labyrinth: How Richard Feynman and John Wheeler Revolutionized Time and Reality

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.

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.

If you have an interest in mathematics and don't mind stretching your mind in unusual ways this is a great book

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.

Dr Cheng made infinity a topic of wonder and enjoyment, providing an easy to understand tour of a subject that could have otherwise been intimidating. Her analogies will appeal to all audiences. Even among "popular math" books, this was one of the easiest reads I've ever encountered. I commend her clarity and enthusiasm.

I got about 40 pages in and found it kind of boring. I am an engineer by profession, so it wasn't a distaste for math that made me feel that way -- I just felt she was taking too long to build up to the points she was trying to make.

I bought this book for my 15 year old son who developed an interest in the concept of infinity. He enjoyed the book and said he’ll be using it as a reference in the future.

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