Beyond Infinity

By Eugenia Cheng
Review by Emilie (Mathematics)

It can be quite difficult to find a book on mathematics, which stretches you beyond your normal school curriculum, while still being entertaining to read. Despite always loving maths in school, most of the time when I would sit down to read about maths outside of classes, I would find that the books were heavy and dull, always filled with countless pages of formulae and graphs. Too many books on mathematics can make such a fascinating subject seem a little dry. Eugenia Cheng’s Beyond Infinity was not that type of book. She wrote this book with the goal of combating “Math-phobia”, producing a book that was informative, creative, entertaining and, surprisingly, an easy read.

In this book Cheng tackles the basics of infinity. Infinity is a concept most people are familiar with from a very young age, but Cheng explores how it is far from an easy concept. She talks about the paradoxes of infinity that you can observe within your everyday life. From there the book explores the mathematical paradoxes that can arise because of infinity.

To me, the most important concept that was introduced was that there essentially exist different types of infinities; some larger than others. In this section of the book, Cheng makes use of a greater amount of proofs and mathematical language, but introduces them in a way that is natural and easy for the reader to follow. The concepts of the different cardinalities of infinite sets has proven to be extremely useful and relevant even during the early stages of my degree in Mathematics. Countability of sets has already been mentioned in many of my courses, and I am sure it will continue to be important in courses to come.

Cheng concludes that there is so much more yet to be understood and discovered about infinity, which left me with the desire to study further in this field. What I most enjoyed about this book was that Cheng was able to convey all the mathematical theory with clarity, but throughout the book she incorporated anecdotes that made the book light-hearted. Beyond Infinity shows how one very well-known concept is extremely complicated and still not fully understood. All in all, Beyond Infinity fuelled my interest to study mathematics by demonstrating that this subject, which is often thought of as very unambiguous, is extremely complicated and that there is still endless amounts of knowledge to be discovered.

Beyond Infinity by Eugenia Cheng
ISBN-10: 1781252866
ISBN-13: 978-1781252864

Try checking the availability of this book at your school or local library or explore second hand bookshops and websites. You may also wish to purchase from either Amazon or Blackwell’s.

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