Review: 1089 and All That by David Acheson

I recently had the pleasure of reading 1089 and all that by David Acheson and I wanted to share my thoughts on it in this review.

1089 and All That by David Acheson is a wonderful little mathematics book I recently read. One thing I really enjoyed about 1089 is that it is written in such a way that it is very easy to pick up and only read a couple of pages, yet even in that short time learn some maths. This book is very accessible to anyone and you almost don’t need to know any maths before you read the book.  I feel 1089 would appeal to a wide range of people, because of this. For example, this book would be very interesting for GCSE to A level students who want to learn something beyond the syllabus without reading a textbook. I feel the real strength of this book is that it covers a wide variety of mathematics in a concise book. This does mean that the detail of each topic is not extensive. However, I felt there was sufficient detail to allow anyone to understand the problems and conjectures discussed. The other reason I like this book so much is that the problems are presented in a very  clear and lucid way so that when the mathematics appears it is very easy to understand. Acheson also uses diagrams and real world problems very cleverly to help the reader understand the wider importance of maths in the real world. It is hard to pick a favourite chapter in this book because the topics range from 3,000 year old geometry to recent areas such as chaos theory. A favourite of mine is the chapter on pi. I enjoyed this so much because Acheson discussed that pi’s importance is not only because it is equal to the area to circumference ratio of circles. Acheson elevates the importance of pi by highlighting that pi is actually important to almost all areas of pure and applied mathematics. I also enjoyed the chapter on great mistakes in mathematics. Here Acheson stresses how important it is for mathematicians to assume nothing when conducting a proof. He explores a famous case where

Mathematicians were changing the order of an infinite series when counting it’s limit. However, they assumed that the order of the sequence was unimportant as is the case for a finite series. However, mathematicians found a paradox where the limit of the infinite sum appeared to take multiple values when the order of the sequence was changed. This is impossible. The only conclusion was that the order one counts an infinite series does change the limit.