Alex’s Adventures in Numberland (2010) by Alex Bellos is a fun, well written tour mathematics. Bellos is a journalist with a maths degree, something that he describes as being fairly fare. He was the Guriands Brazil correspondent for some years.
The book initially looks at how humans read and write numbers and the words we have for them. The book refers to The Number Sense and covers the same territory.
Then Bellos looks at the use of different bases and explains why base 12 is better than base 10. Bellos then uses calculation machines that use base 10 to look at the abacus. After this ancient Greek mathematicians are covered and then Hindu mathematics. Here Bellos shows how different methods for multiplying multiple numbers which are really interesting. He then looks more at multiplication and speed calculators. From here slide rules are his next stop.
Bellos goes on to look at puzzles and mentions Martin Gardner. Bellos then looks at series and uses that to lead toward the golden ratio. Next chance and the normal curve are looked at. Finally geometry and the different types of infinity are investigated.
The book is a worthy addition to popular books about math. What Bellos does so well is to combine talking about mathematical facts with clever examples and puzzles for the reader. Bellos wants to make the reader appreciate the wonder and cleverness of maths and he succeeds. For anyone who has done maths at University level the book will remind them of these wonders and probably introduce some clever new tricks. For anyone else interested in math Bellos does as good a job as anyone in showing the power, insight and cleverness of math.