Innumeracy (1988) by John Allan Paulos is an excellent book about why understanding math matters. It’s one of the best math popularisation books. Along with the equally superb Irrationality it shows why logical, mathematical thinking is so important.
Paulos is a math Prof who specialises in logic and probability. He’s in an ideal position to describe how and why people need to understand numbers and probability.
The book first looks at examples and principles that describes why we need a feel for numbers. Then probability and coincidence are described in a chapter that looks at how without an understanding of this people will constantly err. Psuedoscience and the roll of innumeracy in it is then looked at. Finally Paulos looks at why innumeracy is so common. He suspects poor teaching and a social acceptance that being ‘bad at math’ is fine, while being ‘illiterate and inarticulate’ is viewed as less of a problem.
It’s interesting to look at how, in the 20 plus years since the book has been published that little has changed. Despite that fact that you can’t really get a good understanding of the world without numbers many, if not most, people don’t have this. It’s a great shame.
The book is particularly good on probability and statistics, which is something that hasn’t been sufficiently emphasized from a high school level. The book presents a strong case that probability should be taught shortly after calculus.
The book is very much worth reading for anyone. People who have done a bit more math will be reminded of things and those who have not done much will learn new things.