Books : reviews

Julian Havil.
Nonplussed!: mathematical proof of implausible ideas.
Princeton University Press. 2007

rating : 3.5 : worth reading
review : 22 September 2008

Many mathematical results are very counterintuitive, so they seem paradoxical. Here, Havil presents some of the simpler ones, and goes through the maths to show that they are true. About half of them are probability or statistical paradoxes, the rest range over geometric and numerical cases.

There is some fun stuff in here I hadn't come across before, and some old chestnuts. I would have preferred, especially in the probability cases, a bit more on getting an intuitive feel for why these results are true, in addition to the mathematical demonstrations that they are true. But that aside, there is much here to amuse and inform.

Julian Havil.
The Irrationals: a story of the numbers you can't count on.
Princeton University Press. 2012

The ancient Greeks discovered them, but it wasn’t until the nineteenth century that irrational numbers were properly understood and rigorously defined, and even today not all their mysteries have been revealed. In The Irrationals, the first popular and comprehensive work on the subject, Julian Havil tells the story of irrational numbers and the mathematicians who have tackled their challenges, from antiquity to the twenty-first century. Along the way, he explains why irrational numbers are surprisingly difficult to define—and why so many questions still surround them. Fascinating and illuminating, this is a book for everyone who loves math and the history behind it.