- [
*Gamma: exploring Euler's constant*.] 2003 2007*Nonplussed!*.*The Irrationals*. 2012

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.

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.