Korner’s The Pleasures of Counting is one of those books that reminds you why mathematics matters beyond the syllabus. It is wide-ranging, intellectually serious and written with a dry wit that makes it a genuine pleasure to read. If you are looking for a book that shows students what mathematics looks like when it is applied to real problems in the real world, this is one of the best examples I know.
The book is organised around a series of case studies drawn from history and science: how mathematics helped track down the source of a cholera epidemic, how it shaped naval strategy in the Second World War, how it underlies the physics of waves and the behaviour of populations. Korner uses these stories to introduce genuine mathematics, including calculus, probability, differential equations and scaling arguments, in a way that feels motivated rather than arbitrary.
What sets Korner apart as a writer is that he takes the reader seriously. He does not pretend the mathematics is easier than it is, but he explains it with enough care and context that a well-prepared student can follow the argument and come away with a real understanding rather than just a vague impression. That is a considerable achievement across a book of this length and scope.
The tone throughout is that of a thoughtful, slightly eccentric Cambridge mathematician who genuinely enjoys his subject and wants others to share that enjoyment. It is infectious. I have lent my copy to students more than once and found it difficult to get back.
For any student with serious mathematical ambitions, or any colleague looking for enrichment material that goes well beyond the standard curriculum, this book belongs on the shelf.