Author: Julian Havil
Publisher: Princeton University Press
Price: .95/£14.99
Isbn: 9780691120560

This is a book of math­em­at­ical recreat­ions and cur­ios­it­ies inspired by the work of the late Martin Gardner. Havil, a maths teacher at Win­chester Coll­ege, claims that the sol­ut­ions to all the prob­lems and para­doxes here are sur­pris­ing, clever or both, and that under­stand­ing them requires only the math­em­at­ical abil­ity of a high-school stud­ent. While he largely succ­eeds on the first claim, to easily follow the maths you prob­ably need to be either a very recent stud­ent or have an except­ion­ally good memory.

Around half of the prob­lems them­selves are ess­ent­ially stat­ist­ical, so an int­er­est in the way that large num­bers and prob­ab­il­it­ies can trip people up is import­ant. Many of the para­doxes are cert­ainly int­er­est­ing – for example, why the odds of winn­ing a tennis tourn­a­ment pro­gress­ively and counter­intuit­ively decrease as the game plays out if you are winn­ing – but the detailed explan­at­ions can be abstruse. It’s espec­ially frust­rat­ing when the high-school math­em­at­ics is supp­le­mented by ref­er­ences to fur­ther papers and proofs which are less acc­ess­ible to the ama­teur.

Havil doesn’t help com­pre­hens­ion by his habit of ass­ign­ing non-obvi­ous and incon­sist­ent vari­ables to related prob­lems, and intro­duc­ing new vari­ables half­way through a sol­ut­ion without explan­at­ion. It is often frust­rat­ingly unclear why the author is doing things in one way rather than another (for example, in a chess board prob­lem giving all the squares poly­nom­ial rather than integer values) – poss­ibly there are tech­nical reas­ons, but they are not obvi­ous to the lay reader. The fig­ures are also badly placed within the text, adding to the gen­e­ral con­fus­ion.

On the bright side, there are some fine anec­dotes intro­duc­ing each chap­ter, such as the one about the Comte de Buffon solving a field of prob­lems by throwing bag­uettes around the room. Each chap­ter also feat­ures an intrig­uingly evolv­ing picto­gram at the start, the explan­at­ion of which is arguably the most inter­est­ing part of the book.

While the book will be of inter­est to fans of Martin Gard­ner, its style and ease of read­ing isn’t a patch on his best work. Having said that, I will be lend­ing this to my geek brother.