This book consists mainly of papers presented at the first annual "Gathering for Gardner" in 1993, an event held in tribute to Martin Gardner that brought together people from the many fields in which he was interested, particularly magic, puzzles and mathematical games. I use the word "papers" loosely - many of the articles here are exactly that, presented as academic papers with theorems and proofs and replete with scholarly references. Others are more personal articles, or don't fit any easy categorisation.

But one thing is very clear from this book, and that is Gardner's great skill as a writer in all the fields he worked in. Very few of the articles here are anything like as engaging or well-written as his and a small number come across as the work of real obsessives. Some are only accessible to those with an advanced knowledge of mathematics. There are some gems, though. I'll mention a few.

The opening piece is an interesting attempt to remedy the woeful lack of a biography of Gardner. It's made up entirely of quotes from interviews with him or extracts from articles about him (all of which are sourced) which range over nearly 70 years. It's a very effective way of sketching a portrait of the man and I learnt a good deal from it.

The tale of the floating hourglass puzzle has all the lure of a detective story as two great minds - Martin Gardner and Piet Hein - exchange (incorrect) theories on how a curio reported to have been seen on sale in a shop in Paris might work. Eventually they get their hands on one and manage to prove one of the theories right, as well as managing to construct a model which demonstrates it. The article is fascinating, as the author says in the final paragraphs, because the correspondence demonstrates so much about how each man thinks.

Solomon W. Golomb's remarkable attempt to extend the methods of Lewis Carrol in proving that "No Scotsmen are dragons" raises a smile. An example gives the flavour:

Theorem: Apathetic people are not human beings.
Proof: All human beings are different. All apathetic people are indifferent. Therefore, no apathetic people are human beings.

Less accessible to some, but worthy of mention because of its curiosity, is Ken Knowlton's essay on "Misfiring Tasks", his name for mathematical statements which are true for some integers less than some value N, not true for N but true for all integers greater than N. His aim is to find one such statement for all N. An example is to divide a square into a number of non-overlapping squares. This can be done for 4 squares, and for every number greater than 5, but not for 5. So far he has found very few, and he speculates on why this is so.

Overall, then, a book mainly for completists or enthusiasts for some of the subjects covered. ( )