The tone of this little gem of a book is set by the allusion in its title to the W.C. Sellar and R.J. Yeatman classic 1066 and All That and the outrageous Steve Bell cartoon on its cover. But David Acheson's Journey into Mathematics is never trite or facile.
He starts with a recollection of the magician's 1089 trick (picked up in a children's annual) that gives the book its title: take any three figure number (457, say), reverse it and subtract the smaller from the bigger (754-457=297), reverse the result again and add (297+792=1089). No matter which number the audience chooses, the magician will be able to predict the result of that little calculation. As a small boy, Acheson found this rather more exciting than the algebra taught at school - not only because his teacher did not dress up in leopard skin to make algebra more interesting, as another cartoon in the book suggests.
Acheson sets out to justify algebra by using it to explain the 1089 trick. From there he takes the reader on a scenic tour of mathematics, ending with a vista of chaos and catastrophe theory and a mathematical explanation of the Indian rope trick. This explanation is based on an original research result of the author that won him publication in Nature and had TV stations queuing up for interviews.
The book is such an easy and entertaining read (my non-mathematical family members agree) that one hardly notices how much honest maths the author manages to convey: quadratic equations, elementary topology, differential equations, conic sections and so on, each told in its historical context. And all this in spite of the fact that every other page is taken up by cartoons or illustrations of all kinds.
There are a few mathematicians who succeed in writing popular accounts of their craft without being superficial or condescending. With this little book Acheson has joined the best of them.
H. Geiges