ENCYCLOPAEDIA OF MATHEMATICS ON CD-ROM. Edited by Michael Hazelwinkel. Kluwer Academic Publishers+31 78 639 2392. Single user Pounds 144.00+VAT, network Pounds 1,095.00+VAT Multiplatform CD (Windows 3.1+, NT 3.51+, Mac OS 7+) ISBN 0-7923-4807-9 and 0-7923-4805-2
Famously, snooker languished in the clubs until the invention of colour television. Those 405-line monochrome sets did not do justice to the gaudy geometry of coloured balls on green baize. Snooker had to wait for a technological advance to transform its status, just as the toasted sesame-seed bun led an obscure existence until the invention of the minced beef patty covered in glop.
The same thing is happening to encyclopedias. Large sets of reference books have lurked unregarded on shelves since Caxton, failing to illuminate save in 1666. All this has changed. You can now read the text on screen. Very many large volumes can be neatly parked on a single CD-Rom, and the physical labour of turning giant slabs of paper has been replaced by clicking mice.
Kluwer's Encyclopaedia of Mathematics is a well known and respected ten-volume set that you can find in a university library which was (at one point) properly funded. This is not a series of books from which to learn mathematics. No one should attempt to learn any subject from reference books alone. It is an encyclopedia for people who already know rather a lot, enabling a specialist researcher in one part of mathematics to get a rapid, well-written and educated summary of the key results of another branch. The encyclopedia is laced with expert comments from many leading mathematicians. Unusually curious mathematics undergraduates and other mathematical enthusiasts may also have occasion to want to use it.
Encyclopedias and dictionaries are particularly well suited to display using hypertext. If you have used a browser to surf the Internet, you know exactly what hypertext is. Certain words, phrases or pictures are highlighted on the screen, and if you have enough interest to mouse-click on one of these items, a relevant document or display will appear. This process admits recursion. Thus you have all the pleasure of rummaging through a reference book, without the tiresome business of actually turning the pages, or worse yet, having to reach for another volume.
One particularly nice use of hypertext in this Encyclopaedia of Mathematics concerns referencing of equations. When confronted with a seductive phrase such as "by equation (12), the argument is complete", the (12) is hyperlinked. If you don't happen to remember which equation that was, you click on the link; a window opens and the equation appears. Some of the graphical displays attempt to give a three-dimensional appearance by lighting the diagram from a source to the side. This is more heroic than effective, but until holographic screens are more widely available, this will have to do.
The prices are very favourable compared with the hard copy versions of this work. The stand-alone CD-Rom might be within reach of an overpaid but devoted relative in December. Use a virulent yellow highlighter pen on the previous sentence and leave this review prominently displayed.
A final few words for the reader who plans to use this resource on a personal machine. The main program and a couple of applications need to be installed from the CD-Rom on to your machine. For an effectively instant response time, you can put the whole encyclopedia on your hard drive. However, that is over 400 megabytes of data, so you may not want to do that. You get perfectly adequate service by leaving the data on the CD-Rom, and reading it when needed. Providing your machine is driven by a fast chip and the CD-Rom drive is reasonably quick, the conseqent delays are not irritating. The installation instructions should be read, but they are well written and easy to follow, which is a mercy.
Geoff Smith (www.bath.ac.uk/masgcs/) is a lecturer in mathematics, University of Bath.