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A History of Mathematical Tables

Martin Campbell-Kelly, Mary Croarken, Raymond Flood, and Eleanor Robson, editors
Oxford University Press
Publication Date: 
Number of Pages: 
[Reviewed by
Fernando Q. Gouvêa
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Tables and table-making were, until very recently, a very important part of the practice of mathematics. For mathematicians and (even more so) for users of mathematics, they were a crucial resource: logarithm tables, trigonometric tables, tables of integrals and of transcendental functions. Still in print from Dover, for example, is a Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables; Academic Press offers a huge book called Table [sic!] of Integrals, Series, and Products, and CRC Press has its Standard Mathematical Tables and Formulae.

Nowadays, of course, tables have for the most part been replaced by calculators and computers, and the modern equivalent table-making is the creation of efficient numerical algorithms. Not that tables are completely gone. On the web, one can still find highly technical tables intended as an aid to "experimental mathematics". I've made some myself.

The History of Mathematical Tables is a collection of essays, mostly by British authors. It isn't really a complete history (the story of mathematical table-making in Medieval Islam is not represented at all, a rather glaring gap given its historical importance), but rather a series of interesting snapshots. The first essay, by Eleanor Robson, is about tables in Ancient Sumer, Babylonia, and Assyria. Following that we take a flying leap into sixteenth century Europe and read about logarithm tables and their construction. There are chapters on actuarial tables, on tabulation of data, and on various attempts at mechanizing the creation of tables. (One of the chapter titles refers to the "unerring certainty of mechanical agency", a concept that may surprise readers living in the time of "computer errors.") The final chapter nominates the spreadsheet as the modern successor of the table and traces its evolution from VisiCalc through Lotus 1-2-3 and its clones to Excel (whose name seems to be on its way to replacing "spreadsheet" as Excel replaces all of its rival programs).

Many things are missing. As mentioned above, there is nothing on Medieval Islam. There is also nothing on non-Western cultures. On the contemporary end, an essay on mathematical software would have been nice. The modern role of such software is much closer to the historical role of tables than the role of spreadsheets seems to be. And it would also have been useful to have something on the role of tables in "experimental mathematics."

Those criticisms, however, amount to simply asking for more of a good thing. As it is, this book is a useful source of information on a subject often neglected by the big historical surveys. It will be of interest not just to historians of mathematics proper, but also to those who are interested in the evolution of computing and of statistics. It might be a bit too expensive for individuals, but it's definitely a must-have for libraries.

Fernando Q. Gouvêa is Professor of Mathematics at Colby College and the co-author, with Bill Berlinghoff, of Math through the Ages.

A History of Mathematical Tables, ed. by Martin Campbell-Kelly, Mary Croarken, Raymond Flood, and Eleanor Robson. Oxford University Press, 2003. Hardcover, 361 pp., $89.50. ISBN 0-19-850841-7.