Histories of algorithms: Past, present and future

International audienceThe book under review, first published some twenty years ago, is the product of a group of French historians of mathematics: Jean-Luc Chabert, Evelyn Barbin, Michel Guillemot, Anne Michel-Pajus, Jacques Borowczyk, Ahmed Djebbar et Jean-Claude Martzloff. An English translation by Chris Weeks was published by Springer in 1999 (Chabert et al., 1999) and a second French edition is now available and will be reviewed here. It was at the time of its first appearance—and is still— the sole book-length study of the history of mathematical algorithms. Therefore this second corrected and extended edition of the French original is most welcome. The original edition of Histoire d'algorithmes was published at a time of developing interest in the history of algorithms within the mathematics community and it was, in part, conceived for use in the mathematics classroom. The historical range of the book is impressive; from Ancient Mesopotamia and Egypt to modern computer developments, this volume endeavours to forge a history of mathematics through highlighting the role of algorithms. The book contains 15 chapters and closes with short biographies of the authors discussed and a general index. Each chapter opens with a general overview that introduces the reader to the chapter's topic. The topic is illustrated and developed through a series of excerpts taken (or translated into French) from the original, historical documents. The text is always followed by a rewriting in terms of elementary modern mathematics and by some analysis and posthistoire of the algorithm. While the main text of the book has been largely kept as it was in the first edition, this more recent posthistoire has been updated for this second edition. The book, one finds, falls naturally into two parts. The first (chapters 1–5), comparative in nature, focuses on the structure of an algorithm at different times in different cultures and traditions, principally, though not exclusively, pre-modern and non-Western. The second part remains largely within the realm of modern Western mathematics (17th–20th centuries) and presents a more or less linear story of how certain kinds of algorithms used in numerical analysis were developed and generalized