Ivor Grattan-Guinness: Routes of Learning: Highways, Pathways, and Byways in the History of Mathematics

Abstract

Professor Ivor Grattan-Guinness, an Emeritus Professor of the History of Mathematics and Logic at Middlesex University in England, is one of the leading scholars among historians of mathematics. His prominent role can be attested by the Festschrift in his honor which was published as two issues of History and Philosophy of Logic (vol. 24, no. 4, 2003 and vol. 25, no. 1, 2004). His vast scientific production encompasses a variety of subjects and he has published several important books, some of them written individually, others with co-authors. He also wrote a considerable amount of articles, encyclopedia entries, bibliographical publications and conference reports, besides editing scientific journals and participating in a myriad of professional organizations and societies. In the Preface of his new book, Grattan-Guinness summarizes his broad range of historical interests as: ‘‘the development of the calculus and mathematical analysis from around 1730 to 1930, symbolic logics and set theory from 1820 to 1940, and mechanics and mathematical physics from 1750 to 1850’’. Treating the history of mathematics in great generality, he takes into account historiographic issues and philosophical concerns; he examines the history of mathematics education and the utility of this knowledge for current mathematics education, and wanders into little studied topics like numerology in the music of Mozart and Beethoven. The book reviewed here is a compilation of reprints of some of the resulting articles on these lines in the period from 1974 to 2005. The author states that he has maintained the individual character of each article but that he has taken the liberty to modify a few views when he now objects to the initial formulation. Given the large number of lines of thought and ideas handled in this book and considering the main interest of readers of this mathematics education journal, we will give more attention to matters on mathematics education. Chapter 1, ‘‘Searching for reasons’’, gives a short account of the author’s entry into the ‘‘unusual’’ field of research on the history of mathematics, in his own words. This resolution was motivated by his dislike of the way he was taught as an undergraduate at Oxford. At the time, he came to appreciate the existence of remarkable bodies of knowledge whose ‘‘perfect delivery’’ did not contemplate neither heuristic nor historical issues. Later, as a graduate student, ‘‘mathematics turned out to be a human endeavor, with people working on interesting problems and connections and even making mistakes sometimes’’ (p. 3). The text continues by describing his first research interests and the construction of a scientific net of international mentors and friends; Karl Popper’s philosophy is mentioned as a central guide. In Chapter 2, ‘‘The Mathematics of the Past’’, the author discusses and exemplifies the differences between history and heritage. In broad strokes, history asks ‘‘what happened (or did not) in the past? Why not?’’ Heritage addresses the question ‘‘how did we get here?’’ and often the answer reads like ‘‘the royal road to me’’. The author emphasizes that both points of view are legitimate and important but that ‘‘the confusion of the two kinds of activity is not legitimate’’ (p. 13). The meta-theoretical notion of historysatire is introduced in the short section 3.I3, ‘‘On some consequences for Mathematics Education’’, and is readdressed in subsequent chapters. The author asserts that mathematical education fits well between history and G. de La Rocque Palis (&) Departamento de Matematica e Pos Graduacao do Departamento de Educacao, Pontificia Universidade Catolica do Rio de Janeiro, Rio de Janeiro, RJ 22451-900, Brazil e-mail: gildalarocque@gmail.com