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Navigating the History of Mathematics

Routes of Learning is a collection individual articles by Ivor Grattan-Guinness dealing with various aspects of the history and philosophy of the historiography of mathematics. The articles share a unity, based upon a common general subjectmatter, but not a uniformity, as Grattan-Guinness’s ideas and knowledge have matured and expanded over time. He takes the liberty of updating some of the articles, for example by adding information which he acquired since their original publication, these are indicated for the reader by enclosure within braces; by reformulating some passages for clarity or even for the purpose of adjusting views previously expressed but no longer held; and, while retaining the style of the original articles, has imposed a new organisational scheme, by dividing the articles into numbered sections and adding brief passages to provide links between the essays. The subject with which all of Grattan-Guinness’s articles here collected deal is the historiography of mathematics. The articles, although published over time and in various venues, are well organised. The first article, ‘Searching for Reasons: My Way In and Onward’ (pp. 1 7), elaborates the questions and concerns which GrattanGuinness experienced in his study of mathematics that led him to develop his specialisation in the history of mathematics. A group of essays, collected in Part 1 under the rubric ‘Highways in the History of Mathematics’ discuss various aspects of the history and historiography of mathematics; those collected in Part 2 under the rubric ‘Pathways in Mathematics Education’ consider the historical questions and concerns that arise from the pedagogical difficulties, questions and problems which students and faculty encounter, wittingly or not, when learning or teaching mathematics, and explore the uses of historical examples in assisting in the elucidation of difficult concepts. The essays collected in Part 3 under the rubric ‘Byways in Mathematics and its Culture’ explore topics often neglected by serious historians of mathematics, for example the role of mathematics and mathematically suspect, but apparently once influential, numerical concepts in religious symbology,