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The final prices may differ from the prices shown due to specifics of VAT rules About this book Conflicts Between Generalization, Rigor, and Intuition undertakes a historical analysis of the development of two mathematical concepts -negative numbers and infinitely small quantities, mainly in France and Germany, but also in Britain, and the different paths taken there.
This book not only discusses the history of the two concepts, but it also introduces a wealth of new knowledge and insights regarding their interrelation as necessary foundations for the emergence of the 19th century concept of analysis. The historical investigation unravels several processes underlying and motivating conceptual change: generalization in particular, algebraization as an agent for generalizing and a continued effort of intuitive accessibility which often conflicted with likewise desired rigor.
By researching the development of the concept of negative and infinitely small numbers, the book provides a productive unity to a large number of historical sources. The result is a highly readable study of conceptual history and a new model for the cultural history of mathematics.
Reviews From the reviews: "This is a very ambitious book, both in its methodology and in the amount of material it addresses. The rich and detailed account of textbooks and educational institutions, and the key passages and events Schubring highlights … add greatly to our understanding of the history of mathematics in one of its most exciting periods.
It stands out as special by treating many primary mathematical sources that are rarely subjected to historical study …. It includes a rich variety of institutional and philosophical discussions ….
He critically reviews the work of other authors who have treated the same historical periods. Barbeau, Mathematical Reviews, Issue d.
Conflicts Between Generalization, Rigor, and Intuition
This award is being granted to Gert Schubring in recognition of his outstanding contribution to research on the history of mathematics education. In his doctoral dissertation, defended in , Gert wrote on the genetic principle in approaching historical research in mathematics. Afterwards, he extended his interests, producing wide-ranging writings on the history of mathematics education within and across countries, and publishing on the history of mathematics. By inviting us to place ourselves in front of a mirror, Gert also sparked interest in the history of earliest efforts in mathematics education, including the work of Felix Klein, on which Gert has recently co-edited the important book, The Legacy of Felix Klein , Springer. His seminal works have helped to realize the importance of considering the social context in the study of the history of mathematics education.
GERT SCHUBRING PDF