A History of Mathematics: From Mesopotamia to Modernity covers the evolution of mathematics through time and across the major Eastern and Western civilizations. It begins in Babylon, then describes the trials and tribulations of the Greek mathematicians. The important, and often neglected, influence of both Chinese and Islamic mathematics is covered in detail, placing the description of early Western mathematics in a global context. The book concludes with modern mathematics, covering recent developments such as (...) the advent of the computer, chaos theory, topology, mathematical physics, and the solution of Fermat's Last Theorem.Containing more than 100 illustrations and figures, this text, aimed at advanced undergraduates and postgraduates, addresses the methods and challenges associated with studying the history of mathematics. The reader is introduced to the leading figures in the history of mathematics and their fields. An extensive bibliography with cross-references to key texts will provide invaluable resource to students and exercises will stretch the more advanced reader. (shrink)
A History of Mathematics: From Mesopotamia to Modernity covers the evolution of mathematics through time and across the major Eastern and Western civilizations. It begins in Babylon, then describes the trials and tribulations of the Greek mathematicians. The important, and often neglected, influence of both Chinese and Islamic mathematics is covered in detail, placing the description of early Western mathematics in a global context. The book concludes with modern mathematics, covering recent developments such as (...) the advent of the computer, chaos theory, topology, mathematical physics, and the solution of Fermat's Last Theorem. Containing more than 100 illustrations and figures, this text, aimed at advanced undergraduates and postgraduates, addresses the methods and challenges associated with studying the history of mathematics. The reader is introduced to the leading figures in the history of mathematics and their fields. An extensive bibliography with cross-references to key texts will provide invaluable resource to students and exercises will stretch the more advanced reader. (shrink)
This paper surveys central justifications and approaches adopted by educators interested in incorporating history of mathematics into mathematics teaching and learning. This interest itself has historical roots and different historical manifestations; these roots are examined as well in the paper. The paper also asks what it means for history of mathematics to be treated as genuine historical knowledge rather than a tool for teaching other kinds of mathematical knowledge. If, however, history of mathematics (...) is not subordinated to the ideas and methods at the heart of the usual mathematical curriculum – algebraic equations, functions, derivatives, analytic geometry – if it becomes an essential subject for mathematics, then the attempt to find a place for history of mathematics requires refining our understanding of the nature of mathematics education itself. Thus, the paper asks not only how can history of mathematics be incorporated into mathematics education but also how the idea of mathematics education may need to be adjusted to accommodate history. (shrink)
This radical, profoundly scholarly book explores the purposes and nature of proof in a range of historical settings. It overturns the view that the first mathematical proofs were in Greek geometry and rested on the logical insights of Aristotle by showing how much of that view is an artefact of nineteenth-century historical scholarship. It documents the existence of proofs in ancient mathematical writings about numbers and shows that practitioners of mathematics in Mesopotamian, Chinese and Indian cultures knew how to (...) prove the correctness of algorithms, which are much more prominent outside the limited range of surviving classical Greek texts that historians have taken as the paradigm of ancient mathematics. It opens the way to providing the first comprehensive, textually based history of proof. (shrink)
This edited volume explores the previously underacknowledged 'pre-history' of mathematical structuralism, showing that structuralism has deep roots in the history of modern mathematics. The contributors explore this history along two distinct but interconnected dimensions. First, they reconsider the methodological contributions of major figures in the history of mathematics. Second, they re-examine a range of philosophical reflections from mathematically-inclinded philosophers like Russell, Carnap, and Quine, whose work led to profound conclusions about logical, epistemological, and metaphysic.
Gilles Deleuze’s engagements with mathematics, replete in his work, rely upon the construction of alternative lineages in the history of mathematics, which challenge some of the self imposed limits that regulate the canonical concepts of the discipline. For Deleuze, these challenges provide an opportunity to reconfigure particular philosophical problems – for example, the problem of individuation – and to develop new concepts in response to them. The highly original research presented in this book explores the mathematical construction (...) of Deleuze’s philosophy, as well as addressing the undervalued and often neglected question of the mathematical thinkers who influenced his work. -/- In the wake of Alain Badiou’s recent and seemingly devastating attack on the way the relation between mathematics and philosophy is configured in Deleuze’s work, Simon Duffy offers a robust defence of the structure of Deleuze’s philosophy and, in particular, the adequacy of the mathematical problems used in its construction. By reconciling Badiou and Deleuze’s seeming incompatible engagements with mathematics, Duffy succeeds in presenting a solid foundation for Deleuze’s philosophy, rebuffing the recent challenges against it. -/- Simon B. Duffy is a Senior Lecturer in Philosophy at Yale-NUS College, Singapore, and Honorary Research Associate in the Department of Philosophy at the University of Sydney, Australia. He is the author of The Logic of Expression: Quality, Quantity, and Intensity in Spinoza, Hegel and Deleuze (2006). (shrink)
This Element aims to present an outline of mathematics and its history, with particular emphasis on events that shook up its philosophy. It ranges from the discovery of irrational numbers in ancient Greece to the nineteenth- and twentieth-century discoveries on the nature of infinity and proof. Recurring themes are intuition and logic, meaning and existence, and the discrete and the continuous. These themes have evolved under the influence of new mathematical discoveries and the story of their evolution is, (...) to a large extent, the story of philosophy of mathematics. (shrink)