Anachronisms in the History of Mathematics
Essays on the Historical Interpretation of Mathematical Texts

The controversial matters surrounding the notion of anachronism are difficult ones: they have been broached by literary and art critics, by philosophers, as well as by historians of science. This book adopts a bottom-up approach to the many problems concerning anachronism in the history of mathematics. Some of the leading scholars in the field of history of mathematics reflect on the applicability of present-day mathematical language, concepts, standards, disciplinary boundaries, indeed notions of mathematics itself, to well-chosen historical case studies belonging to the mathematics of the past, in European and non-European cultures. A detailed introduction describes the key themes and binds the various chapters together. The interdisciplinary and transcultural approach adopted allows this volume to cover topics important for history of mathematics, history of the physical sciences, history of science, philosophy of mathematics, history of philosophy, methodology of history, non-European science, and the transmission of mathematical knowledge across cultures.

1. Introduction: The Historical Interpretation of Mathematical Texts and the Problem of Anachronism Niccolò Guicciardini; 2. From Reading Rules to Reading Algorithms: Textual Anachronisms in the History of Mathematics and their Effects on Interpretation Karine Chemla; 3. Anachronism and Anachorism in the Study of Mathematics in India Kim Plofker; 4. On the Need to Re-examine the Relationship between the Mathematical Sciences and Philosophy in Greek Antiquity Jacqueline Feke; 5. Productive Anachronism: On Mathematical Reconstruction as a Historiographical Method Martina R. Schneider; 6. Anachronism in the Renaissance Historiography of Mathematics Robert Goulding; 7. Deceptive Familiarity: Differential Equations in Leibniz and the Leibnizian School (1689–1736) Niccolò Guicciardini; 8. Euler and Analysis: Case Studies and Historiographical Perspectives Craig Fraser and Andrew Schroter; 9. Measuring Past Geometers: A History of Non-Metric Projective Anachronism Jemma Lorenat; 10. Anachronism: Bonola and Non-Euclidean Geometry Jeremy Gray; 11. Anachronism and Incommensurability: Words, Concepts, Contexts, and Intentions Joseph W. Dauben; Index.

Niccolò Guicciardini is Professor in History of Science at the State University of Milan. He holds degrees in physics and philosophy. He has been awarded the Gil Prize (Gulbenkian Foundation), the Bacon Prize (Caltech and the Francis Bacon Foundation), and the Sarton Medal (Ghent University). He is the author of two monographs on Newton's mathematics published by Cambridge University Press.