The Oxford Handbook of Generality in Mathematics and the Sciences

• 1: Karine Chemla, Renaud Chorlay, David Rabouin: Prologue: Generality as a Component of an Epistemological Culture


• Part I: The Meaning of Value of Generality


• 2: Karine Chemla: The Value of Generality in Michel Chasles's Historiography of Geometry


• 3: Eberhard Knobloch: Generality in Leibniz's Mathematics


• 4: David Rabouin: The Problem of a "General" Theory in Mathematics: Aristotle and Euclid


• 5: Igor Ly: Generality and Generalization in Poincaré's Philosophy


• Part II: Statements and Concepts: The Formulation of the General


• 6: Anne Robadey: Elaboration of a Statement on the Degree of Generality of a Property: Poincaré's Work on Recurrence Theorem


• 7: Frédéric Jaëck: Structures in Functional Analysis and Generality in Banach's Ph.D. Dissertation


• 8: Yves Cambefort: How General are Genera? The Genus in Systematic Zoology


• 9: Stéphane Schmitt: Homology: An Expression of Generality in the Life Sciences


• 10: Tatiana Roque: Different Notions of Genericity in the Classification Problem of Dynamical Systems


• Part III: Practices of Generality


• 11: Emily Grosholz: Leibnizian Analysis, Canonical Objects, and Generlization


• 12: Olivier Darrigol: Models, Structure and the Generality in Clerk Maxwell's Theory of Electromagnetism


• 13: Jean-Gaël Barbara: Biological Generality: General Anatomy from Xavier Bichat to Louis Ranvier


• 14: Renaud Chorlay: Questions of Generality as Probes into Nineteenth Century Analysis


• 15: Evelyne Barbin: Universality versus Generality: An Interpretation of the Dispute over Tangents between Descartes and Fermat


• 16: Frédéric Brechenmacher: Algebraic Generality versus Arithmetic Generality in the Controversy between C. Jordan and L. Kronecker (1874)


• 17: Evelyn Fox Keller: Practices of Generalization in Mathematical Physics, in Biology, and in Evolution


• 18: Jacqueline Boniface: Kummer's Generalization of Arithmetical Properties as Applied to Certain Complex Numbers

Karine Chemla is currently Senior Researcher at the French National Center for Scientific Research (CNRS), in the research group SPHERE. Her interest is in the history of mathematics in ancient China within the context of a world history. She also researches modern European mathematics. She focuses, from a historical anthropology viewpoint, on the relationship between mathematics and the various cultures in the context of which it is practiced and cultivated. Chemla published, with Guo Shuchun, Les neuf chapitres (2004). She edited The History of Mathematical Proof in Ancient Traditions (2012), and co-edited with J. Virbel Texts, Textual acts and the History of Science (2015). Since 2011, she works with Agathe Keller and Christine Proust on the ERC project "Mathematical Sciences in the Ancient World" (SAW).

Renaud Chorlay was trained in the social sciences at Sciences-Po Paris, and in mathematics and history of mathematics at Paris Diderot University. He works in the teacher-training department of Paris Sorbonne University. His main research field is the history of mathematics in the modern period, with specific interests in qualitative analysis, topology and differential geometry. He also works on the connections between history of mathematics and teaching of mathematics, either in the classroom, in teacher-training, or in theoretical didactics.

David Rabouin is a Senior Research Fellow (CR1) at the French National Center for Scientific Research (CNRS), in the research group SPHERE. His interest is in the history of philosophy and mathematics in early Modern Times, with special focus on Descartes and Leibniz. He also works in contemporary French Philosophy.

This book astonishes with its richness, its methodological relevance, and its novelty. We must recommend this book to a readership specializing in the history and philosophy of science because of the variety of approaches grouped together and because of its undeniable programmatic virtue. Christophe Eckes and translated by Rachel Keith, The Journal of the International Society for the History of Philosophy of Science