The Richness of the History of Mathematics

This book, a tribute to historian of mathematics Jeremy Gray, offers an overview of the history of mathematics and its inseparable connection to philosophy and other disciplines. Many different approaches to the study of the history of mathematics have been developed. Understanding this diversity is central to learning about these fields, but very few books deal with their richness and concrete suggestions for the what, why and how of these domains of inquiry. The editors and authors approach the basic question of what the history of mathematics is by means of concrete examples. For the how question, basic methodological issues are addressed, from the different perspectives of mathematicians and historians. Containing essays by leading scholars, this book provides a multitude of perspectives on mathematics, its role in culture and development, and connections with other sciences, making it an important resource for students and academics in the history and philosophy of mathematics.

Unique introductions to historiographical questions concerning the history of mathematics Contains essays by leading scholars, aimed at guiding newcomers to the field Provides multiple perspectives on mathematics, role in culture, development, connections with other sciences

Auteur

Karine Chemla is a French historian of mathematics and sinologist who works as a director of research at the Centre national de la recherche scientifique (CNRS), Research group SPHERE. She is also a senior fellow at the New York University Institute for the Study of the Ancient World. She was elected a Member of the American Philosophical Society in 2019 and received the Otto Neugebauer Prize from the European Mathematical Society in 2020.

José Ferreirós is a historian and philosopher of Mathematics, a Professor of Logic and Philosophy of Science at the University of Seville (Spain) and member of the Institute of Mathematics at Seville (IMUS). He is the author of Mathematical Knowledge and the Interplay of Practices (Princeton UP, 2016), and editor of The Architecture of Modern Mathematics (with J. Gray, Oxford UP, 2006). Ferreirós has served as president of the Association for the Philosophy of Mathematical Practice, and has also done research on the physical sciences and the philosophy of experimental science.

Lizhen Ji is a mathematician interested in the history of mathematics. In the past few years, he has started to develop active interest in the history of mathematicshas. In mathematics, he has studied several topics in analysis, geometry, topology and group theory. In particular, he has studied symmetric spaces, locally symmetric spaces, arithmetic groups and related discrete groups from various points of view. SL(n, Z) is one of the most basic examples of arithmetic groups, and it acts on the symmetric space of positive definite matrices of determinant 1. The quotient of the symmetric space by SL(n, Z) is a locally symmetric space, which occurs naturally in many subjects from differential geometry, topology, geometry group theory to number theory. Though these spaces and groups have been studied extensively by many people over a long period of time, there are still many open problems. In the history of mathematics, he has been interested in the works of Poincaré and Galois.

Scholz studied mathematics at the University of Bonn and the University of Warwick from 1968 to 1975 with Diplom from the University of Bonn in 1975. In 1979, he completed his doctorate (Promotion) at the University of Bonn with thesis Entwicklung des Mannigfaltigkeitsbegriffs von Riemann bis Poincaré (Development of the concept of manifold from Riemann to Poincaré) under the supervision of Egbert Brieskorn and Henk J. M. Bos. In 1986, Scholtz habilitated at the University of Wuppertal. There he became in 1989 an associate professor of the history of mathematics and retired in 2012. He also works at the University of Wuppertal's Interdisziplinären Zentrum für Wissenschafts- und Technikforschung (IZWT, Interdisciplinary Center for Science and Technology Research), which he co-founded in 2004. In 1993, he was a visiting professor at the Institut für Wissenschaftsgeschichte (Institute for the History of Science) at the University of Göttingen.

Chang Wang, a professor of the history of mathematics in the Institute for Advanced Studies in History of Science, Northwest University, Xi an, China. He has been studying the history of mathematics, especially the history of topology and Poincaré. He graduated from the Mathematical Department of Northwest University in 2012, and became a lecturer in the same year. In 2016, he became an associate professor of the history of mathematics in the Institute for Advanced Studies in History of Science, and was promoted to professorship in the year 2021. He was a council member of the Chinese Mathematical History Society. He has organized several international conferences in China. He serves as an expert reviewer for the Studies in the History of Natural Sciences and The Chinese Journal for The History of Science and Technology..

Contenu

Part I: Practicing the History of Mathematic.- Chapter 1. A problem-oriented multiple perspective way into history of mathematics what, why and how illustrated by practice.- Chapter 2. Mathematics, history of mathematics and Poncelet: the context of the Ecole Polytechnique.- Chapter 3. Advice to a young mathematician wishing to enter the history of mathematics.- Chapter 4. Why historical research needs mathematicians now more than ever.- Chapter 5. Further thoughts on anachronism: A presentist reading of Newton's Principia.- Part II: Practices of Mathematics.- Chapter 6. On Felix Klein's Early Geometrical Works, 18691872.- Chapter 7. Poincar´e and arithmetic revisited.- Chapter 8. Simplifying a proof of transcendence for letter exchange between Adolf Hurwitz, David Hilbert and Paul Gordan.- Chapter 9. Current and classical notions of function in real analysis.- Chapter 10. 'No mother has ever produced an intuitive mathematician': the question of mathematical heritability at the end of the nineteenth century).- Chapter 11. Learning from the masters (and some of their pupils).- Part III: Mathematics and Natural Sciences.- Chapter 12. Mathematical practice in Chinese mathematical astronomy.- Chapter 13. On Spaceand Geometry in the 19th century.- Chapter 14. Gauging Potentials: Maxwell, Lorenz, Lorentz and others on linking the electric-scalar and vector potentials.- Chapter 15. Ronald Ross and Hilda Hudson: a collaboration on the mathematical theory of epidemics.- Part IV: Modernism.- Chapter 16. How Useful is the term 'modernism' for understanding the history of early twentieth-century mathematics?.- Chapter 17. What is the right way to be modern? Examples from integration theory in the 20th century.- Chapter 18. On set theories and modernism.- Chapter 19. Mathematical modernism, goal or problem? The opposing views of Felix Hausdorff and Hermann Wey.- Part V: Mathematicians and Philosophy.- Chapter 20. The direction-theory of parallels Geometry and philosophy in the age of Kant.- Chapter 21. The geometer's gaze: On H. G. Zeuthen's holistic epistemology of mathematics.- Chapter 22. Variations on Enriques' scientific philosophy.- Part VI: Philosophical Issues.- Chapter 23. Who's afraid of mathematical platonism? On the pre-history of mathematical platonism.- Chapter 24. History of mathematics illuminates philosophy of mathematics: Riemann, Weierstrass and mathematical understanding.- Chapter 25. What we talk about when we talk about mathematics.- Part VII: The Making of a Historian of Mathematics.- Chapter 26. History is a foreign country: a journey through the history of mathematics.- Chapter 27. Reflections.- Appendices.