The Richness of the History of Mathematics

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, 1869-1872.- 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 "Space"and "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

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 onthe 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