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 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.