The Legacy of Tatjana Afanassjewa: Philosophical Insights from the Work of an Original Physicist and Mathematician

Series Foreword
Preface
Introduction
	Part I: Tatiana Afanassjewa’s Life and Forgotten Legacy
	Part II: The Ehrenfests’ Work on the Foundations of Statistical Mechanics
	Part III: Translations from German and Dutch
Contents
Part ITatiana Afanassjewa’s Life and Forgotten Legacy
1 Tatiana Ehrenfest-Afanassjewa: No Talent for Subservience
	1.1 The Alarming Rectilinearity of Her World line
	1.2 Higher Women Courses for the Weaker Sex
	1.3 Afanassjewa’s Analytical Mind and Ehrenfest’s Physics Intuition
	1.4 Undervalued: Kruzhoks and Odd Jobs
	1.5 A Vibrant Household in Traditional Leiden
	1.6 The First Cracks in the Relationship
	1.7 Novel Ideas, not Always Appreciated
	1.8 Drifting Apart, the Downhill Slope
	1.9 Hardship with Integrity
	1.10 Final Years in Her Own Sphere
	References
2 Intuition, Understanding, and Proof: Tatiana Afanassjewa on Teaching and Learning Geometry
	2.1 Introduction
	2.2 Göttingen
	2.3 The Value of Geometry Education
	2.4 Intuition, Understanding, and Logical Thinking
		2.4.1 The Role of Intuition
		2.4.2 Understanding and Logical Thinking
	2.5 The Study of Space and the Axiomatics of Geometry
		2.5.1 The Systematic Approach
		2.5.2 The Experimental Approach
		2.5.3 The Propaedeutic Course and the Systematic Courses
	2.6 The Reception of Afanassjewa's Approach to Teaching Geometry
	References
3 Afanassjewa and the Foundations  of Thermodynamics
	3.1 Introduction
	3.2 The Axiomatic Approach to Thermodynamics: From Carathéodory to Afanassjewa
	3.3 Reversible Processes Versus Quasi-Processes
	3.4 The Distinction Between Heat and Work
	3.5 Afanassjewa on Negative Absolute Temperatures
	3.6 Conclusion
	References
Part IIThe Ehrenfests’ Work on the Foundations of Statistical Mechanics
4 Ehrenfest and Ehrenfest-Afanassjewa on Why Boltzmannian and Gibbsian Calculations Agree
	4.1 Introduction
	4.2 Boltzmannian and Gibbsian Statistical Mechanics
	4.3 Ehrenfest and Ehrenfest-Afanassjewa on Gibbs Versus Boltzmann
	4.4 Assessment of Ehrenfest and Ehrenfest-Afanassjewa's Argument
	4.5 Beyond Dilute Gases
	4.6 An Example Where Boltzmannian Equilibrium Values and Gibbsian Phase Averages Differ
	4.7 When Boltzmann and Gibbs Agree
	4.8 Conclusion
	References
5 Ehrenfest and Ehrenfest-Afanassjewa on the Ergodic Hypothesis
	5.1 Introduction
	5.2 The Origin of the Ergodic Hypothesis
	5.3 Ehrenfest and Ehrenfest-Afanassjewa's Critique of the Ergodic Hypothesis
	5.4 Proof of the Impossibility of Ergodic Systems
	5.5 The Ergodic Theorems and the Notion of Metric Transitivity
	5.6 The Problem of Metric Transitivity
	5.7 Conclusion
	References
6 The Ehrenfests' Use of Toy Models to Explore Irreversibility in Statistical Mechanics
	6.1 Introduction
	6.2 Toy Models and Their Functions
	6.3 The Ehrenfests' Toy-Models
		6.3.1 The Urn Model
		6.3.2 The P–Q model
	6.4 Why These Toy Models Work
	6.5 Complementary Use of Toy Models
	6.6 Conclusion
	References
Part IIITranslations From German and Dutch
7 Translation from German: Foundations of Thermodynamics 1925 and 1956
8 Translation from Dutch: Papers on the Pedagogy of Mathematics
	8.1 Which Use Can Geometry Education Have for Students that Do not Continue with Mathematics?
	8.2 What Is Being Logical?
	8.3 Can Geometry Education Promote the Development of Logic?
	8.4 The Introductory Geometry Course
	8.5 Some Examples of Questions that Would Be Suitable for an Introductory Course