Model and Mathematics : : from the 19th to the 21st Century.

• Superior document: Trends in the History of Science Series
• Author: Friedman, Michael.
• TeilnehmendeR: Krauthausen, Karin.
• Place / Publishing House: Cham : : Springer International Publishing AG,, 2022.; ©2022.
• Year of Publication: 2022
• Edition: 1st ed.
• Language: English
• Series: Trends in the History of Science Series
• Physical Description: 1 online resource (441 pages)

Table of Contents

Intro -- Contents -- 1 How to Grasp an Abstraction: Mathematical Models and Their Vicissitudes Between 1850 and 1950. Introduction -- I. Models at the End of the Nineteenth Century: Between Maxwell's 'Fictitious Substances' and Boltzmann's 'Tangible Representation' -- II. 1850s/1870s: 'Analogy' and 'Model' in Maxwell -- III. 1880-1900: 'Anschauung' and 'Bild' (Klein and Brill) -- IV. 1900s-1930s: From Material Analogies and 'Geometric Models' to Formal Analogies and Language-Oriented Models -- (1) 1891/1899/1936: Mathematics and the New Definition of 'Model' -- (2) 1931/1925-6: The 'Pencil and Paper Models' of Biology and the Precursors of Modeling -- V. 1940s: Lévi-Strauss and Mathematical Models in Anthropology -- VI. Conclusion: The Model in the Twentieth Century: Fictitious, Fragmentary, Temporary -- Part I Historical Perspectives and Case Studies -- 2 Knowing by Drawing: Geometric Material Models in Nineteenth Century France -- Introduction -- Geometry and Model Drawing -- Drawing, Models, and Analysis -- Geometric Drawing in the Royal Engineering Schools -- The Foundation of École Polytechnique -- Mutual Instruction Versus Academic Pedantry -- Monge's "Cabinet Des Modèles" -- A Polytechnic Culture of Drawing -- The Canons of Geometric Drawing: Models and the Artillery School -- The Alliance Between Practice and Theory -- Learning by Drawing at the Conservatoire and Beyond -- Olivier's String Models -- Bardin's Plaster Models -- Model Drawing in Superior Primary Education -- The Models of Higher Geometry -- Naturalistic Mathematics -- The Darboux-Caron Wooden Models -- Models and the 1902 Educational Reform in France -- The Golden Age of Mathematical Models in View of the Decline of Model Drawing -- Open Questions: Models, Mathematical Modelization, and the Graphical Method -- Conclusions.

3 Wilhelm Fiedler and His Models-The Polytechnic Side -- Wilhelm Fiedler -- Some Remarks on Teaching and Early Models -- Models in Fiedler's Correspondence -- Models in Fiedler's Teaching and Publishing -- Conclusions -- 4 Models from the Nineteenth Century Used for Visualizing Optical Phenomena and Line Geometry -- Introduction -- Optics Stimulating Mathematics Simulating Optics -- Constructing Fresnel's Wave Surface -- Constructing Infinitely Thin Pencils of Rays -- Kummer Surfaces -- Plücker's Complex Surfaces -- On Deforming Quartics -- 5 Modeling Parallel Transport -- Introduction -- Historical Context: Localization of the Models in Space and Time -- The Notion of Parallel Transport -- The Context of the History of Mathematics -- The Levi-Civita Connection -- A Mechanical Model of Parallel Transport -- Later History -- Concluding Remarks -- 6 The Great Yogurt Project: Models and Symmetry Principles in Early Particle Physics -- Introduction: The Coral Gables Conferences on "Symmetry Principles at High Energy" and the Yogurt Project -- 'Models' and 'Theories' as Actors' Categories in Early Theoretical Particle Physics -- Mathematical Practices of Rotations and the Emergence of the Gell-Mann-Nishijima Model of Particle Classification -- The Search for a Theory of Isospin and Strangeness in the 1950s -- The Path from SU(2) to SU(3), or: Did Particle Physicist Know Group Theory? -- Beyond SU(3)-The Mathematical Marriage of Space-Time and Internal Symmetries -- The Rise and Fall of SU(6) -- Conclusion: The End of the Yogurt Project? -- 7 Interview with Myfanwy E. Evans: Entanglements On and Models of Periodic Minimal Surfaces -- 8 The Dialectics Archetypes/Types (Universal Categorical Constructions/Concrete Models) in the Work of Alexander Grothendieck -- Archetypes and Types in the Tôhoku and the Rapport.

Types and Archetypes in Pursuing Stacks and Dérivateurs -- Models in Récoltes et Semailles -- Conclusion -- Part II Epistemological and Conceptual Perspectives -- 9 'Analogies,' 'Interpretations,' 'Images,' 'Systems,' and 'Models': Some Remarks on the History of Abstract Representation in the Sciences Since the Nineteenth Century -- Dynamical Analogies, Physical/Mechanical Analogies, Mathematical Analogies -- Interpretations of Non-Euclidean Geometry -- Systems, Spielräume, Euklidische Modelle: Some Remarks by Felix Hausdorff, Ca. 1900 -- Images and Dynamical Models: Heinrich Hertz Once Again -- Epilogue: The Rise of (Modern) Mathematical Models -- 10 Mappings, Models, Abstraction, and Imaging: Mathematical Contributions to Modern Thinking Circa 1900 -- Generalities -- The Riemann Inflexion -- Reflections in Science and Mathematics … and New Flashes -- Helmholtz and Hertz -- Longue Durée -- Other Reflections -- 11 Thinking with Notations: Epistemic Actions and Epistemic Activities in Mathematical Practice -- The Applicability 'Problem' -- Philosophies of Mathematical Practice -- Notations, Formalisms, Models -- Practices, Agents, Actions -- Epistemic Actions and Their Limits -- What 'Epistemic Actions' in Mathematics Might Be -- The Use of Gestures and Symbolic Operations in Instructional Settings -- Applying Material Models to Mathematics -- Re-proving Theorems -- Notations as 'Institutionalized' (Long-Term) Epistemic Actions? -- 12 Matrices-Compensating the Loss of Anschauung -- Introduction -- Immanuel Kant's Philosophy of Applied Mathematics -- The Loss of Anschauung in the Nineteenth Century and the Declaration of Anschaulichkeit as a Model in Geometry -- Matrices as New Tools for Compensating the Loss of Anschauung in Physics -- Early Twentieth Century Debate on Anschauung and Anschaulichkeit in Physics -- Surreality of the New Physics.

Conclusion -- Part III From Production Processes to Exhibition Practices -- 13 Interview with Anja Sattelmacher: Between Viewing and Touching-Models and Their Materiality -- 14 Interview with Ulf Hashagen: Exhibitions and Mathematical Models in the Nineteenth and Twentieth Centuries -- 15 Interview with Andreas Daniel Matt: Real-Time Mathematics.