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.