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Model and Mathematics: From the 19th to the 21st Century

Part of the Trends in the History of Science Book Series

Editors: Friedman, Michael; Krauthausen, Karin

DOI: 10.1007/978-3-030-97833-4

ISBN: 978-3-030-97832-7

Publisher: Springer International Publishing - Springer Journals

Aug 9, 2022

1 - 10 of 15 Chapters

LitStream

Chapter 1How to Grasp an Abstraction: Mathematical Models and Their Vicissitudes Between 1850 and 1950. Introduction

Friedman, Michael; Krauthausen, Karin

Pages: 1 –49

[What is a model? Today, this question can only be answered either with a high degree of abstraction or generality, or with the most specific and precise contextualization, since the concept of the model and the practice of modeling are ubiquitous—in all the sciences and arts, in engineering and...
LitStream

Knowing by Drawing: Geometric Material Models in Nineteenth Century France

Brechenmacher, Frédéric

Pages: 53 –143

[The university collections of mathematical models have aroused a growing interest since the turn of the 21th century.]
LitStream

Wilhelm Fiedler and His Models—The Polytechnic Side

Volkert, Klaus

Pages: 145 –175

[In this article I will present some information on the history of mathematical models.]
LitStream

Models from the Nineteenth Century Used for Visualizing Optical Phenomena and Line Geometry

Rowe, David E.

Pages: 177 –202
LitStream

Modeling Parallel Transport

Sauer, Tilman

Pages: 203 –220

[In 1918, the Dutch geometer Jan Arnoldus Schouten used plaster models of standard curved surfaces to illustrate a novel geometric concept of the geodesic transport of reference frames in curved spaces. This paper discusses Schouten’s use of material modeling in the context of an emerging...
LitStream

The Great Yogurt Project: Models and Symmetry Principles in Early Particle Physics

Borrelli, Arianna

Pages: 221 –254

[According to the received view of the development of particle physics, mathematics, and more specifically group theory, provided the key which, between the late 1950s and the early 1960s, allowed scientists to achieve both a deeper physical understanding and an empirically successful modeling of...
LitStream

Interview with Myfanwy E. Evans: Entanglements On and Models of Periodic Minimal Surfaces

Evans, Myfanwy E.; Friedman, Michael; Krauthausen, Karin

Pages: 255 –266

[KK: Maybe we can start with a question concerning your training and profession.]
LitStream

The Dialectics Archetypes/Types (Universal Categorical Constructions/Concrete Models) in the Work of Alexander Grothendieck

Zalamea, Fernando

Pages: 267 –275

[We present two basic directions that Grothendieck explores in the transit between archetypes (universal categorical constructions) and types (concrete models): (1) projecting archetypes to types in the 1950s (around the Tôhoku and Riemann-Roch), (2) embedding types into archetypes in the 1980s...
LitStream

‘Analogies,’ ‘Interpretations,’ ‘Images,’ ‘Systems,’ and ‘Models’: Some Remarks on the History of Abstract Representation in the Sciences Since the Nineteenth Century

Epple, Moritz

Pages: 279 –307

[Despite the rapidly growing interest in the history of ‘thinking in models’, a detailed historical understanding of the different modes and forms of such thought-forms is still some way off.]
LitStream

Mappings, Models, Abstraction, and Imaging: Mathematical Contributions to Modern Thinking Circa 1900

Ferreirós, José

Pages: 309 –331

[1921, Vienna and Leipzig: the journal Annalen der Naturphilosophie, edited by chemist Wilhelm Ostwald, publishes a hard-to-classify paper, an essay written in aphorisms about knowledge and its limits, about the world and “what cannot be spoken of,” polished during the Great War by Ludwig...

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