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History of Mathematics

• Ying Victor J. Katz
• Published 1 June 2012
• Mathematics, History

44 Citations

Contraband mathematics: a documentary review of the resources available to george green at the nottingham subscription library 1823–1828, chapter 1 – history of measure theory, the lost calculus (1637-1670): tangency and optimization without limits, the algebra of geometric impossibility: descartes and montucla on the impossibility of the duplication of the cube and the trisection of the angle, open problems in mathematical physics, a critique of relativism in mathematics education: the need for an objectivist perspective if we are to facilitate cognitive growth, problems with fallibilism as a philosophy of mathematics education, …and so euler discovered differential equations, omar khayyam, rené descartes and solutions to algebraic equations, a formalization of properties of continuous functions on closed intervals, 36 references, mathematical cuneiform texts, history of one defeat: reform of the julian calendar as envisaged by isaac newton, never at rest. a biography of isaac newton, computer science and the mathematics genealogy project, the evolution of applied harmonic analysis: models of the real world, sir isaac newton's mathematical principles of natural philosophy and his system of the world, diagrams in the arabic euclidean tradition: a preliminary assessment, review: lengths, widths, surfaces. a portrait of old babylonian algebra and its kin, related papers.

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The Richness of the History of Mathematics

A Tribute to Jeremy Gray

• © 2023
• Karine Chemla 0 ,
• José Ferreirós 1 ,
• Lizhen Ji 2 ,
• Erhard Scholz 3 ,
• Chang Wang 4

SPHERE UMR 7219, Université Paris 7 Paris Cité, Paris cedex 13, France

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Faculty of Philosophy, Universidad de Sevilla, Sevilla, Spain

Department of mathematics, university of michigan, ann arbor, usa, school of mathematics, university of wuppertal, wuppertal, germany, institute for advanced studies in history of science, northwest university, xi’an, china.

• Unique introductions to historiographical questions concerning the history of mathematics
• Contains essays by leading scholars, aimed at guiding newcomers to the field
• Provides multiple perspectives on mathematics, role in culture, development, connections with other sciences

Part of the book series: Archimedes (ARIM, volume 66)

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About this book

This book, a tribute to historian of mathematics Jeremy Gray, offers an overview of the history of mathematics and its inseparable connection to philosophy and other disciplines. Many different approaches to the study of the history of mathematics have been developed. Understanding this diversity is central to learning about these fields, but very few books deal with their richness and concrete suggestions for the “what, why and how” of these domains of inquiry. The editors and authors approach the basic question of what the history of mathematics is by means of concrete examples. For the “how” question, basic methodological issues are addressed, from the different perspectives of mathematicians and historians. Containing essays by leading scholars, this book provides a multitude of perspectives on mathematics, its role in culture and development, and connections with other sciences, making it an important resource for students and academics in the history and philosophy of mathematics.

• History of Mathematics
• Philosophy of Mathematics
• Jeremy Gray
• Jeremy Gray philosophy
• historiography of mathematics
• historical perspectives on mathematics

Table of contents (27 chapters)

Front matter, practicing the history of mathematics, a problem-oriented multiple perspective way into history of mathematics – what, why and how illustrated by practice.

• Tinne Hoff Kjeldsen

Mathematics, History of Mathematics and Poncelet: The Context of the Ecole Polytechnique

• Bruno Belhoste, Karine Chemla

Advice to a Young Mathematician Wishing to Enter the History of Mathematics

Why historical research needs mathematicians now more than ever.

• Viktor Blåsjö

Further Thoughts on Anachronism: A Presentist Reading of Newton’s Principia

• Niccolò Guicciardini

Practices of Mathematics

On felix klein’s early geometrical works, 1869–1872.

• David E. Rowe

Poincaré and Arithmetic Revisited

• Catherine Goldstein

Simplifying a Proof of Transcendence for e : A Letter Exchange Between Adolf Hurwitz, David Hilbert and Paul Gordan

• Nicola M. R. Oswald

Current and Classical Notions of Function in Real Analysis

• Colin McLarty

“No Mother Has Ever Produced an Intuitive Mathematician”: The Question of Mathematical Heritability at the End of the Nineteenth Century

• Jemma Lorenat

Learning from the Masters (and Some of Their Pupils)

• John Stillwell

Mathematics and Natural Sciences

Mathematical practice: how an astronomical table was made in the yuanjia li (443 ad), on “space” and “geometry” in the nineteenth century.

• Jesper Lützen

Gauging Potentials: Maxwell, Lorenz, Lorentz and Others on Linking the Electric Scalar and Vector Potentials

• Jed Z. Buchwald

Ronald Ross and Hilda Hudson: A Collaboration on the Mathematical Theory of Epidemics

• June Barrow-Green

Editors and Affiliations

Karine Chemla

José Ferreirós

Erhard Scholz

About the editors

Karine Chemla is a French historian of mathematics and sinologist who works as a director of research at the Centre national de la recherche scientifique (CNRS), Research group SPHERE. She is also a senior fellow at the New York University Institute for the Study of the Ancient World. She was elected a Member of the American Philosophical Society in 2019 and received the Otto Neugebauer Prize from the European Mathematical Society in 2020.

José Ferreirós is a historian and philosopher of Mathematics, a Professor of Logic and Philosophy of Science at the University of Seville (Spain) and member of the Institute of Mathematics at Seville (IMUS). He is the author of Mathematical Knowledge and the Interplay of Practices (Princeton UP, 2016), and editor of The Architecture of Modern Mathematics (with J. Gray, Oxford UP, 2006). Ferreirós has served as president of the Association for the Philosophy of Mathematical Practice, and has also done research onthe physical sciences and the philosophy of experimental science.

Lizhen Ji is a mathematician interested in the history of mathematics. In the past few years, he has started to develop active interest in the history of mathematicshas. In mathematics, he has studied several topics in analysis, geometry, topology and group theory. In particular, he has studied symmetric spaces, locally symmetric spaces, arithmetic groups and related discrete groups from various points of view. SL(n, Z) is one of the most basic examples of arithmetic groups, and it acts on the symmetric space of positive definite matrices of determinant 1. The quotient of the symmetric space by SL(n, Z) is a locally symmetric space, which occurs naturally in many subjects from differential geometry, topology, geometry group theory to number theory. Though these spaces and groups have been studied extensively by many people over a long period of time, there are still many open problems. In the history of mathematics, he has been interested in the works of Poincaré and Galois.

Scholz studied mathematics at the University of Bonn and the University of Warwick from 1968 to 1975 with Diplom from the University of Bonn in 1975. In 1979, he completed his doctorate (Promotion) at the University of Bonn with thesis Entwicklung des Mannigfaltigkeitsbegriffs von Riemann bis Poincaré (Development of the concept of manifold from Riemann to Poincaré) under the supervision of Egbert Brieskorn and Henk J. M. Bos. In 1986, Scholtz habilitated at the University of Wuppertal. There he became in 1989 an associate professor of the history of mathematics and retired in 2012. He also works at the University of Wuppertal's Interdisziplinären Zentrum für Wissenschafts- und Technikforschung (IZWT, Interdisciplinary Center for Science and Technology Research), which he co-founded in 2004. In 1993, he was a visiting professor at the Institut für Wissenschaftsgeschichte (Institute for the History of Science) at the University of Göttingen.

Chang Wang, a professor of the history of mathematics in the Institute for Advanced Studies in History of Science, Northwest University, Xi’an, China. He has been studying the history of mathematics, especially the history of topology and Poincaré. He graduated from the Mathematical Department of Northwest University in 2012, and became a lecturer in the same year. In 2016, he became an associate professor of the history of mathematics in the Institute for Advanced Studies in History of Science, and was promoted to professorship in the year 2021. He was a council member of the Chinese Mathematical History Society. He has organized several international conferences in China. He serves as an expert reviewer for the Studies in the History of Natural Sciences and The Chinese Journal for The History of Science and Technology ..

Bibliographic Information

Book Title : The Richness of the History of Mathematics

Book Subtitle : A Tribute to Jeremy Gray

Editors : Karine Chemla, José Ferreirós, Lizhen Ji, Erhard Scholz, Chang Wang

Series Title : Archimedes

DOI : https://doi.org/10.1007/978-3-031-40855-7

Publisher : Springer Cham

eBook Packages : Mathematics and Statistics , Mathematics and Statistics (R0)

Copyright Information : The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2023

Hardcover ISBN : 978-3-031-40854-0 Published: 28 November 2023

Softcover ISBN : 978-3-031-40857-1 Due: 11 December 2024

eBook ISBN : 978-3-031-40855-7 Published: 27 November 2023

Series ISSN : 1385-0180

Series E-ISSN : 2215-0064

Edition Number : 1

Number of Pages : XX, 705

Number of Illustrations : 1 b/w illustrations

Topics : Mathematics, general , History of Mathematical Sciences , History, general , Philosophy of Science

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The Architecture of Modern Mathematics: Essays in History and Philosophy, edited by J. Ferreirós and J. J. Gray

Related Papers

Teresa Kouri Kissel

José Ferreirós

Gustavo Sámano

I am not the autor, it is a collection of essays edited by Hilary Putnam and Paul Benacerraf. The twentieth century has witnessed an unprecedented 'crisis in the foundations of mathematics', featuring a world-famous paradox (Russell's Paradox), a challenge to 'classical' mathematics from a world-famous mathematician (the 'mathematical intuitionism' of Brouwer), a new foundational school (Hilbert's Formalism), and the profound incompleteness results of Kurt Gödel. In the same period, the cross-fertilization of mathematics and philosophy resulted in a new sort of 'mathematical philosophy', associated most notably (but in different ways) with Bertrand Russell, W. V. Quine, and Gödel himself, and which remains at the focus of Anglo-Saxon philosophical discussion. The present collection brings together in a convenient form the seminal articles in the philosophy of mathematics by these and other major thinkers. It is a substantially revised version of the edition first published in 1964 and includes a revised bibliography. The volume will be welcomed as a major work of reference at this level in the field.

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• Anachronisms in the History of Mathematics

Anachronisms in the History of Mathematics

Essays on the historical interpretation of mathematical texts.

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This Book has been cited by the following publications. This list is generated based on data provided by Crossref .

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• Edited by Niccolò Guicciardini , Università degli Studi di Milano
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Book description

The controversial matters surrounding the notion of anachronism are difficult ones: they have been broached by literary and art critics, by philosophers, as well as by historians of science. This book adopts a bottom-up approach to the many problems concerning anachronism in the history of mathematics. Some of the leading scholars in the field of history of mathematics reflect on the applicability of present-day mathematical language, concepts, standards, disciplinary boundaries, indeed notions of mathematics itself, to well-chosen historical case studies belonging to the mathematics of the past, in European and non-European cultures. A detailed introduction describes the key themes and binds the various chapters together. The interdisciplinary and transcultural approach adopted allows this volume to cover topics important for history of mathematics, history of the physical sciences, history of science, philosophy of mathematics, history of philosophy, methodology of history, non-European science, and the transmission of mathematical knowledge across cultures.

‘… scholarly work … Highly recommended.’

V. V. Raman Source: Choice Magazine

‘excellent examples of the diversity of types of anachronisms that can be found in the history of mathematics … The wide variety of case studies that form the chapters is remarkable.’

Nicolas Michel Source: Revue d'Histoire des Sciences

'The main contribution of the book lies in this rich meta-historical reflection. Apart from contributing to their specific historiographies, the essays of this book provide an important contribution to the methodology of the history of mathematics. As a consequence, the book has an appeal for any historian of mathematics, regardless of their period of specialisation.'

Raffaele Danna Source: Nuncius

‘‘Anachronisms in the History of Mathematics provides a rich series of contributions which will be of interest both to the specialist and to any scholar interested in the analysis of past mathematical sources. … Apart from contributing to their specific historiographies, the essays of this book provide an important contribution to the methodology of the history of mathematics. As a consequence, the book has an appeal for any historian of mathematics, regardless of their period of specialisation.’

‘Mathematicians without historical training may find this a challenging read that is well worth the effort! Historians (and certainly historians of mathematics) will find this an interesting and thought-provoking book.’

Katelynn Kochalski Source: Notices of the American Mathematical Society

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Frontmatter pp i-iv

• Get access Check if you have access via personal or institutional login Log in Register

Contents pp v-x

Contributors pp xi-xi, figures pp xii-xvi, preface pp xvii-xxvi, 1 - introduction: the historical interpretation of mathematical texts and the problem of anachronism pp 1-41.

• By Niccolò Guicciardini

2 - From reading rules to reading algorithms: textual anachronisms in the history of mathematics and their effects on interpretation pp 42-82

• By Karine Chemla

3 - Anachronism and anachorism in the study of mathematics in India pp 83-104

• By Kim Plofker

4 - On the need to re-examine the relationship between the mathematical sciences and philosophy in Greek antiquity pp 105-130

• By Jacqueline Feke

5 - Productive anachronism: on mathematical reconstruction as a historiographical method pp 131-166

• By Martina R. Schneider

6 - Anachronism in the Renaissance historiography of mathematics pp 167-195

• By Robert Goulding

7 - Deceptive familiarity: differential equations in Leibniz and the Leibnizian school (1689–1736) pp 196-222

8 - euler and analysis: case studies and historiographical perspectives pp 223-250.

• By Craig Fraser , Andrew Schroter

9 - Measuring past geometers: a history of non-metric projective anachronism pp 251-280

• By Jemma Lorenat

10 - Anachronism: Bonola and non-Euclidean geometry pp 281-306

• By Jeremy Gray

11 - Anachronism and incommensurability:words, concepts, contexts, and intentions pp 307-357

• By Joseph W. Dauben

Index pp 358-366

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