Selected Essays on Pre- and Early Modern Mathematical Practice

Selected Essays on Pre- and Early Modern Mathematical Practice
Author: Jens Høyrup
Publisher: Springer Nature
Total Pages: 969
Release: 2019-09-20
Genre: Mathematics
ISBN: 303019258X

Download Selected Essays on Pre- and Early Modern Mathematical Practice Book in PDF, Epub and Kindle

This book presents a broad selection of articles mainly published during the last two decades on a variety of topics within the history of mathematics, mostly focusing on particular aspects of mathematical practice. This book is of interest to, and provides methodological inspiration for, historians of science or mathematics and students of these disciplines.

Mathematical Practitioners and the Transformation of Natural Knowledge in Early Modern Europe

Mathematical Practitioners and the Transformation of Natural Knowledge in Early Modern Europe
Author: Lesley B. Cormack
Publisher: Springer
Total Pages: 205
Release: 2017-03-15
Genre: Science
ISBN: 3319494309

Download Mathematical Practitioners and the Transformation of Natural Knowledge in Early Modern Europe Book in PDF, Epub and Kindle

This book argues that we can only understand transformations of nature studies in the Scientific Revolution if we take seriously the interaction between practitioners (those who know by doing) and scholars (those who know by thinking). These are not in opposition, however. Theory and practice are end points on a continuum, with some participants interested only in the practical, others only in the theoretical, and most in the murky intellectual and material world in between. It is this borderland where influence, appropriation, and collaboration have the potential to lead to new methods, new subjects of enquiry, and new social structures of natural philosophy and science. The case for connection between theory and practice can be most persuasively drawn in the area of mathematics, which is the focus of this book. Practical mathematics was a growing field in early modern Europe and these essays are organised into three parts which contribute to the debate about the role of mathematical practice in the Scientific Revolution. First, they demonstrate the variability of the identity of practical mathematicians, and of the practices involved in their activities in early modern Europe. Second, readers are invited to consider what practical mathematics looked like and that although practical mathematical knowledge was transmitted and circulated in a wide variety of ways, participants were able to recognize them all as practical mathematics. Third, the authors show how differences and nuances in practical mathematics typically depended on the different contexts in which it was practiced: social, cultural, political, and economic particularities matter. Historians of science, especially those interested in the Scientific Revolution period and the history of mathematics will find this book and its ground-breaking approach of particular interest.

The World of the Abbaco

The World of the Abbaco
Author: Jens Høyrup
Publisher: Springer Nature
Total Pages: 506
Release: 2024
Genre: Electronic books
ISBN: 3031251644

Download The World of the Abbaco Book in PDF, Epub and Kindle

Research in History and Philosophy of Mathematics

Research in History and Philosophy of Mathematics
Author: Maria Zack
Publisher: Springer Nature
Total Pages: 190
Release: 2024-01-18
Genre: Mathematics
ISBN: 3031461932

Download Research in History and Philosophy of Mathematics Book in PDF, Epub and Kindle

This volume contains 8 papers that have been collected by the Canadian Society for History and Philosophy of Mathematics. It showcases rigorously reviewed contemporary scholarship on an interesting variety of topics in the history and philosophy of mathematics.Some of the topics explored include: A way to rethink how logic is taught to philosophy students by using a rejuvenated version of the Aristotelian idea of an argument schema A quantitative approach using data from Wikipedia to study collaboration between nineteenth-century British mathematicians The depiction and perception of Émilie Du Châtelet’s scientific contributions as viewed through the frontispieces designed for books written by or connected to her A study of the Cambridge Women’s Research Club, a place where British women were able to participate in scholarly scientific discourse in the middle of the twentieth century An examination of the research and writing process of mathematicians by looking at their drafts and other preparatory notes A global history of al-Khwārāzmī’s Kitāb al-jabr wa-l-muqābala as obtained by tracing its reception through numerous translations and commentaries Written by leading scholars in the field, these papers are accessible not only to mathematicians and students of the history and philosophy of mathematics, but also to anyone with a general interest in mathematics.

Encyclopedia of Early Modern Philosophy and the Sciences

Encyclopedia of Early Modern Philosophy and the Sciences
Author: Dana Jalobeanu
Publisher: Springer Nature
Total Pages: 2267
Release: 2022-08-27
Genre: Science
ISBN: 3319310690

Download Encyclopedia of Early Modern Philosophy and the Sciences Book in PDF, Epub and Kindle

This Encyclopedia offers a fresh, integrated and creative perspective on the formation and foundations of philosophy and science in European modernity. Combining careful contextual reconstruction with arguments from traditional philosophy, the book examines methodological dimensions, breaks down traditional oppositions such as rationalism vs. empiricism, calls attention to gender issues, to ‘insiders and outsiders’, minor figures in philosophy, and underground movements, among many other topics. In addition, and in line with important recent transformations in the fields of history of science and early modern philosophy, the volume recognizes the specificity and significance of early modern science and discusses important developments including issues of historiography (such as historical epistemology), the interplay between the material culture and modes of knowledge, expert knowledge and craft knowledge. This book stands at the crossroads of different disciplines and combines their approaches – particularly the history of science, the history of philosophy, contemporary philosophy of science, and intellectual and cultural history. It brings together over 100 philosophers, historians of science, historians of mathematics, and medicine offering a comprehensive view of early modern philosophy and the sciences. It combines and discusses recent results from two very active fields: early modern philosophy and the history of (early modern) science. Editorial Board EDITORS-IN-CHIEF Dana Jalobeanu University of Bucharest, Romania Charles T. Wolfe Ghent University, Belgium ASSOCIATE EDITORS Delphine Bellis University Nijmegen, The Netherlands Zvi Biener University of Cincinnati, OH, USA Angus Gowland University College London, UK Ruth Hagengruber University of Paderborn, Germany Hiro Hirai Radboud University Nijmegen, The Netherlands Martin Lenz University of Groningen, The Netherlands Gideon Manning CalTech, Pasadena, CA, USA Silvia Manzo University of La Plata, Argentina Enrico Pasini University of Turin, Italy Cesare Pastorino TU Berlin, Germany Lucian Petrescu Université Libre de Bruxelles, Belgium Justin E. H. Smith University de Paris Diderot, France Marius Stan Boston College, Chestnut Hill, MA, USA Koen Vermeir CNRS-SPHERE + Université de Paris, France Kirsten Walsh University of Calgary, Alberta, Canada

Mastering the History of Pure and Applied Mathematics

Mastering the History of Pure and Applied Mathematics
Author: Toke Knudsen
Publisher: Walter de Gruyter GmbH & Co KG
Total Pages: 272
Release: 2024-06-04
Genre: History
ISBN: 3110769964

Download Mastering the History of Pure and Applied Mathematics Book in PDF, Epub and Kindle

The present collection of essays are published in honor of the distinguished historian of mathematics Professor Emeritus Jesper Lützen. In a career that spans more than four decades, Professor Lützen's scholarly contributions have enhanced our understanding of the history, development, and organization of mathematics. The essays cover a broad range of areas connected to Professor Lützen's work. In addition to this noteworthy scholarship, Professor Lützen has always been an exemplary colleague, providing support to peers as well as new faculty and graduate students. We dedicate this Festschrift to Professor Lützen—as a scholarly role model, mentor, colleague, and friend.

Ethics and Mathematics Education

Ethics and Mathematics Education
Author: Paul Ernest
Publisher: Springer Nature
Total Pages: 508
Release: 2024
Genre: Electronic books
ISBN: 3031586832

Download Ethics and Mathematics Education Book in PDF, Epub and Kindle

This edited volume is an inquiry into the ethics of mathematics education, and to a lesser extent, the ethics of mathematics. The imposition of mathematics for all raises questions of ethics. What are the ethics of teaching school mathematics? What are the costs as well as the benefits? What are the ethical issues raised by the official aims of mathematics teaching, the planned curriculum, the pedagogies employed in school and college mathematics and the assessment systems? These questions are addressed in the book as well as what systems of ethics we might use. The volume ventures into a burgeoning new field. It offers a unique set of investigations, both theoretical and in terms of practices. It announces the ethics of mathematics education as a new subfield of research and includes valuable contributions from many of the best-known researchers in mathematics education; additionally, it is a valuable resource for students, teachers and researchers in the field. This is an enduring and classic source book in the field. From the wisdom of leading scholars to the little heard voices of students, this collection offers the reader many striking new insights into the ethics of mathematics and education.

Minerva Meets Vulcan: Scientific and Technological Literature – 1450–1750

Minerva Meets Vulcan: Scientific and Technological Literature – 1450–1750
Author: Wolfgang Lefèvre
Publisher: Springer Nature
Total Pages: 198
Release: 2021-06-16
Genre: Science
ISBN: 3030730859

Download Minerva Meets Vulcan: Scientific and Technological Literature – 1450–1750 Book in PDF, Epub and Kindle

This book offers a comprehensive study and account of the co-evolution of technological and scientific literature in the early modern period (1450-1750). It examines the various relationships of these literatures in six areas of knowledge – Architecture, Chemistry, Gunnery, Mechanical Engineering, Mining, and Practical Mathematics – which represent the main types of advanced technological and scientific knowledge of the era. These six fields of technologically advanced knowledge and their interrelations and interactions with learned knowledge are investigated and discussed through a specific lens: by focusing on the technological literature. Among present-day historians of science, it hardly remains controversial that contact and exchange between educated and practical knowledge played a significant role in the development of the natural sciences and technology in early modern Europe. Several paths for such exchange arose from the late Middle Ages onward due to the formation of an economy of knowledge that fostered contacts and exchange between the two worlds. How can this development be adequately described and how, on the basis of such a description, can the significance of this process for the early modern history of knowledge in the West be assessed? These are the overarching questions this book tries to answer. There exists a considerable amount of literature concerning several stations and events in the course of this long development process as well as its various aspects. As meritorious and indispensable as many of these studies are, none of them tried to portray this process as a whole with its most essential branches. What is more, many of them implicitly or explicitly took physics as a model of science, and thus highlighted mechanics and mechanical engineering as the model of all interrelations of practical and learned knowledge. By contrast, this book aims at a more complete portrait of the early modern interrelations and interactions between learned and practical knowledge. It tries to convey a new idea of the variety and disunity of these relations by discussing and comparing altogether six widely different fields of knowledge and practice. The targeted audience of this book is first of all the historians of science and technology. As one of the peer reviewers suggested – the book could very well become a textbook used for teaching the history of science and technology at universities. Furthermore, since the book addresses fundamental aspects of the significance emergence and development of modern science has for the self-image of the West, it can be expected that it will attract the attention and interest of a wider readership than professional historians.

Explorations and False Trails

Explorations and False Trails
Author: Jens Høyrup
Publisher: Springer Nature
Total Pages: 150
Release: 2024
Genre: Algebra
ISBN: 3031481585

Download Explorations and False Trails Book in PDF, Epub and Kindle

This book provides a unique perspective on the history of European algebra up to the advent of Viète and Descartes. The standard version of this history is written on the basis of a narrow and misleading source basis: the Latin translations of al-Khwārizmī, Fibonacci's Liber abbaci, Luca Pacioli's Summa, Cardano's Ars magna -- with neither Fibonacci nor Pacioli being read in detail. The existence of the Italian abacus and German cossic algebra is at most taken note of but they are not read, leading to the idea that Viète's and Descartes' use of genuine symbolism (not only abbreviations), many unknowns, and abstract coefficients seem to be miraculous leaps. This book traces the meandering development of all these techniques along with the mostly ignored but very important parenthesis function, by means of detailed readings of all pertinent sources, including the abacus and cossic algebra and French algebra from Chuquet to Gosselin. It argues for a necessary distinction between abbreviating glyphs and genuine symbols serving within a symbolic syntax, which allows it to trace the emergence of symbolic calculation. Characterization of the mathematical practice of the environment within which Viète and Descartes moved allows for an explanation of how these two figures did not even need to invent abstract coefficients but rather received them as a gift.

Beyond the Learned Academy

Beyond the Learned Academy
Author: Philip Beeley
Publisher: Oxford University Press
Total Pages: 572
Release: 2023-12-06
Genre: Mathematics
ISBN: 0192609491

Download Beyond the Learned Academy Book in PDF, Epub and Kindle

The tremendous growth of the mathematical sciences in the early modern world was reflected contemporaneously in an increasingly sophisticated level of practical mathematics in fields such as merchants' accounts, instrument making, teaching, navigation, and gauging. In many ways, mathematics shaped the knowledge culture of the age, infiltrating workshops, dockyards, and warehouses, before extending through the factories of the Industrial Revolution to the trading companies and banks of the nineteenth century. While theoretical developments in the history of mathematics have been made the topic of numerous scholarly investigations, in many cases based around the work of key figures such as Descartes, Huygens, Leibniz, or Newton, practical mathematics, especially from the seventeenth century onwards, has been largely neglected. The present volume, comprising fifteen essays by leading authorities in the history of mathematics, seeks to fill this gap by exemplifying the richness, diversity, and breadth of mathematical practice from the seventeenth century through to the middle of the nineteenth century.