Karen Hunger Parshall – författare

In the folklore of mathematics, James Joseph Sylvester (1814-1897) is the eccentric, hot-tempered, sword-cane-wielding, nineteenth-century British Jew who, together with the taciturn Arthur Cayley, developed a theory and language of invariants that then died spectacularly in the 1890s as a result of David Hilbert's groundbreaking, `modern' techniques. This, like all folklore, has some grounding in fact but owes much to fiction. The present volume brings together for the first time 140 letters from Sylvester's correspondence in an effort to establish the true picture. It reveals - through the letters as well as through the detailed mathematical and historical commentary accompanying them - Sylvester the friend, man of principle, mathematician, poet, professor, scientific activist, social observer, traveller. It also provides a detailed look at Sylvester's thoughts and thought processes as it shows him acting in both personal and professional spheres over the course of his eighty-two year life. The Sylvester who emerges from this analysis - unlike the Sylvester of the folkloric caricature - offers deep insight into the development of the technical and social structures of mathematics.

In the folklore of mathematics, James Joseph Sylvester (1814-1897) is the eccentric, hot-tempered, sword-cane-wielding, nineteenth-century British Jew who, together with the taciturn Arthur Cayley, developed a theory and language of invariants that then died spectacularly in the 1890s as a result of David Hilbert's groundbreaking, 'modern' techniques. This, like all folklore, has some grounding in fact but owes much to fiction. The present volume brings together for the first time 140 letters from Sylvester's correspondence in an effort to establish the true picture. It reveals - through the letters as well as through the detailed mathematical and historical commentary accompanying them - Sylvester the friend, man of principle, mathematician, poet, professor, scientific activist, social observer, traveller. It also provides a detailed look at Sylvester's thoughts and thought processes as it shows him acting in both personal and professional spheres over the course of his eighty-two year life. The Sylvester who emerges from this analysis - unlike the Sylvester of the folkloric caricature - offers deep insight into the development of the technical and social structures of mathematics.

What is algebra? For some, it is an abstract language of x's and y's. For mathematics majors and professional mathematicians, it is a world of axiomatically defined constructs like groups, rings, and fields. Taming the Unknown considers how these two seemingly different types of algebra evolved and how they relate. Victor Katz and Karen Parshall explore the history of algebra, from its roots in the ancient civilizations of Egypt, Mesopotamia, Greece, China, and India, through its development in the medieval Islamic world and medieval and early modern Europe, to its modern form in the early twentieth century. Defining algebra originally as a collection of techniques for determining unknowns, the authors trace the development of these techniques from geometric beginnings in ancient Egypt and Mesopotamia and classical Greece. They show how similar problems were tackled in Alexandrian Greece, in China, and in India, then look at how medieval Islamic scholars shifted to an algorithmic stage, which was further developed by medieval and early modern European mathematicians.With the introduction of a flexible and operative symbolism in the sixteenth and seventeenth centuries, algebra entered into a dynamic period characterized by the analytic geometry that could evaluate curves represented by equations in two variables, thereby solving problems in the physics of motion. This new symbolism freed mathematicians to study equations of degrees higher than two and three, ultimately leading to the present abstract era. Taming the Unknown follows algebra's remarkable growth through different epochs around the globe.

A meticulously researched history on the development of American mathematics in the three decades following World War IAs the Roaring Twenties lurched into the Great Depression, to be followed by the scourge of Nazi Germany and World War II, American mathematicians pursued their research, positioned themselves collectively within American science, and rose to global mathematical hegemony. How did they do it? The New Era in American Mathematics, 1920–1950 explores the institutional, financial, social, and political forces that shaped and supported this community in the first half of the twentieth century. In doing so, Karen Hunger Parshall debunks the widely held view that American mathematics only thrived after European émigrés fled to the shores of the United States.Drawing from extensive archival and primary-source research, Parshall uncovers the key players in American mathematics who worked together to effect change and she looks at their research output over the course of three decades. She highlights the educational, professional, philanthropic, and governmental entities that bolstered progress. And she uncovers the strategies implemented by American mathematicians in their quest for the advancement of knowledge. Throughout, she considers how geopolitical circumstances shifted the course of the discipline.Examining how the American mathematical community asserted itself on the international stage, The New Era in American Mathematics, 1920–1950 shows the way one nation became the focal point for the field.

What is algebra? For some, it is an abstract language of x's and y’s. For mathematics majors and professional mathematicians, it is a world of axiomatically defined constructs like groups, rings, and fields. Taming the Unknown considers how these two seemingly different types of algebra evolved and how they relate. Victor Katz and Karen Parshall explore the history of algebra, from its roots in the ancient civilizations of Egypt, Mesopotamia, Greece, China, and India, through its development in the medieval Islamic world and medieval and early modern Europe, to its modern form in the early twentieth century.Defining algebra originally as a collection of techniques for determining unknowns, the authors trace the development of these techniques from geometric beginnings in ancient Egypt and Mesopotamia and classical Greece. They show how similar problems were tackled in Alexandrian Greece, in China, and in India, then look at how medieval Islamic scholars shifted to an algorithmic stage, which was further developed by medieval and early modern European mathematicians. With the introduction of a flexible and operative symbolism in the sixteenth and seventeenth centuries, algebra entered into a dynamic period characterized by the analytic geometry that could evaluate curves represented by equations in two variables, thereby solving problems in the physics of motion. This new symbolism freed mathematicians to study equations of degrees higher than two and three, ultimately leading to the present abstract era.Taming the Unknown follows algebra’s remarkable growth through different epochs around the globe.

A meticulously researched history on the development of American mathematics in the three decades following World War IAs the Roaring Twenties lurched into the Great Depression, to be followed by the scourge of Nazi Germany and World War II, American mathematicians pursued their research, positioned themselves collectively within American science, and rose to global mathematical hegemony. How did they do it? The New Era in American Mathematics, 1920–1950 explores the institutional, financial, social, and political forces that shaped and supported this community in the first half of the twentieth century. In doing so, Karen Hunger Parshall debunks the widely held view that American mathematics only thrived after European émigrés fled to the shores of the United States.Drawing from extensive archival and primary-source research, Parshall uncovers the key players in American mathematics who worked together to effect change and she looks at their research output over the course of three decades. She highlights the educational, professional, philanthropic, and governmental entities that bolstered progress. And she uncovers the strategies implemented by American mathematicians in their quest for the advancement of knowledge. Throughout, she considers how geopolitical circumstances shifted the course of the discipline.Examining how the American mathematical community asserted itself on the international stage, The New Era in American Mathematics, 1920–1950 shows the way one nation became the focal point for the field.

This volume, honoring the renowned historian of science, Allen G. Debus, explores ideas of science - "experiences of nature" - from within an historiographical tradition that Debus has done much to define. As his work shows, the sciences do not develop exclusively as a result of a progressive and inexorable logic of discovery. A wide variety of extra-scientific factors, deriving from changing intellectual contexts and differing social millieus, play crucial roles in the overall development of scientific thought. These essays represent case studies in a broad range of scientific settings - from 16th-century astronomy and medicine, through 19th-century biology and mathematics, to the social sciences in the 20th-century - that show the impact of both social settings and the cross-fertilization of ideas on the formation of science. Aimed at a general audience interested in the history of science, this book closes with Debus's personal perspective on the development of the field.

Here, in this first biographical study of James Joseph Sylvester, Karen Hunger Parshall makes a signal contribution to the history of mathematics, Victorian history, and the history of science. A brilliant Cambridge student at first denied a degree because of his faith, Sylvester came twice to America to teach mathematics, ultimately becoming one of Daniel Coit Gilman's faculty recruits at Johns Hopkins in 1876 and winning the coveted Savilian Professorship of Geometry at Oxford in 1883. He held professorships of natural philosophy, worked as an actuary, was called to the bar, and taught mathematics to cadets training for engineering and artillery posts in the British Army. During his long, distinguished career he also edited England's Quarterly Journal of Pure and Applied Mathematics and established the American Journal of Mathematics, the first sustained mathematics research journal in the United States.Situating Sylvester's life within the political, religious, mathematical, and social currents of nineteenth-century England, Parshall penetrates the myth of this venerated figure, revealing how he lived, the choices he made and why, how the world in which he lived affected him-and how he affected that world. The story of Sylvester's life sheds light on the evolution of mathematical thought. It also examines the ways in which mathematics may be done and what factors may shape a mathematician's ideas. Parshall explores the development of academic professionalization, nineteenth-century mathematical culture, and the emergence of modern algebra as a mathematical discipline. She highlights the human side of what many view as that most arcane and otherworldly of intellectual endeavors, mathematics, which indeed answers to such diverse factors as religion, ego, and depression.

This volume traces the transformation of the United States from a mathematical backwater to a major presence during the quarter-century from 1876 to 1900. Presenting a detailed study of the major figures involved in this transformation, it focuses on the three most influential individuals - the British algebraist James Joseph Sylvester, the German standard-bearer Felix Klein, and the American mathematician Eliakim Hastings Moore - and on the principal institutions with which they were associated - the Johns Hopkins University, Gottingen University, and the University of Chicago. This book further analyzes the research traditions these men and their institutions represented, the impact they had on the second generation of American mathematical researchers, and the role of the American Mathematical Society in these developments.This is the first work ever written on the history of American mathematics during this period and one of the few books that examines the historical development of American mathematics from a wide perspective. By placing the development of American mathematics within the context of broader external factors affecting historical events, the authors show how the character of American research was decisively affected by the surrounding scientific, educational, and social contexts of the period. Aimed at a general mathematical audience and at historians of science, this book contains an abundance of unpublished archival material, numerous rare photographs, and an extensive bibliography.

Algebra, as a subdiscipline of mathematics, arguably has a history going back some 4000 years to ancient Mesopotamia. The history, however, of what is recognized today as high school algebra is much shorter, extending back to the sixteenth century, while the history of what practicing mathematicians call ""modern algebra"" is even shorter still. The present volume provides a glimpse into the complicated and often convoluted history of this latter conception of algebra by juxtaposing twelve episodes in the evolution of modern algebra from the early nineteenth-century work of Charles Babbage on functional equations to Alexandre Grothendieck's mid-twentieth-century metaphor of a ``rising sea'' in his categorical approach to algebraic geometry. In addition to considering the technical development of various aspects of algebraic thought, the historians of modern algebra whose work is united in this volume explore such themes as the changing aims and organization of the subject as well as the often complex lines of mathematical communication within and across national boundaries. Among the specific algebraic ideas considered are the concept of divisibility and the introduction of non-commutative algebras into the study of number theory and the emergence of algebraic geometry in the twentieth century. The resulting volume is essential reading for anyone interested in the history of modern mathematics in general and modern algebra in particular. It will be of particular interest to mathematicians and historians of mathematics.