Karen Hunger Parshall

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.

James Joseph Sylvester: Life and Work in Letters

Adrian Clifford Rice

Although today's mathematical research community takes its international character very much for granted, this ''global nature'' is relatively recent, having evolved over a period of roughly 150 years-from the beginning of the nineteenth century to the middle of the twentieth century. During this time, the practice of mathematics changed from being centered on a collection of disparate national communities to being characterized by an international group of scholars for whom thegoal of mathematical research and cooperation transcended national boundaries. Yet, the development of an international community was far from smooth and involved obstacles such as war, political upheaval, and national rivalries. Until now, this evolution has been largely overlooked by historians andmathematicians alike. This book addresses the issue by bringing together essays by twenty experts in the history of mathematics who have investigated the genesis of today's international mathematical community. This includes not only developments within component national mathematical communities, such as the growth of societies and journals, but also more wide-ranging political, philosophical, linguistic, and pedagogical issues. The resulting volume is essential reading for anyone interestedin the history of modern mathematics. It will be of interest to mathematicians, historians of mathematics, and historians of science in general.

The Evolution of an International Mathematical Research Community, 1800-1945

Mathematics Unbound

This text offers a biography of James Joseph Sylvester & his work. A Cambridge student at first denied a degree because of his faith, Sylvester came to America to teach mathematics, becoming Daniel Coit Gilman's faculty recruit at Johns Hopkins in 1876 & winning the coveted Savilian Professorship of Geometry at Oxford in 1883.

Jewish Mathematician in a Victorian World

James Joseph Sylvester

P. Theerman

This volume, honoring the renowned historian of science, Allen G Debus, explores ideas of science - `experiences of nature' - from within a 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 sixteenth-century astronomy and medicine, through nineteenth-century biology and mathematics, to the social sciences in the twentieth-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. Audience: This book will appeal especially to historians of science, of chemistry, and of medicine.

Proceedings of a Conference in Honor of Allen G. Debus

Experiencing Nature

Victor J. Katz

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.

Karen Hunger Parshall

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