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.

This handbook explores the history of mathematics, addressing what mathematics has been and what it has meant to practise it. 36 self-contained chapters provide a fascinating overview of 5000 years of mathematics and its key cultures for academics in mathematics, historians of science, and general historians.

Emil Artin was one of the great mathematicians of the twentieth century. He had the rare distinction of having solved two of the famous problems posed by David Hilbert in 1900. He showed that every positive definite rational function of several variables was a sum of squares. He also discovered and proved the Artin reciprocity law, the culmination of over a century and a half of progress in algebraic number theory. Artin had a great influence on the development of mathematics in his time, both by means of his many contributions to research and by the high level and excellence of his teaching and expository writing. In this volume we gather together in one place a selection of his writings wherein the reader can learn some beautiful mathematics as seen through the eyes of a true master. The volume's Introduction provides a short biographical sketch of Emil Artin, followed by an introduction to the books and papers included in the volume. The reader will first find three of Artin's short books, titled The Gamma Function, Galois Theory, and Theory of Algebraic Numbers, respectively. These are followed by papers on algebra, algebraic number theory, real fields, braid groups, and complex and functional analysis. The three papers on real fields have been translated into English for the first time. The flavor of these works is best captured by the following quote of Richard Brauer. ``There are a number of books and sets of lecture notes by Emil Artin. Each of them presents a novel approach. There are always new ideas and new results. It was a compulsion for him to present each argument in its purest form, to replace computation by conceptual arguments, to strip the theory of unnecessary ballast. What was the decisive point for him was to show the beauty of the subject to the reader.'' Information for our distributors: Copublished with the London Mathematical Society beginning with Volume 4. Members of the LMS may order directly from the AMS at the AMS member price. The LMS is registered with the Charity Commissioners.

Georg Cantor, the founder of set theory, published his last paper on sets in 1897. In 1900, David Hilbert made Cantor's Continuum Problem and the challenge of well-ordering the real numbers the first problem in his famous Paris lecture. It was time for the appearance of the second generation of Cantorians. They emerged in the decade 1900-1909, and foremost among them were Ernst Zermelo and Felix Hausdorff. Zermelo isolated the Choice Principle, proved that every set could be well-ordered, and axiomatized the concept of set. He became the father of abstract set theory. Hausdorff eschewed foundations and pursued set theory as part of the mathematical arsenal. He was recognized as the era's leading Cantorian. From 1901-1909, Hausdorff published seven articles in which he created a representation theory for ordered sets and investigated sets of real sequences partially ordered by eventual dominance, together with their maximally ordered subsets. These papers are translated and appear in this volume. Each is accompanied by an introductory essay. These highly accessible works are of historical significance, not only for set theory, but also for model theory, analysis and algebra.

This is an open access title available under the terms of a CC BY-NC-ND 4.0 International License. It is free to read at Oxford Scholarship Online and offered as a free PDF download from OUP and selected open access locations. History of Universities XXXIV/1 contains the customary mix of learned articles which makes this publication an indispensable tool for the historian of higher education. This volume offers a global history of research education in the ninteenth and twentieth centuries. This volume compares the training of scholars in different disciplines and countries across the globe in a century that laid the foundation for modern academia. The articles in this volume examine the different training "instruments" and methods for text-based disciplines (history and philology), laboratory sciences (such as chemistry), theoretical sciences (mathematics, for instance), fieldwork disciplines (linguistics and paleontology), and clinical science (medicine). They consider countries or societies in Europe, North America, South and East Asia, and Latin America, and analyze the roles of the state, nationalism and internationalism that shaped the institutions and policies for research education. Some of these articles are comparative, while the others are in-depth case studies of individual disciplines in specific countries at different stages of scientific developments. The introduction and conclusion of this volume bring together the important themes that run across the article and make necessary supplements to present a synthetic picture of the global history of research education.

History of Universities XXXIV/1 contains the customary mix of learned articles which makes this publication an indispensable tool for the historian of higher education. This volume offers a global history of research education in the ninteenth and twentieth centuries.

This is the first truly comprehensive and thorough history of the development of a mathematical community in the United States and Canada. This second volume starts at the turn of the twentieth century with a mathematical community that is firmly established and traces its growth over the next forty years, at the end of which the American mathematical community is pre-eminent in the world. In the preface to the first volume of this work Zitarelli reveals his animating philosophy, “I find that the human factor lends life and vitality to any subject.” History of mathematics, in the Zitarelli conception, is not just a collection of abstract ideas and their development. It is a community of people and practices joining together to understand, perpetuate, and advance those ideas and each other. Telling the story of mathematics means telling the stories of these people: their accomplishments and triumphs; the institutions and structures they built; their interpersonal and scientific interactions; and their failures and shortcomings. One of the most hopeful developments of the period 1900–1941 in American mathematics was the opening of the community to previously excluded populations. Increasing numbers of women were welcomed into mathematics, many of whom—including Anna Pell Wheeler, Olive Hazlett, and Mayme Logsdon—are profiled in these pages. Black mathematicians were often systemically excluded during this period, but, in spite of the obstacles, Elbert Frank Cox, Dudley Woodard, David Blackwell, and others built careers of significant accomplishment that are described here. The effect on the substantial community of European immigrants is detailed through the stories of dozens of individuals. In clear and compelling prose Zitarelli, Dumbaugh, and Kennedy spin a tale accessible to experts, general readers, and anyone interested in the history of science in North America.