Writing the History of Mathematics: Its Historical Development

Author: Joseph W. Dauben,Christoph J. Scriba

Publisher: Springer Science & Business Media

ISBN: 9783764361679

Category: Mathematics

Page: 689

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As an historiographic monograph, this book offers a detailed survey of the professional evolution and significance of an entire discipline devoted to the history of science. It provides both an intellectual and a social history of the development of the subject from the first such effort written by the ancient Greek author Eudemus in the Fourth Century BC, to the founding of the international journal, Historia Mathematica, by Kenneth O. May in the early 1970s.

Labyrinth of Thought

A History of Set Theory and Its Role in Modern Mathematics

Author: Jose Ferreiros

Publisher: Birkhäuser

ISBN: 3034850492

Category: Mathematics

Page: 440

View: 5507

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"José Ferreirós has written a magisterial account of the history of set theory which is panoramic, balanced, and engaging. Not only does this book synthesize much previous work and provide fresh insights and points of view, but it also features a major innovation, a full-fledged treatment of the emergence of the set-theoretic approach in mathematics from the early nineteenth century. This takes up Part One of the book. Part Two analyzes the crucial developments in the last quarter of the nineteenth century, above all the work of Cantor, but also Dedekind and the interaction between the two. Lastly, Part Three details the development of set theory up to 1950, taking account of foundational questions and the emergence of the modern axiomatization." (Bulletin of Symbolic Logic)

Historiography of Mathematics in the 19th and 20th Centuries

Author: Volker R. Remmert,Martina Schneider,Henrik Kragh Sørensen

Publisher: Birkhäuser

ISBN: 3319396498

Category: Mathematics

Page: 276

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This book addresses the historiography of mathematics as it was practiced during the 19th and 20th centuries by paying special attention to the cultural contexts in which the history of mathematics was written. In the 19th century, the history of mathematics was recorded by a diverse range of people trained in various fields and driven by different motivations and aims. These backgrounds often shaped not only their writing on the history of mathematics, but, in some instances, were also influential in their subsequent reception. During the period from roughly 1880-1940, mathematics modernized in important ways, with regard to its content, its conditions for cultivation, and its identity; and the writing of the history of mathematics played into the last part in particular. Parallel to the modernization of mathematics, the history of mathematics gradually evolved into a field of research with its own journals, societies and academic positions. Reflecting both a new professional identity and changes in its primary audience, various shifts of perspective in the way the history of mathematics was and is written can still be observed to this day. Initially concentrating on major internal, universal developments in certain sub-disciplines of mathematics, the field gradually gravitated towards a focus on contexts of knowledge production involving individuals, local practices, problems, communities, and networks. The goal of this book is to link these disciplinary and methodological changes in the history of mathematics to the broader cultural contexts of its practitioners, namely the historians of mathematics during the period in question.

Mathematics across the Iron Curtain

A History of the Algebraic Theory of Semigroups

Author: Christopher Hollings

Publisher: American Mathematical Society

ISBN: 1470414937

Category: Mathematics

Page: 441

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The theory of semigroups is a relatively young branch of mathematics, with most of the major results having appeared after the Second World War. This book describes the evolution of (algebraic) semigroup theory from its earliest origins to the establishment of a full-fledged theory. Semigroup theory might be termed `Cold War mathematics' because of the time during which it developed. There were thriving schools on both sides of the Iron Curtain, although the two sides were not always able to communicate with each other, or even gain access to the other's publications. A major theme of this book is the comparison of the approaches to the subject of mathematicians in East and West, and the study of the extent to which contact between the two sides was possible.

The World as a Mathematical Game

John von Neumann and Twentieth Century Science

Author: Giorgio Israel,Ana Millán Gasca

Publisher: Springer Science & Business Media

ISBN: 3764398965

Category: Science

Page: 208

View: 3513

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Galileo and Newton’s work towards the mathematisation of the physical world; Leibniz’s universal logical calculus; the Enlightenment’s mathématique sociale. John von Neumann inherited all these aims and philosophical intuitions, together with an idea that grew up around the Vienna Circle of an ethics in the form of an exact science capable of guiding individuals to make correct decisions. With the help of his boundless mathematical capacity, von Neumann developed a conception of the world as a mathematical game, a world globally governed by a universal logic in which individual consciousness moved following different strategies: his vision guided him from set theory to quantum mechanics, to economics and to his theory of automata (anticipating artificial intelligence and cognitive science). This book provides the first comprehensive scientific and intellectual biography of John von Neumann, a man who perhaps more than any other is representative of twentieth century science.

Plato's Ghost

The Modernist Transformation of Mathematics

Author: Jeremy Gray

Publisher: Princeton University Press

ISBN: 9781400829040

Category: Mathematics

Page: 528

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Plato's Ghost is the first book to examine the development of mathematics from 1880 to 1920 as a modernist transformation similar to those in art, literature, and music. Jeremy Gray traces the growth of mathematical modernism from its roots in problem solving and theory to its interactions with physics, philosophy, theology, psychology, and ideas about real and artificial languages. He shows how mathematics was popularized, and explains how mathematical modernism not only gave expression to the work of mathematicians and the professional image they sought to create for themselves, but how modernism also introduced deeper and ultimately unanswerable questions. Plato's Ghost evokes Yeats's lament that any claim to worldly perfection inevitably is proven wrong by the philosopher's ghost; Gray demonstrates how modernist mathematicians believed they had advanced further than anyone before them, only to make more profound mistakes. He tells for the first time the story of these ambitious and brilliant mathematicians, including Richard Dedekind, Henri Lebesgue, Henri Poincaré, and many others. He describes the lively debates surrounding novel objects, definitions, and proofs in mathematics arising from the use of naïve set theory and the revived axiomatic method--debates that spilled over into contemporary arguments in philosophy and the sciences and drove an upsurge of popular writing on mathematics. And he looks at mathematics after World War I, including the foundational crisis and mathematical Platonism. Plato's Ghost is essential reading for mathematicians and historians, and will appeal to anyone interested in the development of modern mathematics.

Imagined Civilizations

China, the West, and Their First Encounter

Author: Roger Hart

Publisher: JHU Press

ISBN: 1421407124

Category: Mathematics

Page: 384

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Accounts of the seventeenth-century Jesuit Mission to China have often celebrated it as the great encounter of two civilizations. The Jesuits portrayed themselves as wise men from the West who used mathematics and science in service of their mission. Chinese literati-official Xu Guangqi (1562–1633), who collaborated with the Italian Jesuit Matteo Ricci (1552–1610) to translate Euclid’s Elements into Chinese, reportedly recognized the superiority of Western mathematics and science and converted to Christianity. Most narratives relegate Xu and the Chinese to subsidiary roles as the Jesuits' translators, followers, and converts. Imagined Civilizations tells the story from the Chinese point of view. Using Chinese primary sources, Roger Hart focuses in particular on Xu, who was in a position of considerable power over Ricci. The result is a perspective startlingly different from that found in previous studies. Hart analyzes Chinese mathematical treatises of the period, revealing that Xu and his collaborators could not have believed their declaration of the superiority of Western mathematics. Imagined Civilizations explains how Xu’s West served as a crucial resource. While the Jesuits claimed Xu as a convert, he presented the Jesuits as men from afar who had traveled from the West to China to serve the emperor.

The Architecture of Modern Mathematics:Essays in History and Philosophy

Essays in History and Philosophy

Author: J. Ferreiros,J. J. Gray

Publisher: OUP Oxford

ISBN: 0198567936

Category: Mathematics

Page: 456

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This edited volume, aimed at both students and researchers in philosophy, mathematics and history of science, highlights leading developments in the overlapping areas of philosophy and the history of modern mathematics. It is a coherent, wide ranging account of how a number of topics in the philosophy of mathematics must be reconsidered in the light of the latest historical research, and how a number of historical accounts can be deepened by embracing philosophical questions.

Modern Algebra and the Rise of Mathematical Structures

Author: Leo Corry

Publisher: Springer Science & Business Media

ISBN: 9783764370022

Category: Mathematics

Page: 451

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The notion of a mathematical structure is among the most pervasive ones in twentieth-century mathematics. Modern Algebra and the Rise of Mathematical Structures describes two stages in the historical development of this notion: first, it traces its rise in the context of algebra from the mid-nineteenth century to its consolidation by 1930, and then it considers several attempts to formulate elaborate theories after 1930 aimed at elucidating, from a purely mathematical perspective, the precise meaning of this idea. Part one dicusses the process whereby the aims and scope of the discipline of algebra were deeply transformed, turning it into that branch of mathematics dealing with a new kind of mathematical entities: the "algebraic structures". The transition from the classical, nineteenth-century, image of the discipline to the thear of ideals, from Richard Dedekind to Emmy Noether, and culminating with the publication in 1930 of Bartel L. van der Waerden's Moderne Algebra. Following its enormous success in algebra, the structural approach has been widely adopted in other mathematical domains since 1930s. But what is a mathematical structure and what is the place of this notion within the whole fabric of mathematics? Part Two describes the historical roots, the early stages and the interconnections between three attempts to address these questions from a purely formal, mathematical perspective: Oystein Ore's lattice-theoretical theory of structures, Nicolas Bourbaki's theory of structures, and the theory of categories and functors.

A Cultural History of Physics

Author: Károly Simonyi

Publisher: CRC Press

ISBN: 1439865116

Category: Mathematics

Page: 636

View: 2908

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While the physical sciences are a continuously evolving source of technology and of understanding about our world, they have become so specialized and rely on so much prerequisite knowledge that for many people today the divide between the sciences and the humanities seems even greater than it was when C. P. Snow delivered his famous 1959 lecture, "The Two Cultures." In A Cultural History of Physics, Hungarian scientist and educator Károly Simonyi succeeds in bridging this chasm by describing the experimental methods and theoretical interpretations that created scientific knowledge, from ancient times to the present day, within the cultural environment in which it was formed. Unlike any other work of its kind, Simonyi’s seminal opus explores the interplay of science and the humanities to convey the wonder and excitement of scientific development throughout the ages. These pages contain an abundance of excerpts from original resources, a wide array of clear and straightforward explanations, and an astonishing wealth of insight, revealing the historical progress of science and inviting readers into a dialogue with the great scientific minds that shaped our current understanding of physics. Beautifully illustrated, accurate in its scientific content and broad in its historical and cultural perspective, this book will be a valuable reference for scholars and an inspiration to aspiring scientists and humanists who believe that science is an integral part of our culture.

A History of Mathematics

Author: Carl B. Boyer,Uta C. Merzbach

Publisher: John Wiley & Sons

ISBN: 0470630566

Category: Mathematics

Page: 688

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The updated new edition of the classic and comprehensive guide to the history of mathematics For more than forty years, A History of Mathematics has been the reference of choice for those looking to learn about the fascinating history of humankind’s relationship with numbers, shapes, and patterns. This revised edition features up-to-date coverage of topics such as Fermat’s Last Theorem and the Poincaré Conjecture, in addition to recent advances in areas such as finite group theory and computer-aided proofs. Distills thousands of years of mathematics into a single, approachable volume Covers mathematical discoveries, concepts, and thinkers, from Ancient Egypt to the present Includes up-to-date references and an extensive chronological table of mathematical and general historical developments. Whether you're interested in the age of Plato and Aristotle or Poincaré and Hilbert, whether you want to know more about the Pythagorean theorem or the golden mean, A History of Mathematics is an essential reference that will help you explore the incredible history of mathematics and the men and women who created it.

Japanese Mathematics in the Edo Period (1600-1868)

A study of the works of Seki Takakazu (?-1708) and Takebe Katahiro (1664-1739)

Author: Annick Horiuchi

Publisher: Birkhäuser

ISBN: 9783764387440

Category: Mathematics

Page: 350

View: 4156

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The book presents the main features of the Wasan tradition, which is the indigenous mathematics that developed in Japan during the Edo period. (1600-1868). It begins with a description of the first mathematical textbooks published in the 17th century, then shifts to the work of the two leading mathematicians of this tradition, Seki Takakazu and Takebe Katahiro. The book provides substantial information on the historical and intellectual context, the role played by the Chinese mathematical treatises introduced at the late 16th century, and an analysis of Seki’s and Takebe’s contribution to the development of algebra and calculus in Japan.

A History of [pi] (pi)

Author: Petr Beckmann

Publisher: Barnes & Noble Publishing

ISBN: 9780880294188

Category: Mathematics

Page: 200

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Documents the calculation, numerical value, and use of the ratio from 2000 B.C. to the modern computer age, detailing social conditions in eras when progress was made.

International Mathematical News

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Mathematics

Page: N.A

View: 4012

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Issues for Dec. 1952- include section: Nachrichten der Österreichischen Mathematischen Gesellschaft.

The New Suburban History

Author: Thomas J. Sugrue

Publisher: University of Chicago Press

ISBN: 0226456633

Category: Architecture

Page: 289

View: 4949

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America has become a nation of suburbs. Confronting the popular image of suburbia as simply a refuge for affluent whites, The New Suburban History rejects the stereotypes of a conformist and conflict-free suburbia. The seemingly calm streets of suburbia were, in fact, battlegrounds over race, class, and politics. With this collection, Kevin Kruse and Thomas Sugrue argue that suburbia must be understood as a central factor in the modern American experience. Kruse and Sugrue here collect ten essays—augmented by their provocative introduction—that challenge our understanding of suburbia. Drawing from original research on suburbs across the country, the contributors recast important political and social issues in the context of suburbanization. Their essays reveal the role suburbs have played in the transformation of American liberalism and conservatism; the contentious politics of race, class, and ethnicity; and debates about the environment, land use, and taxation. The contributors move the history of African Americans, Latinos, Asians, and blue-collar workers from the margins to the mainstream of suburban history. From this broad perspective, these innovative historians explore the way suburbs affect—and are affected by—central cities, competing suburbs, and entire regions. The results, they show, are far-reaching: the emergence of a suburban America has reshaped national politics, fostered new social movements, and remade the American landscape. The New Suburban History offers nothing less than a new American history—one that claims the nation cannot be fully understood without a history of American suburbs at its very center.

The Structure and Dynamics of Networks

Author: Mark Newman,Albert-László Barabási,Duncan J. Watts

Publisher: Princeton University Press

ISBN: 1400841356

Category: Mathematics

Page: 592

View: 1911

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From the Internet to networks of friendship, disease transmission, and even terrorism, the concept--and the reality--of networks has come to pervade modern society. But what exactly is a network? What different types of networks are there? Why are they interesting, and what can they tell us? In recent years, scientists from a range of fields--including mathematics, physics, computer science, sociology, and biology--have been pursuing these questions and building a new "science of networks." This book brings together for the first time a set of seminal articles representing research from across these disciplines. It is an ideal sourcebook for the key research in this fast-growing field. The book is organized into four sections, each preceded by an editors' introduction summarizing its contents and general theme. The first section sets the stage by discussing some of the historical antecedents of contemporary research in the area. From there the book moves to the empirical side of the science of networks before turning to the foundational modeling ideas that have been the focus of much subsequent activity. The book closes by taking the reader to the cutting edge of network science--the relationship between network structure and system dynamics. From network robustness to the spread of disease, this section offers a potpourri of topics on this rapidly expanding frontier of the new science.