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

View: 1023

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: 7762

"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)

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: 3022

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.

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

View: 7190

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

View: 950

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.

Plato's Ghost

The Modernist Transformation of Mathematics

Author: Jeremy Gray

Publisher: Princeton University Press

ISBN: 9781400829040

Category: Mathematics

Page: 528

View: 5985

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.

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

View: 9854

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.

Imagined Civilizations

China, the West, and Their First Encounter

Author: Roger Hart

Publisher: JHU Press

ISBN: 1421407124

Category: Mathematics

Page: 384

View: 4816

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.

Modern Algebra and the Rise of Mathematical Structures

Author: Leo Corry

Publisher: Springer Science & Business Media

ISBN: 9783764370022

Category: Mathematics

Page: 451

View: 7472

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: 6384

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.

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: 9614

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.

Instruments of Science

An Historical Encyclopedia

Author: Robert Bud,Deborah Jean Warner

Publisher: Taylor & Francis

ISBN: 9780815315612

Category: Science

Page: 709

View: 9496

This authoritative reference covers 325 scientific instruments ranging from antiquity to the present, and from the mundane to the highly sophisticated. Entries explain how they work and trace their invention, development, distribution and use. Fully illustrated and complete with bibliographies, it will be particularly useful to students and scholars of modern science and technology. Reflecting contemporary practice, it examines instruments used for testing and monitoring, as well as those used for research, and even considers a number of widely used laboratory organisms (such as drosophila and e.coli) as instruments.

The New Suburban History

Author: Thomas J. Sugrue

Publisher: University of Chicago Press

ISBN: 0226456633

Category: Architecture

Page: 289

View: 4770

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.

A History of [pi] (pi)

Author: Petr Beckmann

Publisher: Barnes & Noble Publishing

ISBN: 9780880294188

Category: Mathematics

Page: 200

View: 5004

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.


A Global History of Divided Cities

Author: Carl H. Nightingale

Publisher: University of Chicago Press

ISBN: 0226580776

Category: History

Page: 536

View: 8208

When we think of segregation, what often comes to mind is apartheid South Africa, or the American South in the age of Jim Crow—two societies fundamentally premised on the concept of the separation of the races. But as Carl H. Nightingale shows us in this magisterial history, segregation is everywhere, deforming cities and societies worldwide. Starting with segregation’s ancient roots, and what the archaeological evidence reveals about humanity’s long-standing use of urban divisions to reinforce political and economic inequality, Nightingale then moves to the world of European colonialism. It was there, he shows, segregation based on color—and eventually on race—took hold; the British East India Company, for example, split Calcutta into “White Town” and “Black Town.” As we follow Nightingale’s story around the globe, we see that division replicated from Hong Kong to Nairobi, Baltimore to San Francisco, and more. The turn of the twentieth century saw the most aggressive segregation movements yet, as white communities almost everywhere set to rearranging whole cities along racial lines. Nightingale focuses closely on two striking examples: Johannesburg, with its state-sponsored separation, and Chicago, in which the goal of segregation was advanced by the more subtle methods of real estate markets and housing policy. For the first time ever, the majority of humans live in cities, and nearly all those cities bear the scars of segregation. This unprecedented, ambitious history lays bare our troubled past, and sets us on the path to imagining the better, more equal cities of the future.

Tales of Physicists and Mathematicians

Author: Simon Gindikin

Publisher: Springer Science & Business Media

ISBN: 1461239427

Category: Mathematics

Page: 158

View: 5107

This revised and greatly expanded edition of the Russian classic contains a wealth of new information about the lives of many great mathematicians and scientists, past and present. Written by a distinguished mathematician and featuring a unique mix of mathematics, physics, and history, this text combines original source material and provides careful explanations for some of the most significant discoveries in mathematics and physics. What emerges are intriguing, multifaceted biographies that will interest readers at all levels.

Religion and the Sciences of Origins

Historical and Contemporary Discussions

Author: Kelly James Clark

Publisher: Springer

ISBN: 1137414812

Category: Religion

Page: 274

View: 7646

This concise introduction to science and religion focuses on Christianity and modern Western science (the epicenter of issues in science and religion in the West) with a concluding chapter on Muslim and Jewish Science and Religion. This book also invites the reader into the relevant literature with ample quotations from original texts.

The Search for Mathematical Roots, 1870-1940

Logics, Set Theories and the Foundations of Mathematics from Cantor through Russell to Gödel

Author: I. Grattan-Guinness

Publisher: Princeton University Press

ISBN: 9781400824045

Category: Mathematics

Page: 624

View: 9153

While many books have been written about Bertrand Russell's philosophy and some on his logic, I. Grattan-Guinness has written the first comprehensive history of the mathematical background, content, and impact of the mathematical logic and philosophy of mathematics that Russell developed with A. N. Whitehead in their Principia mathematica (1910-1913). ? This definitive history of a critical period in mathematics includes detailed accounts of the two principal influences upon Russell around 1900: the set theory of Cantor and the mathematical logic of Peano and his followers. Substantial surveys are provided of many related topics and figures of the late nineteenth century: the foundations of mathematical analysis under Weierstrass; the creation of algebraic logic by De Morgan, Boole, Peirce, Schröder, and Jevons; the contributions of Dedekind and Frege; the phenomenology of Husserl; and the proof theory of Hilbert. The many-sided story of the reception is recorded up to 1940, including the rise of logic in Poland and the impact on Vienna Circle philosophers Carnap and Gödel. A strong American theme runs though the story, beginning with the mathematician E. H. Moore and the philosopher Josiah Royce, and stretching through the emergence of Church and Quine, and the 1930s immigration of Carnap and GödeI. Grattan-Guinness draws on around fifty manuscript collections, including the Russell Archives, as well as many original reviews. The bibliography comprises around 1,900 items, bringing to light a wealth of primary materials. Written for mathematicians, logicians, historians, and philosophers--especially those interested in the historical interaction between these disciplines--this authoritative account tells an important story from its most neglected point of view. Whitehead and Russell hoped to show that (much of) mathematics was expressible within their logic; they failed in various ways, but no definitive alternative position emerged then or since.