"The true method of foreseeing the future of mathematics is to study its history and its actual state." With these words Henri Poincare began his presentation to the Fourth International Congress of Mathematicians at Rome in 1908. Although Poincare himself never actively pursued the history of mathematics, his remarks have given both historians of mathematics and working mathematicians a valuable methodological guideline, not so much for indulging in improbable prophecies about the future state of mathematics, as for finding in history the origins and moti va tions of contemporary theories, and for finding in the present the most fruitful statements of these theories. At the time Poincare spoke, at the beginning of this century, historical research in the various branches of rna thema tics was emerging with distinctive autonomy. In Germany the last volume of Cantor's monumental Vorlesungell iiber die Gesehiehte der Mathematik had just appeared, and many new specialized journals were appearing to complement those already in existence, from Enestrom's Bibliotheea mathematiea to Loria's Bollettino di bibliogra/ia e di storia delle seienze matematiehe. The annual Jahresberiehte of the German Mathematical Society included noteworthy papers of a historical nature, as did the Enzyklopadie der mathematisehen Wissenseha/ten, an imposing work constructed according to the plan of Felix Klein.
Mathematics is one of the most basic -- and most ancient -- types of knowledge. Yet the details of its historical development remain obscure to all but a few specialists. The two-volume Companion Encyclopedia of the History and Philosophy of the Mathematical Sciences recovers this mathematical heritage, bringing together many of the world's leading historians of mathematics to examine the history and philosophy of the mathematical sciences in a cultural context, tracing their evolution from ancient times to the twentieth century. In 176 concise articles divided into twelve parts, contributors describe and analyze the variety of problems, theories, proofs, and techniques in all areas of pure and applied mathematics, including probability and statistics. This indispensable reference work demonstrates the continuing importance of mathematics and its use in physics, astronomy, engineering, computer science, philosophy, and the social sciences. Also addressed is the history of higher education in mathematics. Carefully illustrated, with annotated bibliographies of sources for each article, The Companion Encyclopedia is a valuable research tool for students and teachers in all branches of mathematics. Contents of Volume 1: Â•Ancient and Non-Western Traditions Â•The Western Middle Ages and the Renaissance Â•Calculus and Mathematical Analysis Â•Functions, Series, and Methods in Analysis Â•Logic, Set Theories, and the Foundations of Mathematics Â•Algebras and Number Theory Contents of Volume 2: Â•Geometries and Topology Â•Mechanics and Mechanical Engineering Â•Physics, Mathematical Physics, and Electrical Engineering Â•Probability, Statistics, and the Social Sciences Â•Higher Education and Institutions Â•Mathematics and Culture Â•Select Bibliography, Chronology, Biographical Notes, and Index
* Examines the history and philosophy of the mathematical sciences in a cultural context, tracing their evolution from ancient times up to the twentieth century * 176 articles contributed by authors of 18 nationalities * Chronological table of main events in the development of mathematics * Fully integrated index of people, events and topics * Annotated bibliographies of both classic and contemporary sources * Unique coverage of Ancient and non-Western traditions of mathematics
This book comprises five parts. The first three contain ten historical essays on important topics: number theory, calculus/analysis, and proof, respectively. Part four deals with several historically oriented courses, and Part five provides biographies of five mathematicians who played major roles in the historical events described in the first four parts of the work. Excursions in the History of Mathematics was written with several goals in mind: to arouse mathematics teachers’ interest in the history of their subject; to encourage mathematics teachers with at least some knowledge of the history of mathematics to offer courses with a strong historical component; and to provide an historical perspective on a number of basic topics taught in mathematics courses.
The unifying approach of functional analysis is to view functions as points in abstract vector space and the differential and integral operators as linear transformations on these spaces. The author's goal is to present the basics of functional analysis in a way that makes them comprehensible to a student who has completed courses in linear algebra and real analysis, and to develop the topics in their historical contexts.
This book does nothing less than provide an account of the intellectual lineage of abstract algebra. The development of abstract algebra was propelled by the need for new tools to address certain classical problems that appeared insoluble by classical means. A major theme of the book is to show how abstract algebra has arisen in attempting to solve some of these classical problems, providing a context from which the reader may gain a deeper appreciation of the mathematics involved. Mathematics instructors, algebraists, and historians of science will find the work a valuable reference.
This book contains a history of real and complex analysis in the nineteenth century, from the work of Lagrange and Fourier to the origins of set theory and the modern foundations of analysis. It studies the works of many contributors including Gauss, Cauchy, Riemann, and Weierstrass. This book is unique owing to the treatment of real and complex analysis as overlapping, inter-related subjects, in keeping with how they were seen at the time. It is suitable as a course in the history of mathematics for students who have studied an introductory course in analysis, and will enrich any course in undergraduate real or complex analysis.
Key Message: A History of Mathematics, Third Edition, provides a solid background in the history of mathematics, helping readers gain a deeper understanding of mathematical concepts in their historical context. This book's global perspective covers how contributions from Chinese, Indian, and Islamic mathematicians shaped our modern understanding of mathematics. This book also includes discussions of important historical textbooks and primary sources to help readers further understand the development of modern mathematics. Key Topics: Ancient Mathematics: Egypt and Mesopotamia, The Beginnings of Mathematics in Greece, Euclid, Archimedes and Apollonius, Mathematical Methods in Hellenistic Times, The Final Chapter of Greek Mathematics; Medieval Mathematics: Ancient and Medieval China, Ancient and Medieval India, The Mathematics of Islam, Medieval Europe, Mathematics Elsewhere; Early Modern Mathematics: Algebra in the Renaissance, Mathematical Methods in the Renaissance, Geometry, Algebra and Probability in the Seventeenth Century, The Beginnings of Calculus, Newton and Leibniz; Modern Mathematics: Analysis in the Eighteenth Century, Probability and Statistics in the Eighteenth Century, Algebra and Number Theory in the Eighteenth Century, Geometry in the Eighteenth Century, Algebra and Number Theory in the Nineteenth Century, Analysis in the Nineteenth Century, Probability and Statistics in the Nineteenth Century, Geometry in the Nineteenth Century, Aspects of the Twentieth Century Market: For all readers interested in the history of mathematics.
One of the leading historians in the mathematics field, Victor Katz provides a world view of mathematics, balancing ancient, early modern, and modern history. Egypt and Mesopotamia, Greek Mathematics to the Time of Euclid, Greek Mathematics from Archimedes to Ptolemy, Diophantus to Hypatia, Ancient and Medieval China, Ancient and Medieval India, The Mathematics of Islam, Mathematics in Medieval Europe, Mathematics in the Renaissance, Precalculus in the Seventeenth Century, Calculus in the Seventeenth Century, Analysis in the Eighteenth Century, Probability and Statistics in the Eighteenth Century, Algebra and Number Theory in the Eighteenth Century, Geometry in the Eighteenth Century, Algebra and Number Theory in the Nineteenth Century, Analysis in the Nineteenth Century, Statistics in the Nineteenth Century, Geometry in the Nineteenth Century, Aspects of the Twentieth Century For all readers interested in the history of mathematics.
A collection of 13 articles relating to developments in the history of 18th-century exact science, focusing on the writings of such figures as Jean d'Alembert, Leonhard Euler, and Joseph Louis Lagrange. The volume presents their work on the principles of calculus and the theory of motion, and serves to clarify the conceptual foundation of analysis and mechanics in the century following Newton. A detailed historical and critical study of conceptual change involving fundamental links between pure and applied mathematics is provided.
Also available online as part of the Gale Virtual Reference Library under the title Complete dictionary of scientific biography.
This book presents a fascinating story of the long life and great accomplishments of Jacques Hadamard (1865-1963), who was once called "the living legend of mathematics". As one of the last universal mathematicians, Hadamard's contributions to mathematics are landmarks in various fields. His life is linked with world history of the 20th century in a dramatic way. This work provides an inspiring view of the development of various branches of mathematics during the 19th and 20th centuries. Hadamard's life is described in a readable and inviting way. The authors humorously weave throughout his jokes and the myths about him. They also movingly recount the tragic side of his life. Stories about his relatives and friends, and old letters and documents create an authentic and colorful picture. The book contains over 300 photographs and illustrations.
Appropriate for undergraduate and select graduate courses in the history of mathematics, and in the history of science. This edited volume of readings contains more than 130 selections from eminent mathematicians from A `h-mose' to Hilbert and Noether. The chapter introductions comprise a concise history of mathematics based on critical textual analysis and the latest scholarship. Each reading is preceded by a substantial biography of its author.
This book is a history of complex function theory from its origins to 1914, when the essential features of the modern theory were in place. It is the first history of mathematics devoted to complex function theory, and it draws on a wide range of published and unpublished sources. In addition to an extensive and detailed coverage of the three founders of the subject – Cauchy, Riemann, and Weierstrass – it looks at the contributions of authors from d’Alembert to Hilbert, and Laplace to Weyl. Particular chapters examine the rise and importance of elliptic function theory, differential equations in the complex domain, geometric function theory, and the early years of complex function theory in several variables. Unique emphasis has been devoted to the creation of a textbook tradition in complex analysis by considering some seventy textbooks in nine different languages. The book is not a mere sequence of disembodied results and theories, but offers a comprehensive picture of the broad cultural and social context in which the main actors lived and worked by paying attention to the rise of mathematical schools and of contrasting national traditions. The book is unrivaled for its breadth and depth, both in the core theory and its implications for other fields of mathematics. It documents the motivations for the early ideas and their gradual refinement into a rigorous theory.