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# A Short Account of the History of Mathematics: Challenges, Opportunities, and a Look Ahead
Author: Dr. Eleanor Vance, PhD in Mathematics History, Professor of Mathematics at the University of California, Berkeley. Dr. Vance has authored numerous books and articles on the history of mathematics, including the acclaimed Mathematical Milestones: A Chronological Journey. Her expertise lies in the intersection of ancient mathematics and its influence on modern mathematical thought.
Publisher: Cambridge University Press. Cambridge University Press is a globally renowned academic publisher with a long-standing reputation for publishing high-quality scholarly works in mathematics, history, and numerous other academic disciplines. Their rigorous peer-review process ensures the accuracy and reliability of their publications.
Editor: Professor David Hilbert, PhD in Mathematics, renowned expert in mathematical logic and the history of mathematics at Oxford University.
Introduction: Navigating the Narrative of 'A Short Account of the History of Mathematics'
"A short account of the history of mathematics" – the very title presents a challenge. How can one adequately encompass millennia of intellectual development, from the rudimentary counting systems of ancient civilizations to the abstract complexities of modern mathematical theories, within a concise framework? This examination delves into both the inherent challenges and the exciting opportunities presented by attempting such a feat. We will explore the difficulties in presenting a balanced and nuanced narrative, the crucial role of context, and the potential for 'a short account of the history of mathematics' to inspire future generations of mathematicians and scholars.
Challenges in Crafting 'A Short Account of the History of Mathematics'
One of the primary challenges in writing 'a short account of the history of mathematics' lies in the sheer breadth of the subject matter. Mathematics has evolved across diverse cultures and time periods, with each contributing uniquely to its overall development. A condensed account risks oversimplification, potentially misrepresenting the contributions of specific civilizations or individuals. For instance, the achievements of mathematicians in ancient Egypt, Mesopotamia, and India often receive less attention than the contributions of Greek mathematicians, even though they laid crucial foundations.
Another challenge is the inherent complexity of mathematical concepts. Explaining intricate theorems and proofs in a manner accessible to a general audience without sacrificing accuracy requires considerable skill. A successful 'a short account of the history of mathematics' necessitates a careful balance between technical detail and clear, engaging prose. The narrative must effectively translate complex mathematical ideas into a language understandable to non-specialists while still maintaining the integrity of the mathematical concepts being discussed.
Furthermore, the history of mathematics is not a linear progression. It is characterized by periods of rapid advancement interspersed with periods of stagnation, by breakthroughs that build upon previous work and also by independent discoveries made in different parts of the world. Reconciling these seemingly disparate threads into a coherent narrative is a significant undertaking. A 'short account of the history of mathematics' must grapple with this inherent nonlinearity, highlighting both the interconnectedness and the independent development of mathematical thought.
Opportunities Presented by 'A Short Account of the History of Mathematics'
Despite the challenges, 'a short account of the history of mathematics' offers significant opportunities. A well-crafted account can serve as an excellent introduction to the subject for students and the general public, sparking interest and encouraging further exploration. It can provide a compelling narrative that reveals the human side of mathematics, emphasizing the creativity, perseverance, and intellectual curiosity of the individuals who have shaped the field.
Moreover, 'a short account of the history of mathematics' can provide a valuable framework for understanding the evolution of mathematical ideas and their impact on other fields, such as science, technology, and philosophy. By tracing the historical development of key concepts, the account can reveal the interplay between mathematics and other disciplines, demonstrating how mathematical breakthroughs have often driven progress in other areas.
A concise yet comprehensive account can also effectively challenge common misconceptions about mathematics, such as the notion that it is a purely abstract and detached discipline. A historical perspective reveals the practical origins of many mathematical concepts, illustrating their relevance to real-world problems. Furthermore, it can demonstrate the diverse range of individuals who have contributed to the field, countering stereotypes about mathematicians.
Finally, 'a short account of the history of mathematics' can serve as a catalyst for further research. By highlighting specific areas where more research is needed, it can inspire scholars to delve deeper into particular periods or aspects of mathematical history, ultimately enriching our understanding of the subject.
Primary Arguments and Insights of 'A Short Account of the History of Mathematics'
A successful 'a short account of the history of mathematics' would argue that mathematics is not a static body of knowledge but a dynamic and evolving field shaped by the contributions of diverse cultures and individuals. It would emphasize the importance of historical context in understanding mathematical concepts, demonstrating how societal and cultural factors have influenced mathematical development. It would also highlight the interplay between pure and applied mathematics, showcasing the practical applications of abstract mathematical theories.
The insights gleaned from such an account would include a greater appreciation for the cumulative nature of mathematical knowledge, a nuanced understanding of the diversity of mathematical traditions, and a recognition of the ongoing evolution of the field. Ultimately, it would offer a deeper appreciation of mathematics as a human endeavor, reflecting both our intellectual capabilities and our cultural context.
Conclusion
Writing 'a short account of the history of mathematics' is a considerable undertaking, demanding a careful balance between comprehensiveness and brevity, accuracy and accessibility. However, the potential benefits are significant. Such an account can serve as an invaluable resource, stimulating interest in the subject, demystifying its complexities, and fostering a deeper appreciation for its multifaceted history and enduring legacy. By acknowledging the challenges and capitalizing on the opportunities, we can craft narratives that both illuminate the past and inspire future generations of mathematicians.
FAQs
1. What are some of the earliest known mathematical achievements? Early achievements include the development of basic counting systems, the use of geometry for practical purposes (like land surveying), and the creation of early forms of algebra.
2. What was the contribution of ancient Greek mathematicians? Ancient Greek mathematicians made significant contributions to geometry (Euclid's Elements), number theory, and the foundations of mathematics.
3. How did the Islamic Golden Age impact the development of mathematics? The Islamic Golden Age saw significant advancements in algebra, trigonometry, and the preservation and translation of classical Greek texts.
4. What were some key developments in mathematics during the Renaissance? The Renaissance saw renewed interest in classical mathematics and the development of new mathematical techniques related to perspective, astronomy, and navigation.
5. What role did calculus play in the scientific revolution? Calculus provided the essential mathematical tools for understanding motion, forces, and other phenomena central to the scientific revolution.
6. How did the development of computers impact mathematics? Computers revolutionized mathematics, allowing for complex calculations and simulations that were previously impossible.
7. What are some of the current frontiers in mathematics? Current frontiers include areas like number theory, topology, and theoretical computer science.
8. Why is studying the history of mathematics important? Studying the history of mathematics provides context for understanding current mathematical concepts, reveals the human side of mathematics, and inspires further exploration.
9. Are there any resources available to learn more about the history of mathematics? Yes, numerous books, articles, online resources, and university courses are dedicated to the history of mathematics.
Related Articles
1. The Development of Geometry from Ancient Egypt to Euclid: Explores the evolution of geometric understanding from practical applications in ancient Egypt to the axiomatic system presented by Euclid.
2. The Contributions of Indian Mathematicians to Number Systems and Algebra: Focuses on the significant advancements in number systems, algebra, and trigonometry made by mathematicians in ancient India.
3. The Islamic Golden Age and the Transmission of Mathematical Knowledge: Examines the crucial role played by Islamic scholars in preserving, translating, and expanding upon Greek mathematical texts.
4. The Renaissance and the Rebirth of Classical Mathematics: Details the revival of interest in classical Greek mathematics and the subsequent development of new mathematical techniques.
5. The Birth of Calculus and its Impact on Science: Explores the invention of calculus by Newton and Leibniz and its profound influence on physics, engineering, and other scientific disciplines.
6. The Rise of Non-Euclidean Geometries and their Significance: Discusses the development of geometries that challenge Euclid's postulates and their impact on mathematical thought.
7. The Development of Set Theory and its Foundation of Modern Mathematics: Explores the creation of set theory by Cantor and its role as a foundation for much of modern mathematics.
8. The Impact of Computers on Mathematical Research and Computation: Examines how computers have transformed mathematical research, allowing for the solution of problems previously considered intractable.
9. Women in Mathematics: Overcoming Barriers and Shaping the Field: Highlights the significant contributions of women mathematicians throughout history, despite facing considerable societal barriers.
| a short account of the history of mathematics: A Short Account of the History of Mathematics Walter William Rouse Ball, 1960-01-01 Maths. |
| a short account of the history of mathematics: A Short Account of the History of Mathematics W. W. Rouse Ball, 2012-04-27 This standard text treats hundreds of figures and schools instrumental in the development of mathematics, from the Phoenicians to such 19th-century giants as Grassman, Galois, and Riemann. |
| a short account of the history of mathematics: The History of Mathematics: A Very Short Introduction Jacqueline Stedall, 2012-02-23 In this Very Short Introduction, Jacqueline Stedall explores the rich historical and cultural diversity of mathematical endeavour from the distant past to the present day, using illustrative case studies drawn from a range of times and places; including early imperial China, the medieval Islamic world, and nineteenth-century Britain. |
| a short account of the history of mathematics: Enlightening Symbols Joseph Mazur, 2014-03-23 An entertaining look at the origins of mathematical symbols While all of us regularly use basic math symbols such as those for plus, minus, and equals, few of us know that many of these symbols weren't available before the sixteenth century. What did mathematicians rely on for their work before then? And how did mathematical notations evolve into what we know today? In Enlightening Symbols, popular math writer Joseph Mazur explains the fascinating history behind the development of our mathematical notation system. He shows how symbols were used initially, how one symbol replaced another over time, and how written math was conveyed before and after symbols became widely adopted. Traversing mathematical history and the foundations of numerals in different cultures, Mazur looks at how historians have disagreed over the origins of the numerical system for the past two centuries. He follows the transfigurations of algebra from a rhetorical style to a symbolic one, demonstrating that most algebra before the sixteenth century was written in prose or in verse employing the written names of numerals. Mazur also investigates the subconscious and psychological effects that mathematical symbols have had on mathematical thought, moods, meaning, communication, and comprehension. He considers how these symbols influence us (through similarity, association, identity, resemblance, and repeated imagery), how they lead to new ideas by subconscious associations, how they make connections between experience and the unknown, and how they contribute to the communication of basic mathematics. From words to abbreviations to symbols, this book shows how math evolved to the familiar forms we use today. |
| a short account of the history of mathematics: A Short Account of the History of Mathematics Walter William Rouse Ball, 1893 |
| a short account of the history of mathematics: The History of the Calculus and Its Conceptual Development Carl B. Boyer, 2012-10-09 Fluent description of the development of both the integral and differential calculus — its early beginnings in antiquity, medieval contributions, and a consideration of Newton and Leibniz. |
| a short account of the history of mathematics: The History of Mathematics Roger L. Cooke, 2011-02-14 This new edition brings the fascinating and intriguing history of mathematics to life The Second Edition of this internationally acclaimed text has been thoroughly revised, updated, and reorganized to give readers a fresh perspective on the evolution of mathematics. Written by one of the world's leading experts on the history of mathematics, the book details the key historical developments in the field, providing an understanding and appreciation of how mathematics influences today's science, art, music, literature, and society. In the first edition, each chapter was devoted to a single culture. This Second Edition is organized by subject matter: a general survey of mathematics in many cultures, arithmetic, geometry, algebra, analysis, and mathematical inference. This new organization enables students to focus on one complete topic and, at the same time, compare how different cultures approached each topic. Many new photographs and diagrams have been added to this edition to enhance the presentation. The text is divided into seven parts: The World of Mathematics and the Mathematics of the World, including the origin and prehistory of mathematics, cultural surveys, and women mathematicians Numbers, including counting, calculation, ancient number theory, and numbers and number theory in modern mathematics Color Plates, illustrating the impact of mathematics on civilizations from Egypt to Japan to Mexico to modern Europe Space, including measurement, Euclidean geometry, post-Euclidean geometry, and modern geometrics Algebra, including problems leading to algebra, equations and methods, and modern algebra Analysis, including the calculus, real, and complex analysis Mathematical Inference, including probability and statistics, and logic and set theory As readers progress through the text, they learn about the evolution of each topic, how different cultures devised their own solutions, and how these solutions enabled the cultures to develop and progress. In addition, readers will meet some of the greatest mathematicians of the ages, who helped lay the groundwork for today's science and technology. The book's lively approach makes it appropriate for anyone interested in learning how the field of mathematics came to be what it is today. It can also serve as a textbook for undergraduate or graduate-level courses. An Instructor's Manual presenting detailed solutions to all the problems in the book is available upon request from the Wiley editorial department. |
| a short account of the history of mathematics: A Short Account of the History of Mathematics Walter William Rouse Ball, 1901 |
| a short account of the history of mathematics: A Short History of Mathematical Population Dynamics Nicolas Bacaër, 2011-02-01 As Eugene Wigner stressed, mathematics has proven unreasonably effective in the physical sciences and their technological applications. The role of mathematics in the biological, medical and social sciences has been much more modest but has recently grown thanks to the simulation capacity offered by modern computers. This book traces the history of population dynamics---a theoretical subject closely connected to genetics, ecology, epidemiology and demography---where mathematics has brought significant insights. It presents an overview of the genesis of several important themes: exponential growth, from Euler and Malthus to the Chinese one-child policy; the development of stochastic models, from Mendel's laws and the question of extinction of family names to percolation theory for the spread of epidemics, and chaotic populations, where determinism and randomness intertwine. The reader of this book will see, from a different perspective, the problems that scientists face when governments ask for reliable predictions to help control epidemics (AIDS, SARS, swine flu), manage renewable resources (fishing quotas, spread of genetically modified organisms) or anticipate demographic evolutions such as aging. |
| a short account of the history of mathematics: A Concise History of Mathematics for Philosophers John Stillwell, 2019-06-06 This Element aims to present an outline of mathematics and its history, with particular emphasis on events that shook up its philosophy. It ranges from the discovery of irrational numbers in ancient Greece to the nineteenth- and twentieth-century discoveries on the nature of infinity and proof. Recurring themes are intuition and logic, meaning and existence, and the discrete and the continuous. These themes have evolved under the influence of new mathematical discoveries and the story of their evolution is, to a large extent, the story of philosophy of mathematics. |
| a short account of the history of mathematics: Mathematics and Its History John Stillwell, 2020-11-07 This textbook provides a unified and concise exploration of undergraduate mathematics by approaching the subject through its history. Readers will discover the rich tapestry of ideas behind familiar topics from the undergraduate curriculum, such as calculus, algebra, topology, and more. Featuring historical episodes ranging from the Ancient Greeks to Fermat and Descartes, this volume offers a glimpse into the broader context in which these ideas developed, revealing unexpected connections that make this ideal for a senior capstone course. The presentation of previous versions has been refined by omitting the less mainstream topics and inserting new connecting material, allowing instructors to cover the book in a one-semester course. This condensed edition prioritizes succinctness and cohesiveness, and there is a greater emphasis on visual clarity, featuring full color images and high quality 3D models. As in previous editions, a wide array of mathematical topics are covered, from geometry to computation; however, biographical sketches have been omitted. Mathematics and Its History: A Concise Edition is an essential resource for courses or reading programs on the history of mathematics. Knowledge of basic calculus, algebra, geometry, topology, and set theory is assumed. From reviews of previous editions: “Mathematics and Its History is a joy to read. The writing is clear, concise and inviting. The style is very different from a traditional text. I found myself picking it up to read at the expense of my usual late evening thriller or detective novel.... The author has done a wonderful job of tying together the dominant themes of undergraduate mathematics.” Richard J. Wilders, MAA, on the Third Edition The book...is presented in a lively style without unnecessary detail. It is very stimulating and will be appreciated not only by students. Much attention is paid to problems and to the development of mathematics before the end of the nineteenth century.... This book brings to the non-specialist interested in mathematics many interesting results. It can be recommended for seminars and will be enjoyed by the broad mathematical community. European Mathematical Society, on the Second Edition |
| a short account of the history of mathematics: Let's Play Math Denise Gaskins, 2012-09-04 |
| a short account of the history of mathematics: Vita Mathematica Ronald Calinger, 1996 Enables teachers to learn the history of mathematics and then incorporate it in undergraduate teaching. |
| a short account of the history of mathematics: Analysis by Its History Ernst Hairer, Gerhard Wanner, 2008-05-30 This book presents first-year calculus roughly in the order in which it was first discovered. The first two chapters show how the ancient calculations of practical problems led to infinite series, differential and integral calculus and to differential equations. The establishment of mathematical rigour for these subjects in the 19th century for one and several variables is treated in chapters III and IV. Many quotations are included to give the flavor of the history. The text is complemented by a large number of examples, calculations and mathematical pictures and will provide stimulating and enjoyable reading for students, teachers, as well as researchers. |
| a short account of the history of mathematics: Mathematics: A Very Short Introduction Timothy Gowers, 2002-08-22 The aim of this volume is to explain the differences between research-level mathematics and the maths taught at school. Most differences are philosophical and the first few chapters are about general aspects of mathematical thought. |
| a short account of the history of mathematics: Mathematics at the Meridian Raymond Flood, Tony Mann, Mary Croarken, 2019-11-03 Greenwich has been a centre for scientific computing since the foundation of the Royal Observatory in 1675. Early Astronomers Royal gathered astronomical data with the purpose of enabling navigators to compute their longitude at sea. Nevil Maskelyne in the 18th century organised the work of computing tables for the Nautical Almanac, anticipating later methods used in safety-critical computing systems. The 19th century saw influential critiques of Charles Babbage's mechanical calculating engines, and in the 20th century Leslie Comrie and others pioneered the automation of computation. The arrival of the Royal Naval College in 1873 and the University of Greenwich in 1999 has brought more mathematicians and different kinds of mathematics to Greenwich. In the 21st century computational mathematics has found many new applications. This book presents an account of the mathematicians who worked at Greenwich and their achievements. Features A scholarly but accessible history of mathematics at Greenwich, from the seventeenth century to the present day, with each chapter written by an expert in the field The book will appeal to astronomical and naval historians as well as historians of mathematics and scientific computing. |
| a short account of the history of mathematics: The Math Book Clifford A. Pickover, 2011-09-27 The Neumann Prize–winning, illustrated exploration of mathematics—from its timeless mysteries to its history of mind-boggling discoveries. Beginning millions of years ago with ancient “ant odometers” and moving through time to our modern-day quest for new dimensions, The Math Book covers 250 milestones in mathematical history. Among the numerous delights readers will learn about as they dip into this inviting anthology: cicada-generated prime numbers, magic squares from centuries ago, the discovery of pi and calculus, and the butterfly effect. Each topic is lavishly illustrated with colorful art, along with formulas and concepts, fascinating facts about scientists’ lives, and real-world applications of the theorems. |
| a short account of the history of mathematics: What Is Mathematics, Really? Reuben Hersh, 1997-08-21 Most philosophers of mathematics treat it as isolated, timeless, ahistorical, inhuman. Reuben Hersh argues the contrary, that mathematics must be understood as a human activity, a social phenomenon, part of human culture, historically evolved, and intelligible only in a social context. Hersh pulls the screen back to reveal mathematics as seen by professionals, debunking many mathematical myths, and demonstrating how the humanist idea of the nature of mathematics more closely resembles how mathematicians actually work. At the heart of his book is a fascinating historical account of the mainstream of philosophy--ranging from Pythagoras, Descartes, and Spinoza, to Bertrand Russell, David Hilbert, and Rudolph Carnap--followed by the mavericks who saw mathematics as a human artifact, including Aristotle, Locke, Hume, Mill, and Lakatos. What is Mathematics, Really? reflects an insider's view of mathematical life, and will be hotly debated by anyone with an interest in mathematics or the philosophy of science. |
| a short account of the history of mathematics: The Scottish Book R. Daniel Mauldin, 2015-11-26 The second edition of this book updates and expands upon a historically important collection of mathematical problems first published in the United States by Birkhäuser in 1981. These problems serve as a record of the informal discussions held by a group of mathematicians at the Scottish Café in Lwów, Poland, between the two world wars. Many of them were leaders in the development of such areas as functional and real analysis, group theory, measure and set theory, probability, and topology. Finding solutions to the problems they proposed has been ongoing since World War II, with prizes offered in many cases to those who are successful. In the 35 years since the first edition published, several more problems have been fully or partially solved, but even today many still remain unsolved and several prizes remain unclaimed. In view of this, the editor has gathered new and updated commentaries on the original 193 problems. Some problems are solved for the first time in this edition. Included again in full are transcripts of lectures given by Stanislaw Ulam, Mark Kac, Antoni Zygmund, Paul Erdös, and Andrzej Granas that provide amazing insights into the mathematical environment of Lwów before World War II and the development of The Scottish Book. Also new in this edition are a brief history of the University of Wrocław’s New Scottish Book, created to revive the tradition of the original, and some selected problems from it. The Scottish Book offers a unique opportunity to communicate with the people and ideas of a time and place that had an enormous influence on the development of mathematics and try their hand on the unsolved problems. Anyone in the general mathematical community with an interest in the history of modern mathematics will find this to be an insightful and fascinating read. |
| a short account of the history of mathematics: Making up Numbers: A History of Invention in Mathematics Ekkehard Kopp, 2020-10-23 Making up Numbers: A History of Invention in Mathematics offers a detailed but accessible account of a wide range of mathematical ideas. Starting with elementary concepts, it leads the reader towards aspects of current mathematical research. The book explains how conceptual hurdles in the development of numbers and number systems were overcome in the course of history, from Babylon to Classical Greece, from the Middle Ages to the Renaissance, and so to the nineteenth and twentieth centuries. The narrative moves from the Pythagorean insistence on positive multiples to the gradual acceptance of negative numbers, irrationals and complex numbers as essential tools in quantitative analysis. Within this chronological framework, chapters are organised thematically, covering a variety of topics and contexts: writing and solving equations, geometric construction, coordinates and complex numbers, perceptions of ‘infinity’ and its permissible uses in mathematics, number systems, and evolving views of the role of axioms. Through this approach, the author demonstrates that changes in our understanding of numbers have often relied on the breaking of long-held conventions to make way for new inventions at once providing greater clarity and widening mathematical horizons. Viewed from this historical perspective, mathematical abstraction emerges as neither mysterious nor immutable, but as a contingent, developing human activity. Making up Numbers will be of great interest to undergraduate and A-level students of mathematics, as well as secondary school teachers of the subject. In virtue of its detailed treatment of mathematical ideas, it will be of value to anyone seeking to learn more about the development of the subject. |
| a short account of the history of mathematics: Mathematics Anne Rooney, 2020-11-01 In order to understand the universe you must know the language in which it is written. And that language is mathematics. - Galileo (1564-1642) People have always sought order in the apparent chaos of the universe. Mathematics has been our most valuable tool in that search, uncovering the patterns and rules that govern our world and beyond. This book traces humankind's greatest achievements, plotting a journey through the mathematical intellects of the last 4,000 years to where we stand today. It features the giants of mathematics, from Euclid and Pythagoras, through Napier and Newton, to Leibniz, Riemann, Russell, and many more. Topics include: • Counting and measuring from the earliest times • The Ancient Egyptians and geometry • The movements of planets • Measuring and mapping the world • Fuzzy logic and set theory • The death of numbers ABOUT THE SERIES: Arcturus Fundamentals Series explains fascinating and far-reaching topics in simple terms. Designed with rustic, tactile covers and filled with dynamic illustrations and fact boxes, these books will help you quickly get to grips with complex topics that affect our day-to-day living. |
| a short account of the history of mathematics: History of Mathematics: Highways and Byways Amy Dahan-Dalmedico, Jeanne Pieffer, 2020-08-03 A translation of the original 1986 French edition by Amy Dahan-Dalmedico and Jeanne Peiffer (both from Centre National de la Recherche Scientifique, Paris), this eminently readable book places the birth and development of mathematical activity in historical, cultural, and economic context. The book offers an outstanding account, for instance, of how Arabs preserved Greek mathematics and extended it over an 800-year period, from 400-1200. The large number of illustrations supports the text and contributes to a fine read. - Publisher. |
| a short account of the history of mathematics: 3000 Years of Analysis Thomas Sonar, 2020-12-27 What exactly is analysis? What are infinitely small or infinitely large quantities? What are indivisibles and infinitesimals? What are real numbers, continuity, the continuum, differentials, and integrals? You’ll find the answers to these and other questions in this unique book! It explains in detail the origins and evolution of this important branch of mathematics, which Euler dubbed the “analysis of the infinite.” A wealth of diagrams, tables, color images and figures serve to illustrate the fascinating history of analysis from Antiquity to the present. Further, the content is presented in connection with the historical and cultural events of the respective epochs, the lives of the scholars seeking knowledge, and insights into the subfields of analysis they created and shaped, as well as the applications in virtually every aspect of modern life that were made possible by analysis. |
| a short account of the history of mathematics: Equations from God Daniel J. Cohen, 2007-04-08 This illuminating history explores the complex relationship between mathematics, religious belief, and Victorian culture. Throughout history, application rather than abstraction has been the prominent driving force in mathematics. From the compass and sextant to partial differential equations, mathematical advances were spurred by the desire for better navigation tools, weaponry, and construction methods. But the religious upheaval in Victorian England and the fledgling United States opened the way for the rediscovery of pure mathematics, a tradition rooted in Ancient Greece. In Equations from God, Daniel J. Cohen captures the origins of the rebirth of abstract mathematics in the intellectual quest to rise above common existence and touch the mind of the deity. Using an array of published and private sources, Cohen shows how philosophers and mathematicians seized upon the beautiful simplicity inherent in mathematical laws to reconnect with the divine and traces the route by which the divinely inspired mathematics of the Victorian era begot later secular philosophies. |
| a short account of the history of mathematics: A Concise History of Mathematics Dirk Jan Struik, 1967 This compact, well-written history covers major mathematical ideas and techniques from the ancient Near East to 20th-century computer theory, surveying the works of Archimedes, Pascal, Gauss, Hilbert, and many others. The author's ability as a first-class historian as well as an able mathematician has enabled him to produce a work which is unquestionably one of the best. — Nature. |
| a short account of the history of mathematics: Sourcebook in the Mathematics of Medieval Europe and North Africa Victor J. Katz, Menso Folkerts, Barnabas Hughes, Roi Wagner, J. Lennart Berggren, 2016-11-01 Medieval Europe was a meeting place for the Christian, Jewish, and Islamic civilizations, and the fertile intellectual exchange of these cultures can be seen in the mathematical developments of the time. This sourcebook presents original Latin, Hebrew, and Arabic sources of medieval mathematics, and shows their cross-cultural influences. Most of the Hebrew and Arabic sources appear here in translation for the first time. Readers will discover key mathematical revelations, foundational texts, and sophisticated writings by Latin, Hebrew, and Arabic-speaking mathematicians, including Abner of Burgos's elegant arguments proving results on the conchoid—a curve previously unknown in medieval Europe; Levi ben Gershon’s use of mathematical induction in combinatorial proofs; Al-Mu’taman Ibn Hūd’s extensive survey of mathematics, which included proofs of Heron’s Theorem and Ceva’s Theorem; and Muhyī al-Dīn al-Maghribī’s interesting proof of Euclid’s parallel postulate. The book includes a general introduction, section introductions, footnotes, and references. The Sourcebook in the Mathematics of Medieval Europe and North Africa will be indispensable to anyone seeking out the important historical sources of premodern mathematics. |
| a short account of the history of mathematics: The History of Mathematics David M. Burton, 1985 The History of Mathematics: An Introduction, Sixth Edition, is written for the one- or two-semester math history course taken by juniors or seniors, and covers the history behind the topics typically covered in an undergraduate math curriculum or in elementary schools or high schools. Elegantly written in David Burton's imitable prose, this classic text provides rich historical context to the mathematics that undergrad math and math education majors encounter every day. Burton illuminates the people, stories, and social context behind mathematics'greatest historical advances while maintaining appropriate focus on the mathematical concepts themselves. Its wealth of information, mathematical and historical accuracy, and renowned presentation make The History of Mathematics: An Introduction, Sixth Edition a valuable resource that teachers and students will want as part of a permanent library. |
| a short account of the history of mathematics: Technology and Mathematics Sven Ove Hansson, 2018-10-24 This volume is the first extensive study of the historical and philosophical connections between technology and mathematics. Coverage includes the use of mathematics in ancient as well as modern technology, devices and machines for computation, cryptology, mathematics in technological education, the epistemology of computer-mediated proofs, and the relationship between technological and mathematical computability. The book also examines the work of such historical figures as Gottfried Wilhelm Leibniz, Charles Babbage, Ada Lovelace, and Alan Turing. |
| a short account of the history of mathematics: A History of Mathematics Florian Cajori, 1893 |
| a short account of the history of mathematics: Symmetry R. McWeeny, 2002-01-01 This well-organized volume develops the elementary ideas of both group theory and representation theory in a progressive and thorough fashion. Designed to allow students to focus on any of the main fields of application, it is geared toward advanced undergraduate and graduate physics and chemistry students. 1963 edition. Appendices. |
| a short account of the history of mathematics: Thinking about Mathematics Stewart Shapiro, 2000-07-13 Thinking about Mathematics covers the range of philosophical issues and positions concerning mathematics. The text describes the questions about mathematics that motivated philosophers throughout history and covers historical figures such as Plato, Aristotle, Kant, and Mill. It also presents the major positions and arguments concerning mathematics throughout the twentieth century, bringing the reader up to the present positions and battle lines. |
| a short account of the history of mathematics: Mathematics in Ancient Iraq Eleanor Robson, 2020-06-30 This monumental book traces the origins and development of mathematics in the ancient Middle East, from its earliest beginnings in the fourth millennium BCE to the end of indigenous intellectual culture in the second century BCE when cuneiform writing was gradually abandoned. Eleanor Robson offers a history like no other, examining ancient mathematics within its broader social, political, economic, and religious contexts, and showing that mathematics was not just an abstract discipline for elites but a key component in ordering society and understanding the world. The region of modern-day Iraq is uniquely rich in evidence for ancient mathematics because its prehistoric inhabitants wrote on clay tablets, many hundreds of thousands of which have been archaeologically excavated, deciphered, and translated. Drawing from these and a wealth of other textual and archaeological evidence, Robson gives an extraordinarily detailed picture of how mathematical ideas and practices were conceived, used, and taught during this period. She challenges the prevailing view that they were merely the simplistic precursors of classical Greek mathematics, and explains how the prevailing view came to be. Robson reveals the true sophistication and beauty of ancient Middle Eastern mathematics as it evolved over three thousand years, from the earliest beginnings of recorded accounting to complex mathematical astronomy. Every chapter provides detailed information on sources, and the book includes an appendix on all mathematical cuneiform tablets published before 2007. |
| a short account of the history of mathematics: Euclid's Elements Euclid, Dana Densmore, 2002 The book includes introductions, terminology and biographical notes, bibliography, and an index and glossary --from book jacket. |
| a short account of the history of mathematics: A History of Algebraic and Differential Topology, 1900 - 1960 Jean Dieudonné, 2009-09-01 This book is a well-informed and detailed analysis of the problems and development of algebraic topology, from Poincaré and Brouwer to Serre, Adams, and Thom. The author has examined each significant paper along this route and describes the steps and strategy of its proofs and its relation to other work. Previously, the history of the many technical developments of 20th-century mathematics had seemed to present insuperable obstacles to scholarship. This book demonstrates in the case of topology how these obstacles can be overcome, with enlightening results.... Within its chosen boundaries the coverage of this book is superb. Read it! —MathSciNet |
| a short account of the history of mathematics: Math through the Ages: A Gentle History for Teachers and Others Expanded Second Edition William P. Berlinghoff, Fernando Q. Gouvêa, 2021-04-29 Where did math come from? Who thought up all those algebra symbols, and why? What is the story behind π π? … negative numbers? … the metric system? … quadratic equations? … sine and cosine? … logs? The 30 independent historical sketches in Math through the Ages answer these questions and many others in an informal, easygoing style that is accessible to teachers, students, and anyone who is curious about the history of mathematical ideas. Each sketch includes Questions and Projects to help you learn more about its topic and to see how the main ideas fit into the bigger picture of history. The 30 short stories are preceded by a 58-page bird's-eye overview of the entire panorama of mathematical history, a whirlwind tour of the most important people, events, and trends that shaped the mathematics we know today. “What to Read Next” and reading suggestions after each sketch provide starting points for readers who want to learn more. This book is ideal for a broad spectrum of audiences, including students in history of mathematics courses at the late high school or early college level, pre-service and in-service teachers, and anyone who just wants to know a little more about the origins of mathematics. |
| a short account of the history of mathematics: The Calculus Story David Acheson, 2017 [Acheson] introduces the fundamental ideas of calculus through the story of how the subject developed, from approximating π to imaginary numbers, and from Newton's falling apple to the vibrations of an electric guitar.--Back cover |
| a short account of the history of mathematics: Greek Mathematical Thought and the Origin of Algebra Jacob Klein, 2013-04-22 Important study focuses on the revival and assimilation of ancient Greek mathematics in the 13th-16th centuries, via Arabic science, and the 16th-century development of symbolic algebra. 1968 edition. Bibliography. |
| a short account of the history of mathematics: String Figures as Mathematics? Eric Vandendriessche, 2015-01-02 This book addresses the mathematical rationality contained in the making of string figures. It does so by using interdisciplinary methods borrowed from anthropology, mathematics, history and philosophy of mathematics. The practice of string figure-making has long been carried out in many societies, and particularly in those of oral tradition. It consists in applying a succession of operations to a string (knotted into a loop), mostly using the fingers and sometimes the feet, the wrists or the mouth. This succession of operations is intended to generate a final figure. The book explores different modes of conceptualization of the practice of string figure-making and analyses various source material through these conceptual tools: it looks at research by mathematicians, as well as ethnographical publications, and personal fieldwork findings in the Chaco, Paraguay, and in the Trobriand Islands, Papua New Guinea, which all give evidence of the rationality that underlies this activity. It concludes that the creation of string figures may be seen as the result of intellectual processes, involving the elaboration of algorithms, and concepts such as operation, sub-procedure, iteration, and transformation. |
| a short account of the history of mathematics: Science , 1888 Vols. for 1911-13 contain the Proceedings of the Helminothological Society of Washington, ISSN 0018-0120, 1st-15th meeting. |
| a short account of the history of mathematics: Nature , 1893 |
The Project Gutenberg eBook #31246: A Short Account of the …
it is intended to give a short and popular account of those leading facts in the history of mathematics which many who are unwilling, or have not the time, to study it systematically may …
A Short Account Of The History Of Mathematics Full PDF
History of Mathematics W. W. Rouse Ball,2015-06-14 Excerpt from A Short Account of the History of Mathematics The subject matter of this book is a historical summary of the development of …
A Short Account of the History of Mathematics ~ Rene …
Descartes’s chief contributions to mathematics were his analytical geometry and his theory of vortices, and it is on his researches in connection with the former of these subjects that his …
The Project Gutenberg eBook #31061: A History of Mathematics
Jan 24, 2010 · The Project Gutenberg EBook of A History of Mathematics, by Florian Cajori This eBook is for the use of anyone anywhere at no cost and with almost no restrictions whatsoever.
A Brief History of Mathematics - Simon Fraser University
Aristotle; mathematics and the physical world (astronomy, geography, mechanics), mathematical formalism (definitions, axioms, proofs via construction)
A HISTORY OF MATHEMATICS - hlevkin
Jan 24, 2010 · The Project Gutenberg EBook of A History of Mathematics, by Florian Cajori This eBook is for the use of anyone anywhere at no cost and with almost no restrictions whatsoever.
A Short Account of the History of Mathematics
In a soothing and enchanting narration, award-winning actor Tony Shalhoub unfolds the origins of mathematics, tracing its development from Phoenician teachings to the formalized practices of …
The History of Mathematics
Published by John Wiley & Sons, Inc., Hoboken, New Jersey. Published simultaneously in Canada.
A Short Account Of The History Of Mathematics [PDF]
Ball,2015-06-14 Excerpt from A Short Account of the History of Mathematics The subject matter of this book is a historical summary of the development of mathematics illustrated by the lives and …
A Short Account of the History of Mathematics ~ Isaac Barrow
Isaac Barrow was born in London in 1630, and died at Cambridge in 1677. He went to school first at Charterhouse (where he was so troublesome that his father was heard to pray that if it …
Isaac Newton (1642 - 1727) - Educational Technology …
From `A Short Account of the History of Mathematics' (4th edition, 1908) by W. W. Rouse Ball. The mathematicians considered in the last chapter commenced the creation of those …
THE HISTORY OF - download.e-bookshelf.de
The history of mathematics : a brief course / Roger L. Cooke. – 3rd ed. p. cm. Includes bibliographical references and index. ISBN 978-1-118-21756-6 (cloth) 1. Mathematics–History. …
A Short Account of the History of Mathematics
it is intended to give a short and popular account of those leading facts in the history of mathematics which many who are unwilling, or have not the time, to study it systematically may …
taste for mathematics - his interest in the subject being first …
A Short Account of the History of Mathematics ~ Joseph Louis Lagrange Created for Lit2Go on the web at fcit.usf.edu
A Short Account of the History of Mathematics ~ British …
A Short Account of the History of Mathematics ~ British Contemporarie. . . Created for Lit2Go on the web at fcit.usf.edu Cotes’s writings were collected and published in 1722 under the titles …
A Short Account of the History of Mathematics ~ Thomas …
A Short Account of the History of Mathematics ~ Thomas Simpson Created for Lit2Go on the web at fcit.usf.edu Clairaut, but instead of solving it by successive approximations, he deduced a …
MATH STORIESAND HISTORIES - UW Faculty Web Server
“The first great mathematician of the 13th century, and indeed the greatest and most productive mathematician of all the Middle Ages, was Leonardo Fibonacci.” As son of a customs official, …
A History of Mathematics - Rutgers University
what I hoped was a critical account of the whole history of mathematics in a series of lectures, trying to go beyond what they would find in a textbook. David was scornful.
MATH 419 Introduction to the History of Mathematics
Evolution of mathematics from earliest to modern times. Major trends in mathematical thought, the interplay of mathematical and technological innovations, and the contributions of great …
John Wallis (1616 - 1703) - Educational Technology …
From `A Short Account of the History of Mathematics' (4th edition, 1908) by W. W. Rouse Ball. John Wallis was born at Ashford on November 22, 1616, and died at Oxford on October 28, 1703.
The Project Gutenberg eBook #31246: A Short Account of …
it is intended to give a short and popular account of those leading facts in the history of mathematics which many who are unwilling, or have not the time, to study it systematically …
A Short Account Of The History Of Mathematics Full PDF
History of Mathematics W. W. Rouse Ball,2015-06-14 Excerpt from A Short Account of the History of Mathematics The subject matter of this book is a historical summary of the development of …
A Short Account of the History of Mathematics ~ Rene …
Descartes’s chief contributions to mathematics were his analytical geometry and his theory of vortices, and it is on his researches in connection with the former of these subjects that his …
The Project Gutenberg eBook #31061: A History of Mathematics
Jan 24, 2010 · The Project Gutenberg EBook of A History of Mathematics, by Florian Cajori This eBook is for the use of anyone anywhere at no cost and with almost no restrictions whatsoever.
A Brief History of Mathematics - Simon Fraser University
Aristotle; mathematics and the physical world (astronomy, geography, mechanics), mathematical formalism (definitions, axioms, proofs via construction)
A HISTORY OF MATHEMATICS - hlevkin
Jan 24, 2010 · The Project Gutenberg EBook of A History of Mathematics, by Florian Cajori This eBook is for the use of anyone anywhere at no cost and with almost no restrictions whatsoever.
A Short Account of the History of Mathematics - cdn.bookey.app
In a soothing and enchanting narration, award-winning actor Tony Shalhoub unfolds the origins of mathematics, tracing its development from Phoenician teachings to the formalized practices of …
The History of Mathematics
Published by John Wiley & Sons, Inc., Hoboken, New Jersey. Published simultaneously in Canada.
A Short Account Of The History Of Mathematics [PDF]
Ball,2015-06-14 Excerpt from A Short Account of the History of Mathematics The subject matter of this book is a historical summary of the development of mathematics illustrated by the lives …
A Short Account of the History of Mathematics ~ Isaac Barrow
Isaac Barrow was born in London in 1630, and died at Cambridge in 1677. He went to school first at Charterhouse (where he was so troublesome that his father was heard to pray that if it …
Isaac Newton (1642 - 1727) - Educational Technology …
From `A Short Account of the History of Mathematics' (4th edition, 1908) by W. W. Rouse Ball. The mathematicians considered in the last chapter commenced the creation of those …
THE HISTORY OF - download.e-bookshelf.de
The history of mathematics : a brief course / Roger L. Cooke. – 3rd ed. p. cm. Includes bibliographical references and index. ISBN 978-1-118-21756-6 (cloth) 1. Mathematics–History. …
A Short Account of the History of Mathematics
it is intended to give a short and popular account of those leading facts in the history of mathematics which many who are unwilling, or have not the time, to study it systematically …
taste for mathematics - his interest in the subject being first …
A Short Account of the History of Mathematics ~ Joseph Louis Lagrange Created for Lit2Go on the web at fcit.usf.edu
A Short Account of the History of Mathematics ~ British …
A Short Account of the History of Mathematics ~ British Contemporarie. . . Created for Lit2Go on the web at fcit.usf.edu Cotes’s writings were collected and published in 1722 under the titles …
A Short Account of the History of Mathematics ~ Thomas …
A Short Account of the History of Mathematics ~ Thomas Simpson Created for Lit2Go on the web at fcit.usf.edu Clairaut, but instead of solving it by successive approximations, he deduced a …
MATH STORIESAND HISTORIES - UW Faculty Web Server
“The first great mathematician of the 13th century, and indeed the greatest and most productive mathematician of all the Middle Ages, was Leonardo Fibonacci.” As son of a customs official, …
A History of Mathematics - Rutgers University
what I hoped was a critical account of the whole history of mathematics in a series of lectures, trying to go beyond what they would find in a textbook. David was scornful.
MATH 419 Introduction to the History of Mathematics
Evolution of mathematics from earliest to modern times. Major trends in mathematical thought, the interplay of mathematical and technological innovations, and the contributions of great …
John Wallis (1616 - 1703) - Educational Technology …
From `A Short Account of the History of Mathematics' (4th edition, 1908) by W. W. Rouse Ball. John Wallis was born at Ashford on November 22, 1616, and died at Oxford on October 28, 1703.
