Describes the development and the ultimate demise of the practice of mathematics insixteenth century Antwerp. Against the background of the violent history of the Religious Wars the story of the practice of mathematics in Antwerp is told through the lives of two protagonists Michiel Coignet and Peeter Heyns. The book touches on all aspects of practical mathematics from teaching and instrument making to the practice of building fortifications of the practice of navigation. "

This book is a history, analysis, and criticism of what the author calls "postmodern interpretations of science" (PIS) and the closely related "sociology of scientific knowledge" (SSK). This movement traces its origin to Thomas Kuhn's revolutionary work, The Structure of Scientific Revolutions (1962), but is more extreme. It believes that science is a "social construction", having little to do with nature, and is determined by contextual forces such as the race, class, gender of the scientist, laboratory politics, or the needs of the military industrial complex.Since the 1970s, PIS has become fashionable in the humanities, social sciences, and ethnic or women's studies, as well as in the new academic discipline of Science, Technology, and Society (STS). It has been attacked by numerous authors and the resulting conflicts led to the so-called Science Wars of the 1990s. While the present book is also critical of PIS, it focuses on its intellectual and political origins and tries to understand why it became influential in the 1970s. The book is both an intellectual and a political history. It examines the thoughts of Karl Popper, Karl Mannheim, Ludwik Fleck, Thomas Kuhn, Paul Feyerabend, David Bloor, Steve Woolgar, Steve Shapin, Bruno Latour, and PIS-like doctrines in mathematics. It also describes various philosophical contributions to PIS ranging from the Greek sophists to 20th century post-structuralists and argues that the disturbed political atmosphere of the Vietnam War era was critical to the rise of PIS.

In 1644 the Qing dynasty seized power in China. Its Manchu elite were at first seen by most of their subjects as foreigners from beyond the Great Wall, and the consolidation of Qing rule presented significant cultural and political problems, as well as military challenges. It was the Kangxi emperor (r. 1662-1722) who set the dynasty on a firm footing, and one of his main stratagems to achieve this was the appropriation for imperial purposes of the scientific knowledge brought to China by the Jesuit mission (1582-1773). For almost two centuries, the Jesuits put the sciences in the service of evangelization, teaching and practising what came to be known as 'Western learning' among Chinese scholars, many of whom took an active interest in it. After coming to the throne as a teenager, Kangxi began his life-long intervention in mathematical and scientific matters when he forced a return to the use of Western methods in official astronomy. In middle life, he studied astronomy, musical theory and mathematics, with Jesuits as his teachers. In his last years he sponsored a great compilation covering these three disciplines, and set several of his sons to work on this project. All of this activity formed a vital part of his plan to establish Manchu authority over the Chinese. This book explains why Kangxi made the sciences a tool for laying the foundations of empire, and to show how, as part of this process, mathematics was reconstructed as a branch of imperial learning.

Guicciardini presents a comprehensive survey of both the research and teaching of Newtonian calculus, the calculus of "fluxions," over the period between 1700 and 1810. Although Newton was one of the inventors of calculus, the developments in Britain remained separate from the rest of Europe for over a century. While it is usually maintained that after Newton there was a period of decline in British mathematics, the author's research demonstrates that the methods used by researchers of the period yielded considerable success in laying the foundations and investigating the applications of the calculus. Even when "decline" set in, in mid century, the foundations of the reform were being laid, which were to change the direction and nature of the mathematics community. The book considers the importance of Isaac Newton, Roger Cotes, Brook Taylor, James Stirling, Abraham de Moivre, Colin Maclaurin, Thomas Bayes, John Landen and Edward Waring. This will be a useful book for students and researchers in the history of science, philosophers of science and undergraduates studying the history of mathematics.

This volume contains the texts and translations of two Arabic treatises on magic squares, which are undoubtedly the most important testimonies on the early history of that science. It is divided into the three parts: the first and most extensive is on tenth-century construction methods, the second is the translations of the texts, and the third contains the original Arabic texts, which date back to the tenth century.

The Finnish mathematician and astronomer Anders Johan Lexell (1740-1784) was a long-time close collaborator as well as the academic successor of Leonhard Euler at the Imperial Academy of Sciences in Saint Petersburg. Lexell was initially invited by Euler from his native town of Abo (Turku) in Finland to Saint Petersburg to assist in the mathematical processing of the astronomical data of the forthcoming transit of Venus of 1769. A few years later he became an ordinary member of the Academy. This is the first-ever full-length biography devoted to Lexell and his prolific scientific output. His rich correspondence especially from his grand tour to Germany, France and England reveals him as a lucid observer of the intellectual landscape of enlightened Europe. In the skies, a comet, a minor planet and a crater on the Moon named after Lexell also perpetuate his memory.

This book presents a novel methodology to study economic texts. The author investigates discrepancies in these writings by focusing on errors, mistakes, and rounding numbers. In particular, he looks at the acquisition, use, and development of practical mathematics in an ancient society: The Old Babylonian kingdom of Larsa (beginning of the second millennium BCE Southern Iraq). In so doing, coverage bridges a gap between the sciences and humanities. Through this work, the reader will gain insight into discrepancies encountered in economic texts in general and rounding numbers in particular. They will learn a new framework to explain error as a form of economic practice. Researchers and students will also become aware of the numerical and metrological basis for calculation in these writings and how the scribes themselves conceptualized value. This work fills a void in Assyriological studies. It provides a methodology to explore, understand, and exploit statistical data. The anlaysis also fills a void in the history of mathematics by presenting historians of mathematics a method to study practical texts. In addition, the author shows the importance mathematics has as a tool for ancient practitioners to cope with complex economic processes. This serves as a useful case study for modern policy makers into the importance of education in any economy.

Does the universe embody beautiful ideas? Artists as well as scientists throughout human history have pondered this "beautiful question." With Nobel laureate Frank Wilczek as your guide, embark on a voyage of related discoveries, from Plato and Pythagoras up to the present. Wilczek's groundbreaking work in quantum physics was inspired by his intuition to look for a deeper order of beauty in nature. This is the deep logic of the universe-and it is no accident that it is also at the heart of what we find aesthetically pleasing and inspiring. Wilczek is hardly alone among great scientists in charting his course using beauty as his compass. As he reveals in A Beautiful Question, this has been the heart of scientific pursuit from Pythagoras and the ancient belief in the music of the spheres to Galileo, Newton, Maxwell, Einstein, and into the deep waters of twentieth-century physics. Wilczek brings us right to the edge of knowledge today, where the core insights of even the craziest quantum ideas apply principles we all understand. The equations for atoms and light are almost the same ones that govern musical instruments and sound; the subatomic particles that are responsible for most of our mass are determined by simple geometric symmetries. Gorgeously illustrated, A Beautiful Question is a mind-shifting book that braids the age-old quest for beauty and the age-old quest for truth into a thrilling synthesis. It is a dazzling and important work from one of our best thinkers, whose humor and infectious sense of wonder animate every page. Yes: The world is a work of art, and its deepest truths are ones we already feel, as if they were somehow written in our souls.

This volume introduces the reader to Greek and Roman ways of expressing numbers, weights and measures. These are matters often relegated to footnotes or an appendix. Yet the words, the symbols and the calculations used in the classical world have an interest in themselves and often reveal unexpected facets of the culture that employed them. The subject can be complex but this book seeks to cut it to the essentials and to avoid the aridity of larger, more technical treatments. It offers a fluid and readable text, liberally enhanced with tables and specific examples. Chapters cover the cardinal numbers, other number words, inclusive reckoning, symbols, fractions, simple arithmetic, linear measurements, measuring area and volume, measuring weight, capacity and value; financial matters; sizes of pipes and nozzles; measuring time. It is quite simply an indispensable point of reference for every student of classical culture or of ancient texts.

This is a collection of surveys on important mathematical ideas, their origin, their evolution and their impact in current research. The authors are mathematicians who are leading experts in their fields. The book is addressed to all mathematicians, from undergraduate students to senior researchers, regardless of the specialty.

In MATH WITH BAD DRAWINGS, Ben Orlin answers math's three big questions: Why do I need to learn this? When am I ever going to use it? Why is it so hard? The answers come in various forms-cartoons, drawings, jokes, and the stories and insights of an empathetic teacher who believes that math should belong to everyone. Eschewing the tired old curriculum that begins in the wading pool of addition and subtraction and progresses to the shark infested waters of calculus (AKA the Great Weed Out Course), Orlin instead shows us how to think like a mathematician by teaching us a new game of Tic-Tac-Toe, how to understand an economic crisis by rolling a pair of dice, and the mathematical reason why you should never buy a second lottery ticket. Every example in the book is illustrated with his trademark "bad drawings," which convey both his humor and his message with perfect pitch and clarity. Organized by unconventional but compelling topics such as "Statistics: The Fine Art of Honest Lying," "Design: The Geometry of Stuff That Works," and "Probability: The Mathematics of Maybe," MATH WITH BAD DRAWINGS is a perfect read for fans of illustrated popular science.

In 1900, David Hilbert posed a set of 23 unsolved mathematical problems, thus setting an agenda for mathematics that lasted throughout the 20th Century. Some, like Fermat's last theorem, have now been solved; others, such as the Riemann hypothesis, continue to challenge the best mathematical brains of our time. This book addresses the nature of Hilbert and his problems, and their significance for the progress of mathematics in our time.

**The First Ever Maths Book to be a No.1 Bestseller** 'Wonderful ... superb' Daily Mail What makes a bridge wobble when it's not meant to? Billions of dollars mysteriously vanish into thin air? A building rock when its resonant frequency matches a gym class leaping to Snap's 1990 hit I've Got The Power? The answer is maths. Or, to be precise, what happens when maths goes wrong in the real world. As Matt Parker shows us, our modern lives are built on maths: computer programmes, finance, engineering. And most of the time this maths works quietly behind the scenes, until ... it doesn't. Exploring and explaining a litany of glitches, near-misses and mishaps involving the internet, big data, elections, street signs, lotteries, the Roman empire and a hapless Olympic shooting team, Matt Parker shows us the bizarre ways maths trips us up, and what this reveals about its essential place in our world. Mathematics doesn't have good 'people skills', but we would all be better off, he argues, if we saw it as a practical ally. This book shows how, by making maths our friend, we can learn from its pitfalls. It also contains puzzles, challenges, geometric socks, jokes about binary code and three deliberate mistakes. Getting it wrong has never been more fun.

Kurt Goedel (1906 - 1978) was the most outstanding logician of the twentieth century, famous for his hallmark works on the completeness of logic, the incompleteness of number theory, and the consistency of the axiom of choice and the continuum hypothesis. He is also noted for his work on constructivity, the decision problem, and the foundations of computability theory, as well as for the strong individuality of his writings on the philosophy of mathematics. He is less well known for his discovery of unusual cosmological models for Einstein's equations, in theory permitting time travel into the past. The Collected Works is a landmark resource that draws together a lifetime of creative thought and accomplishment. The first two volumes were devoted to Goedel's publications in full (both in original and translation), and the third volume featured a wide selection of unpublished articles and lecture texts found in Goedel's Nachlass. These long-awaited final two volumes contain Goedel's correspondence of logical, philosophical, and scientific interest. Volume IV covers A to G, with H to Z in volume V; in addition, Volume V contains a full inventory of Goedel's Nachlass. All volumes include introductory notes that provide extensive explanatory and historical commentary on each body of work, English translations of material originally written in German (some transcribed from the Gabelsberger shorthand), and a complete bibliography of all works cited. Kurt Goedel: Collected Works is designed to be useful and accessible to as wide an audience as possible without sacrificing scientific or historical accuracy. The only comprehensive edition of Goedel's work available, it will be an essential part of the working library of professionals and students in logic, mathematics, philosophy, history of science, and computer science and all others who wish to be acquainted with one of the great minds of the twentieth century.

Statisticians of the Centuries aims to demonstrate the achievements of statistics to a broad audience, and to commemorate the work of celebrated statisticians. This is done through short biographies that put the statistical work in its historical and sociological context, emphasizing contributions to science and society in the broadest terms rather than narrow technical achievement. The discipline is treated from its earliest times and only individuals born prior to the 20th Century are included. The volume arose through the initiative of the International Statistical Institute (ISI), the principal representative association for international statistics (founded in 1885). Extensive consultations within the statistical community, and with prominent members of ISI in particular, led to the names of the 104 individuals who are included in the volume. The biographies were contributed by 73 authors from across the world. The editors are the well-known statisticians Chris Heyde and Eugene Seneta. Chris Heyde is Professor of Statistics at both Columbia University in New York and the Australian National University in Canberra. He is also Director of the Center for Applied Probability at Columbia. He has twice served as Vice President of the ISI, and also as President of the ISI's Bernoulli Society. Eugene Seneta is Professor of Mathematical Statistics at the University of Sydney and a Member of the ISI. His historical writings focus on 19th Century France and the Russian Empire. He has taught courses on the history of probability-based statistics in U.S. universities. Both editors are Fellows of the Australian Academy of Science and have, at various times, been awarded the Pitman Medal of the Statistical Society of Australia for their distinguished research contributions.

This volume reviews conceptual conflicts at the foundations of physics now and in the past century. The focus is on the conditions and consequences of Einstein's pathbreaking achievements that sealed the decline of the classical notions of space, time, radiation, and matter, and resulted in the theory of relativity. Particular attention is paid to the implications of conceptual conflicts for scientific views of the world at large, thus providing the basis for a comparison of the demise of the mechanical worldview at the turn of the 20th century with the challenges presented by cosmology at the turn of the 21st century. Throughout the work, Einstein's contributions are not seen in isolation but instead set into the wider intellectual context of dealing with the problem of gravitation in the twilight of classical physics; the investigation of the historical development is carried out with a number of epistemological questions in mind, concerning, in particular, the transformation process of knowledge associated with the changing worldviews of physics.

Saunders Mac Lane was an extraordinary mathematician, a dedicated teacher, and a good citizen who cared deeply about the values of science and education. In his autobiography, he gives us a glimpse of his "life and times," mixing the highly personal with professional observations. His recollections bring to life a century of extraordinary accomplishments and tragedies that inspire and educate. Saunders Mac Lane's life covers nearly a century of mathematical developments. During the earlier part of the twentieth century, he participated in the exciting happenings in Goettingen---the Mecca of mathematics. He studied under David Hilbert, Hermann Weyl, and Paul Bernays and witnessed the collapse of a great tradition under the political pressure of a brutal dictatorship. Later, he contributed to the more abstract and general mathematical viewpoints developed in the twentieth century. Perhaps the most outstanding accomplishment during his long and extraordinary career was the development of the concept of categories, together with Samuel Eilenberg, and the creation of a theory that has broad applications in different areas of mathematics, in particular topology and foundations. He was also a keen observer and active participant in the social and political events. As a member and vice president of the National Academy of Science and an advisor to the Administration, he exerted considerable influence on science and education policies in the post-war period. Mac Lane's autobiography takes the reader on a journey through the most important milestones of the mathematical world in the twentieth century.

This volume consists of the English translations of the letters exchanged between Emil Artin to Helmut Hasse written from 1921 until 1958. The letters are accompanied by extensive comments explaining the mathematical background and giving the information needed for understanding these letters. Most letters deal with class field theory and shed a light on the birth of one of its most profound results: Artin's reciprocity law.

This book seeks to explore the history of descriptive geometry in relation to its circulation in the 19th century, which had been favoured by the transfers of the model of the Ecole Polytechnique to other countries. The book also covers the diffusion of its teaching from higher instruction to technical and secondary teaching. In relation to that, there is analysis of the role of the institution - similar but definitely not identical in the different countries - in the field under consideration. The book contains chapters focused on different countries, areas, and institutions, written by specialists of the history of the field. Insights on descriptive geometry are provided in the context of the mathematical aspect, the aspect of teaching in particular to non-mathematicians, and the institutions themselves.

Dirk van Dalen's biography studies the fascinating life of the famous Dutch mathematician and philosopher Luitzen Egbertus Jan Brouwer. Brouwer belonged to a special class of genius; complex and often controversial and gifted with a deep intuition, he had an unparalleled access to the secrets and intricacies of mathematics. Most mathematicians remember L.E.J. Brouwer from his scientific breakthroughs in the young subject of topology and for the famous Brouwer fixed point theorem. Brouwer's main interest, however, was in the foundation of mathematics which led him to introduce, and then consolidate, constructive methods under the name 'intuitionism'. This made him one of the main protagonists in the 'foundation crisis' of mathematics. As a confirmed internationalist, he also got entangled in the interbellum struggle for the ending of the boycott of German and Austrian scientists. This time during the twentieth century was turbulent; nationalist resentment and friction between formalism and intuitionism led to the Mathematische Annalen conflict ('The war of the frogs and the mice'). It was here that Brouwer played a pivotal role. The present biography is an updated revision of the earlier two volume biography in one single book. It appeals to mathematicians and anybody interested in the history of mathematics in the first half of the twentieth century.

How a simple equation reshaped mathematics Leonhard Euler's polyhedron formula describes the structure of many objects-from soccer balls and gemstones to Buckminster Fuller's buildings and giant all-carbon molecules. Yet Euler's theorem is so simple it can be explained to a child. From ancient Greek geometry to today's cutting-edge research, Euler's Gem celebrates the discovery of Euler's beloved polyhedron formula and its far-reaching impact on topology, the study of shapes. Using wonderful examples and numerous illustrations, David Richeson presents this mathematical idea's many elegant and unexpected applications, such as showing why there is always some windless spot on earth, how to measure the acreage of a tree farm by counting trees, and how many crayons are needed to color any map. Filled with a who's who of brilliant mathematicians who questioned, refined, and contributed to a remarkable theorem's development, Euler's Gem will fascinate every mathematics enthusiast. This paperback edition contains a new preface by the author.

The oldest known mathematical table was found in the ancient Sumerian city of Shuruppag in southern Iraq. Since then, tables have been an important feature of mathematical activity and are important precursors to modern computing and information processing. This book contains a series of articles summarising the history of mathematical tables from earliest times until the late twentieth century.

This book offers a new and original hypothesis on the origin of modal ontology, whose roots can be traced back to the mathematical debate about incommensurable magnitudes, which forms the implicit background for Plato's later dialogues and culminates in the definition of being as dynamis in the Sophist. Incommensurable magnitudes - also called dynameis by Theaetetus - are presented as the solution to the problem of non-being and serve as the cornerstone for a philosophy of difference and becoming. This shift also marks the passage to another form of rationality - one not of the measure, but of the mediation. The book argues that the ontology and the rationality which arise out of the discovery of incommensurable constitutes a thread that runs through the entire history of philosophy, one that leads to Kantian transcendentalism and to the philosophies derived from it, such as Hegelianism and philosophical hermeneutics. Readers discover an insightful exchange with some of the most important issues in philosophy, newly reconsidered from the point of view of an ontology of the incommensurable. These issues include the infinite, the continuum, existence, and difference. This text appeals to students and researchers in the fields of ancient philosophy, German idealism, philosophical hermeneutics and the history of mathematics.

In a series of 50 accessible essays, Tony Crilly explains and introduces the mathematical laws and principles - ancient and modern, theoretical and practical, everyday and esoteric - that allow us to understand the world around us. From Pascal's triangle to money management, ideas of relativity to the very real uses of imaginary numbers, 50 Maths Ideas is a complete introduction to the most important mathematical concepts in history.

This book presents contributions of mathematicians covering topics from ancient India, placing them in the broader context of the history of mathematics. Although the translations of some Sanskrit mathematical texts are available in the literature, Indian contributions are rarely presented in major Western historical works. Yet some of the well-known and universally-accepted discoveries from India, including the concept of zero and the decimal representation of numbers, have made lasting contributions to the foundation of modern mathematics. Through a systematic approach, this book examines these ancient mathematical ideas that were spread throughout India, China, the Islamic world, and Western Europe.