The emigration of mathematicians from Europe during the Nazi era signaled an irrevocable and important historical shift for the international mathematics world. "Mathematicians Fleeing from Nazi Germany" is the first thoroughly documented account of this exodus. In this greatly expanded translation of the 1998 German edition, Reinhard Siegmund-Schultze describes the flight of more than 140 mathematicians, their reasons for leaving, the political and economic issues involved, the reception of these emigrants by various countries, and the emigrants' continuing contributions to mathematics. The influx of these brilliant thinkers to other nations profoundly reconfigured the mathematics world and vaulted the United States into a new leadership role in mathematics research.

Based on archival sources that have never been examined before, the book discusses the preeminent emigrant mathematicians of the period, including Emmy Noether, John von Neumann, Hermann Weyl, and many others. The author explores the mechanisms of the expulsion of mathematicians from Germany, the emigrants' acculturation to their new host countries, and the fates of those mathematicians forced to stay behind. The book reveals the alienation and solidarity of the emigrants, and investigates the global development of mathematics as a consequence of their radical migration.

An in-depth yet accessible look at mathematics both as a scientific enterprise and human endeavor, "Mathematicians Fleeing from Nazi Germany" provides a vivid picture of a critical chapter in the history of international science.

Mathematics did not spring spontaneously into life, with rules set in stone for all time. Its story is closely linked with the problems of measurement and money that have often driven its progress. Quite Right explains how mathematical ideas have gradually emerged since prehistoric times, so that they pervade almost every aspect of life in the twenty-first century. Many histories of mathematics focus on the activities of those for whom mathematics itself was the motivation. Professor Biggs adopts a wider viewpoint. Making use of new discoveries of artefacts and documents, he explains the part that mathematics has played in the human story, and what that tells us about the nature of mathematics. The story reveals the power and beauty of mathematical concepts, which often belie their utilitarian origins. The twin paradigms of logical justification and algorithmic calculation recur throughout the book. No other book tells the story of mathematics, measurement, and money in this way. Includes secontions on: - The origins of calculation in ancient and medieval times - How mathematics provides answers that are right, and what that means - The impact of trade and the use of money on the development of mathematical algorithms - The use of mathematics for secure communications - How money and information are linked in our electronic world Quite Right is a fascinating story, suitable for anyone interested in the mathematical foundations of the world we live in. Norman Biggs is Professor (Emeritus) of Mathematics at the London School of Economics. He is the author of 12 books, including a perennial best-selling book Discrete Mathematics (Oxford University Press). He has a special interest in measurement and was Chair of the International Society of Weights and Scales Collectors from 2009-14. He served as a Vice President of the British Society for the History of Mathematics in 2014 and is an active member of the British Numismatic Society. 'This is a history of mathematics book with a difference. Instead of the usual chronological sequence of events, presented with mathematical hindsight (interpreting mathematical achievements from a modern point of view), this book tries to see things more from the context of the time - presenting the topics thematically rather than strictly chronologically, and including results and problems only when they fit into the themes ... the level of exposition is first-rate, with a far greater fluency than most mathematical writers can attain ... I am very happy to recommend it wholeheartedly.' Professor Robin Wilson, University of Oxford

Per la prima volta sono riuniti e didatticamente rielaborati a fondo in un manuale e in un CD i testi di base della geometria della visione. L'opera raccoglie i testi originali di Euclide (l'Ottica), Menelao (La Sferica), Alberti (De Pictura), Piero della Francesca (De Prospectiva Pingendi), che hanno dato origine al disegno prospettico rinascimentale e alla moderna geometria proiettiva. L'opera offre la possibilita di unire intuizione e ragionamento, costruendo un'immagine chiara dello sviluppo della matematica legata alla visione, dalle origini classiche, al rinascimento, alla moderna geometria proiettiva. Numerose schede e animazioni interattive facilitano l'intuizione degli argomenti, che sono comunque trattati con il massimo rigore e chiarezza, in una esposizione didatticamente molto efficace."

In 1859, German mathematician Bernhard Riemann presented a paper to the Berlin Academy that would forever change mathematics. The subject was the mystery of prime numbers. At the heart of the presentation was an idea that Riemann had not yet proved--one that baffles mathematicians to this day.

Solving the Riemann Hypothesis could change the way we do business, since prime numbers are the lynchpin for security in banking and e-commerce. It would also have a profound impact on the cutting edge of science, affecting quantum mechanics, chaos theory, and the future of computing. Leaders in math and science are trying to crack the elusive code, and a prize of $1 million has been offered to the winner. In this engaging book, Marcus du Sautoy reveals the extraordinary history behind the holy grail of mathematics and the ongoing quest to capture it.

In line with the emerging field of philosophy of mathematical practice, this book pushes the philosophy of mathematics away from questions about the reality and truth of mathematical entities and statements and toward a focus on what mathematicians actually do--and how that evolves and changes over time. How do new mathematical entities come to be? What internal, natural, cognitive, and social constraints shape mathematical cultures? How do mathematical signs form and reform their meanings? How can we model the cognitive processes at play in mathematical evolution? And how does mathematics tie together ideas, reality, and applications? Roi Wagner uniquely combines philosophical, historical, and cognitive studies to paint a fully rounded image of mathematics not as an absolute ideal but as a human endeavor that takes shape in specific social and institutional contexts. The book builds on ancient, medieval, and modern case studies to confront philosophical reconstructions and cutting-edge cognitive theories. It focuses on the contingent semiotic and interpretive dimensions of mathematical practice, rather than on mathematics' claim to universal or fundamental truths, in order to explore not only what mathematics is, but also what it could be. Along the way, Wagner challenges conventional views that mathematical signs represent fixed, ideal entities; that mathematical cognition is a rigid transfer of inferences between formal domains; and that mathematics' exceptional consensus is due to the subject's underlying reality. The result is a revisionist account of mathematical philosophy that will interest mathematicians, philosophers, and historians of science alike.

In diesem essential beschreibt Heinz Klaus Strick anhand von zahlreichen Beispielen aus verschiedenen Teilgebieten der Wahrscheinlichkeitsrechnung und Statistik, warum es bei stochastischen Fragestellungen immer wieder dazu kommt, dass Aussagen uber Wahrscheinlichkeiten paradox erscheinen, also scheinbar im Widerspruch zu den eigenen Vorstellungen uber Zufallsvorgange stehen. Dabei stellt sich heraus, dass es sich in solchen Fallen oft nur um die Verwechslung von Wahrscheinlichkeiten oder um falsche Modellierungen von zufallsbedingten Vorgangen handelt. Nach der Lekture des essentials werden der Leserin/dem Leser mit Sicherheit manche Phanomene nicht mehr "paradox" vorkommen.

Dieses Buch ladt Sie zum Staunen ein: Erleben Sie, wie etwa Archimedes bereits 1800 Jahre vor der Erfindung der "klassischen" Integralrechnung den Flacheninhalt eines Parabelsegments bestimmen konnte, leiten Sie mit Ibn al-Haitham eine Summenformel fur Quadratzahlen her oder entdecken Sie mit Hamilton die Quaternionen. Die 18 ausgewahlten Ideen werden mithilfe zahlreicher farbiger Abbildungen anschaulich entwickelt - Sie werden von den Gedankengangen der langst verstorbenen Mathematiker verblufft sein! Viele geniale Ansatze wurden von der Nachwelt regelrecht vergessen - die Universalgelehrten aus dem islamischen Kulturkreis etwa sind in Europa kaum noch bekannt, obwohl sie einen wichtigen Beitrag zur Entwicklung der Mathematik geleistet haben. In jedem Kapitel finden Sie daher auch Informationen uber das Leben dieser Personen sowie uber die Zeit, in der sie gelebt haben, Hinweise und Erlauterungen zu weiteren Fragestellungen, mit denen sie sich beschaftigt haben, sowie umfangreiche Hinweise auf weitergehende Literatur, die allgemein zuganglich ist. Die Kapitel sind unabhangig voneinander lesbar - wo es sinnvoll ist, werden Bezuge zu anderen Kapiteln aufgezeigt. Die allermeisten Themen sind mit solidem schulischem Vorwissen aus der Ober- oder Mittelstufe nachvollziehbar, daher eignet sich das Buch fur alle, die sich gern mit Mathematik beschaftigen - aber auch fur Arbeitsgemeinschaften an Schulen und als Anregung fur Facharbeiten.

The classic Heath translation, in a completely new layout with plenty of space and generous margins. An affordable but sturdy student and teacher sewn softcover edition in one volume, with minimal notes and a new index/glossary.

James Clerk Maxwell (1831-1879) had a relatively brief, but remarkable life, lived in his beloved rural home of Glenlair, and variously in Edinburgh, Aberdeen, London and Cambridge. His scholarship also ranged wide - covering all the major aspects of Victorian natural philosophy. He was one of the most important mathematical physicists of all time, coming only after Newton and Einstein. In scientific terms his immortality is enshrined in electromagnetism and Maxwell's equations, but as this book shows, there was much more to Maxwell than electromagnetism, both in terms of his science and his wider life. Maxwell's life and contributions to science are so rich that they demand the expertise of a range of academics - physicists, mathematicians, and historians of science and literature - to do him justice. The various chapters will enable Maxwell to be seen from a range of perspectives. Chapters 1 to 4 deal with wider aspects of his life in time and place, at Aberdeen, King's College London and the Cavendish Laboratory. Chapters 5 to 12 go on to look in more detail at his wide ranging contributions to science: optics and colour, the dynamics of the rings of Saturn, kinetic theory, thermodynamics, electricity, magnetism and electromagnetism with the concluding chapters on Maxwell's poetry and Christian faith.

Was hat ein Gelehrter des 17.Jahrhunderts noch fur die heutigen Naturwissenschaften zu sagen? Eine ganze Menge, so zeigt sich in diesem Buch. Gottfried Wilhelm Leibniz (1646-1716) war ein Universalgenie, und ihm gelangen bahnbrechende Leistungen in fast allen Gebieten der Wissenschaft, insbesondere in der Philosophie (Relativitat von Raum und Zeit), der Mathematik (Infinitesimalrechnung, Determinantentheorie, binares Zahlsystem, Konstruktion einer Rechenmaschine), der Logik (Pradikaten- und Modallogik, Konzept der moeglichen Welten), der Physik (Energieerhaltung und Aktionsprinzip), der Erd- und Menschheitsgeschichte, der Rechtswissenschaft und der Theologie. Diese Leistungen waren aber nicht isoliert, sondern eingebettet in ein umfassendes System, das auf dem Satz vom Widerspruch, dem Satz vom zureichenden Grunde und dem Kontinuitatsprinzip beruhte. Erst durch das Verstandnis dieses Systems erschliessen sich die Einheit und die Spannweite seines Denkens. Jurgen Jost, der wie nur wenige andere die verschiedenen Wissenschaften uberblickt, konfrontiert dieses leibnizsche System mit den Ansatzen, Denkweisen und Ergebnissen der heutigen Naturwissenschaften, insbesondere der Quantenphysik, der Relativitatstheorie und Kosmologie, der modernen Logik, der Evolutionsbiologie und der Hirnforschung. Es zeigt sich, dass das leibnizsche System in vieler Hinsicht noch aktuell ist und sich bewahrt, aber auch in manchen Positionen revidiert werden muss. Hieraus ergeben sich neue Einsichten sowohl in das leibnizsche System als auch in die heutigen Naturwissenschaften.

This is the story of the intellectual and social life of a community, and of its interactions with the wider world. For eight centuries mathematics has been researched and studied at Oxford, and the subject and its teaching have undergone profound changes during that time. This highly readable and beautifully illustrated book reveals the richness and influence of Oxford's mathematical tradition and the fascinating characters that helped to shape it. The story begins with the founding of the University of Oxford and the establishing of the medieval curriculum, in which mathematics had an important role. The Black Death, the advent of printing, the Civil War, and the Newtonian revolution all had a great influence on the development of mathematics at Oxford. So too did many well-known figures: Roger Bacon, Henry Savile, Robert Hooke, Christopher Wren, Edmond Halley, Florence Nightingale, Charles Dodgson (Lewis Carroll), and G. H. Hardy, to name but a few. Later chapters bring us to the 20th century, with some entertaining reminiscences by Sir Michael Atiyah of the thirty years he spent as an Oxford mathematician. In this second edition the story is brought right up to the opening of the new Mathematical Institute in 2013 with a foreword from Marcus du Sautoy and recent developments from Peter M. Neumann.

Who first presented Pascal's triangle? (It was not Pascal.) Who first presented Hamiltonian graphs? (It was not Hamilton.) Who first presented Steiner triple systems? (It was not Steiner.) The history of mathematics is a well-studied and vibrant area of research, with books and scholarly articles published on various aspects of the subject. Yet, the history of combinatorics seems to have been largely overlooked. This book goes some way to redress this and serves two main purposes: 1) it constitutes the first book-length survey of the history of combinatorics; and 2) it assembles, for the first time in a single source, researches on the history of combinatorics that would otherwise be inaccessible to the general reader. Individual chapters have been contributed by sixteen experts. The book opens with an introduction by Donald E. Knuth to two thousand years of combinatorics. This is followed by seven chapters on early combinatorics, leading from Indian and Chinese writings on permutations to late-Renaissance publications on the arithmetical triangle. The next seven chapters trace the subsequent story, from Euler's contributions to such wide-ranging topics as partitions, polyhedra, and latin squares to the 20th century advances in combinatorial set theory, enumeration, and graph theory. The book concludes with some combinatorial reflections by the distinguished combinatorialist, Peter J. Cameron. This book is not expected to be read from cover to cover, although it can be. Rather, it aims to serve as a valuable resource to a variety of audiences. Combinatorialists with little or no knowledge about the development of their subject will find the historical treatment stimulating. A historian of mathematics will view its assorted surveys as an encouragement for further research in combinatorics. The more general reader will discover an introduction to a fascinating and too little known subject that continues to stimulate and inspire the work of scholars today.

Dieses Buch macht einen Spaziergang durch die vielfaltige Welt der Zahl Drei. Sie zeigt sich hierbei in vielen unterschiedlichen Verkleidungen, denn von der Musik uber die bildende Kunst bis hin zur Geschichte spielt die Drei eine wichtige, meist unverzichtbare Rolle. Das Buch geht darauf ein und zeigt, dass diese Zahl bemerkenswerte Eigenschaften hat, die auch Nicht-Mathematikern zuganglich sind und die hier im leichten Ton des Spaziergangers ausgebreitet werden: Musikalische Harmonien werden mathematisch gedeutet, die Konstruktion von Fraktalen wird durch einfache Programme demonstriert, ein beruhmtes Gemalde der italienischen Renaissance wird in Bezug auf die Drei analysiert, die antike chinesische Wehrtechnik wird mit moderner, effizienter Computerarithmetik zusammengefuhrt. Papierfaltungen, die Heiligen Drei Koenige sowie die papstliche Tiara durfen hier naturlich nicht fehlen. Der mathematischen Sorgfalt, der Vorgehensweise und den Techniken der Mathematik wird besonderes Augenmerk gewidmet, ohne dass der Text durch mathematische Einzelheiten uberladen wird. So wird aus der Diskussion der Zahl Drei ein Streifzug durch vertrautes Gelande mit unerwarteten Ausblicken.

Dieser Band enthalt zum ersten Mal eine Darstellung der Mathematik Altagyptens und Mesopotamiens in deutscher Sprache. Einer der beiden Hochkulturen verdanken wir den Ursprung der Schrift und damit auch der Zahldarstellung; sie stellen damit den Ursprung unserer Zivilisation dar. Infolge der geringen Anzahl erhaltener mathematischer Papyri gelingt die Beschreibung der altagyptischen Mathematik umfassend. Anders die UEberlieferungssituation in Mesopotamien: Die dort verwendeten Tontafeln wurden meist getrocknet oder gebrannt und haben damit die Jahrhunderte uberdauert. Von der Vielzahl der uberlieferten mathematischen Tontafeln wird hier nur ein reprasentativer Ausschnitt gegeben; dabei werden neuere Tendenzen der geometrischen Interpretation verwendet. Die Darstellung erfolgt anschaulich und exemplarisch; es werden keine Kenntnisse von Hieroglyphen oder Keilschrift voraussetzt.

Infinity is a profoundly counter-intuitive and brain-twisting subject that has inspired some great thinkers - and provoked and shocked others. The ancient Greeks were so horrified by the implications of an endless number that they drowned the man who gave away the secret. And a German mathematician was driven mad by the repercussions of his discovery of transfinite numbers. Brian Clegg and Oliver Pugh's brilliant graphic tour of infinity features a cast of characters ranging from Archimedes and Pythagoras to al-Khwarizmi, Fibonacci, Galileo, Newton, Leibniz, Cantor, Venn, Goedel and Mandelbrot, and shows how infinity has challenged the finest minds of science and mathematics. Prepare to enter a world of paradox.

During the Victorian era, industrial and economic growth led to a phenomenal rise in productivity and invention. That spirit of creativity and ingenuity was reflected in the massive expansion in scope and complexity of many scientific disciplines during this time, with subjects evolving rapidly and the creation of many new disciplines. The subject of mathematics was no exception and many of the advances made by mathematicians during the Victorian period are still familiar today; matrices, vectors, Boolean algebra, histograms, and standard deviation were just some of the innovations pioneered by these mathematicians.
This book constitutes perhaps the first general survey of the mathematics of the Victorian period. It assembles in a single source research on the history of Victorian mathematics that would otherwise be out of the reach of the general reader. It charts the growth and institutional development of mathematics as a profession through the course of the 19th century in England, Scotland, Ireland, and across the British Empire. It then focuses on developments in specific mathematical areas, with chapters ranging from developments in pure mathematical topics (such as geometry, algebra, and logic) to Victorian work in the applied side of the subject (including statistics, calculating machines, and astronomy). Along the way, we encounter a host of mathematical scholars, some very well known (such as Charles Babbage, James Clerk Maxwell, Florence Nightingale, and Lewis Carroll), others largely forgotten, but who all contributed to the development of Victorian mathematics.

Inspired by Albert Einstein's theory of relativity and Bertrand Russell and David Hilbert's pursuit of the fundamental rules of mathematics, some of the most brilliant minds of the generation came together in post-World War I Vienna to present the latest theories in mathematics, science, and philosophy and to build a strong foundation for scientific investigation. Composed of such luminaries as Kurt Goedel and Rudolf Carnap, and stimulated by the works of Ludwig Wittgenstein and Karl Popper, the Vienna Circle left an indelible mark on science. Exact Thinking in Demented Times tells the often outrageous, sometimes tragic, and never boring stories of the men who transformed scientific thought. A revealing work of history, this landmark book pays tribute to those who dared to reinvent knowledge from the ground up.

What is the best way to photograph a speeding bullet? Why does light move through glass in the least amount of time possible? How can lost hikers find their way out of a forest? What will rainbows look like in the future? Why do soap bubbles have a shape that gives them the least area?

By combining the mathematical history of extrema with contemporary examples, Paul J. Nahin answers these intriguing questions and more in this engaging and witty volume. He shows how life often works at the extremes--with values becoming as small (or as large) as possible--and how mathematicians over the centuries have struggled to calculate these problems of minima and maxima. From medieval writings to the development of modern calculus to the current field of optimization, Nahin tells the story of Dido's problem, Fermat and Descartes, Torricelli, Bishop Berkeley, Goldschmidt, and more. Along the way, he explores how to build the shortest bridge possible between two towns, how to shop for garbage bags, how to vary speed during a race, and how to make the perfect basketball shot.

Written in a conversational tone and requiring only an early undergraduate level of mathematical knowledge, "When Least Is Best" is full of fascinating examples and ready-to-try-at-home experiments. This is the first book on optimization written for a wide audience, and math enthusiasts of all backgrounds will delight in its lively topics.

On the road toward a history of turbulence, this book focuses on what the actors in this research field have identified as the "turbulence problem". Turbulent flow rose to prominence as one of the most persistent challenges in science. At different times and in different social and disciplinary settings, the nature of this problem has changed in response to changing research agendas. This book does not seek to provide a comprehensive account, but instead an exemplary exposition on the environments in which problems become the subjects of research agendas, with particular emphasis on the first half of the 20th century.

A central figure in the early years of the French Revolution, Nicolas de Condorcet (1743-94) was active as a mathematician, philosopher, politician and economist. He argued for the values of the Enlightenment, from religious toleration to the abolition of slavery, believing that society could be improved by the application of rational thought. In this essay, first published in 1785, Condorcet analyses mathematically the process of making majority decisions, and seeks methods to improve the likelihood of their success. The work was largely forgotten in the nineteenth century, while those who did comment on it tended to find the arguments obscure. In the second half of the twentieth century, however, it was rediscovered as a foundational work in the theory of voting and societal preferences. Condorcet presents several significant results, among which Condorcet's paradox (the non-transitivity of majority preferences) is now seen as the direct ancestor of Arrow's paradox.

Der Band enthalt zum ersten Mal in deutscher Sprache grundlegende Themen der chinesischen und indischen Mathematik, die den Nahrboden fur spatere Fragestellungen bereiten. Die nicht zu uberschatzende Rolle, die islamische Gelehrte bei der Entwicklung der Algebra und der Verbreitung des Ziffernsystems gespielt haben, wird in exemplarischen Episoden veranschaulicht. Unterhaltsam wird geschildert, wie Fibonacci die orientalische Aufgabenkultur nach Italien bringt. Zahlreiche Beispiele demonstrieren das neue kaufmannische Rechnen, dessen Methoden sich in ganz Europa verbreiten. In Deutschland erwachst eine neue Generation von Rechenmeistern, die mit ihren erstmals im Druck verbreiteten Schriften eine ungeheure Popularisierung des Rechnens bewirken. UEberraschende Einblicke in die Historie bieten die Kapitel uber die Vermittlung mathematischen Wissens in Kloestern und Universitaten. Das Buch ist eine Fundgrube fur historisch Interessierte; zahlreiche Aufgaben bieten vergnuglichen Stoff fur Unterricht, Vorlesung und Selbststudium.

Dieser Band fuhrt 16 Aufsatze von Herbert Breger zusammen, die um Leibniz' Arbeiten zur Mathematik und Physik und ihre philosophischen Voraussetzungen kreisen. Drei interessante und ungewoehnliche Aspekte stehen hierbei im Vordergrund: Kontinuum, Analysis und Informales. Leibniz' Kontinuum und seine Analysis sind gerade wegen ihres Unterschieds zur heutigen Mathematik interessant. Anhand zahlreicher Beispiele wird ferner die Frage nach dem Verhaltnis zwischen der mathematischen Rationalitat und der Kunst gestellt und die nach den engen Beziehungen zwischen Mathematik und Philosophie bei Leibniz eroertert. Es wird gezeigt, dass der Leibniz zugeschriebene Brief zum Prinzip der kleinsten Wirkung, der Anlass zu einem Streit zwischen Maupertuis, Samuel Koenig und Voltaire wurde, eine Falschung war. Das Buch erscheint im Leibniz-Jahr 2016, in dem auch der X. Leibniz-Kongress stattfindet.

This classic study by the eminent Dutch historian of science E. J. Dijksterhuis (1892-1965) presents the work of the Greek mathematician and mechanical engineer to the modern reader. With meticulous scholarship, Dijksterhuis surveys the whole range of evidence on Archimedes' life and the 2000-year history of the manuscripts and editions of the text, and then undertakes a comprehensive examination of all the extant writings. Originally published in 1987. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

These selected mathematical writings cover the years when the foundations were laid for the theory of numbers, analytic geometry, and the calculus. Originally published in 1986. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.