Science & Scientists in Berlin is a richly illustrated guidebook providing informative biographies of 22 major scientists and 11 mathematicians linked to the metropolis, from polymath Gottfried W. Leibniz (b. 1646) to computer inventor Konrad Zuse (d. 1995). As well as renowned figures like Albert Einstein, the book includes scientists who deserve to be better known, such as flight pioneer Otto Lilienthal. Their world-changing achievements are described in a lively and accessible style.   Follow in the footsteps of the protagonists using the comprehensive gazetteer and 18 colour maps which guide you to almost 200 sites associated with their lives: such as plaques, monuments, laboratories, museums, residences & graves.   Anyone who is interested in both science and Berlin’s history, and who wants to learn about the people who created this unique past and experience the places where it comes alive, needs a guidebook like this…

Originally published in 1927, this book presents the collected papers of the renowned Indian mathematician Srinivasa Ramanujan (1887-1920), with editorial contributions from G. H. Hardy (1877-1947). Detailed notes are incorporated throughout and appendices are also included. This book will be of value to anyone with an interest in the works of Ramanujan and the history of mathematics.

When John Napier published his invention of logarithms in 1614 he was announcing one of the greatest advances in the history of mathematics, and log tables were used universally until the mid 1970s. With his Rabdologia, an ingenious calculating tool composed of numbered rods which came to be known as 'Napier's Bones', he enabled people in the marketplace to do multiplication sums without knowing any multiplication tables. Perhaps the most extraordinary thing about this most extrordinary man was that his great inventions were made without the stimulus of talking to other mathematicians in mainstream Europe. Working away in comparative isolation in a tower house in Scotland, Napier produced methods of calculation that literally changed lives all over the world. He is the father of the slide-rule and the grandfather of today's calculators. Despite his achievements, he remains curiously uncelebrated, and this absorbing story of his life aims to give John Napier his true status. This new edition has been redesigned in a new format and has a new cover.

This book traces the history of the MIT Department of Mathematics one of the most important mathematics departments in the world through candid, in-depth, lively conversations with a select and diverse group of its senior members. The process reveals much about the motivation, path, and impact of research mathematicians in a society that owes so much to this little understood and often mystifying section of its intellectual fabric.

At a time when the mathematical experience touches and attracts more laypeople than ever, such a book contributes to our understanding and entertains through its personal approach.

""Leonhard Euler and the Bernoullis" is a fascinating tale of the Bernoulli family and Euler's association with them. Successful merchants in the 16th and 17th centuries, the Bernoullis were driven out of Antwerp during the persecution of the Huguenots and settled first in Frankfurt, and then in Basel, where one of the most remarkable mathematical dynasties evolved with Jacob, Johann, and Daniel Bernoulli the most prominent among them. Euler, fortunate to have had Johann Bernoulli as a tutor, quickly rose to prominence in the academies of Berlin and St. Petersburg, and became the most prolific and profound mathematician that ever lived.

The story of these remarkable men, their great ambitions and dedication to their science-often against parental authority-is skillfully told by the author. Refreshing fictional dialogue is interspersed throughout into an otherwise accurate historical scenario. The book is intended for the young adult audience of middle school and early high school ages, but surely will also appeal to a general audience, with or without mathematical background."

--Walter Gautschi, Purdue University

A symbol of the Divine, a good luck charm, a cosmogram of the world order, a template for fengshui through the ages, the luoshu, or magic squre of order three, has fascinated people of many different cultures.

In this riveting account of cultural detective work, renowned mathematics educator, Frank J. Swetz relates how he uncovered the previously hidden history of the luoshu, from its Chinese origins, shrouded in legend, through its eventual association with Chinese fortunetelling, Daoism, and fengshui, to its incorporation into Islamic astrology and alchemy and its migration into Kabbalistic lore and other occult traditions of the West.

Drawing primarily from historical examples, this book explains the tremendous role that numbers and, in particular, mathematics play in all aspects of our civilization and culture. The lively style and illustrative examples will engage the reader who wants to understand the many ways in which mathematics enables science, technology, art, music, politics, and rational foundations of human thought. Each chapter focuses on the influence of mathematics in a specific field and on a specific historical figure, such as "Pythagoras: Numbers and Symbol"; "Bach: Numbers and Music"; "Descartes: Numbers and Space."

Mathematics has long suffered in the public eye through portrayals of mathematicians as socially inept geniuses devoted to an arcane discipline. In this book, Philip J. Davis addresses this image through a question-and-answer dialogue that lays to rest many of the misnomers and misunderstandings of mathematical study. He answers these questions and more: What is Mathematics? Why is mathematics difficult, and why do I spontaneously react negatively when I hear the word? Davis demonstrates how mathematics surrounds, imbues, and maintains our everyday lives: the digitization and automation of processes like pumping gas, withdrawing cash, and buying groceries are all fueled by mathematics. He takes the reader through a point-by-point explanation of many frequently asked questions about mathematics, gently introducing this Handmaiden of Science and telling you everything you've ever wanted to know about her.

Paul Erdos published more papers during his lifetime than any other mathematician, especially in discrete mathematics. He had a nose for beautiful, simply-stated problems with solutions that have far-reaching consequences across mathematics. This captivating book, written for students, provides an easy-to-understand introduction to discrete mathematics by presenting questions that intrigued Erdos, along with his brilliant ways of working toward their answers. It includes young Erdos's proof of Bertrand's postulate, the Erdos-Szekeres Happy End Theorem, De Bruijn-Erdos theorem, Erdos-Rado delta-systems, Erdos-Ko-Rado theorem, Erdos-Stone theorem, the Erdos-Renyi-Sos Friendship Theorem, Erdos-Renyi random graphs, the Chvatal-Erdos theorem on Hamilton cycles, and other results of Erdos, as well as results related to his work, such as Ramsey's theorem or Deza's theorem on weak delta-systems. Its appendix covers topics normally missing from introductory courses. Filled with personal anecdotes about Erdos, this book offers a behind-the-scenes look at interactions with the legendary collaborator.

This book represents a new departure in science studies: an analysis of a scientific style of writing, situating it within the context of the contemporary style of literature. Its philosophical significance is that it provides a novel way of making sense of the notion of a scientific style. For the first time, the Hellenistic mathematical corpus - one of the most substantial extant for the period - is placed centre-stage in the discussion of Hellenistic culture as a whole. Professor Netz argues that Hellenistic mathematical writings adopt a narrative strategy based on surprise, a compositional form based on a mosaic of apparently unrelated elements, and a carnivalesque profusion of detail. He further investigates how such stylistic preferences derive from, and throw light on, the style of Hellenistic poetry. This important book will be welcomed by all scholars of Hellenistic civilization as well as historians of ancient science and Western mathematics.

The studies brought together in this second collection of articles by Paul Kunitzsch continue the lines of research evident in his previous volume (The Arabs and the Stars). The Arabic materials discussed stem mostly from the early period of the development of Arabic-Islamic astronomy up to about 1000AD, while the Latin materials belong to the first stage of Western contact with Arabic science at the end of the 10th century, and to the peak of Arabic-Latin translation activity in 12th century Spain. The first set of articles focuses upon Ptolemy in the Arabic-Latin tradition, followed by further ones on Arabic astronomy and its reception in the West; the final group looks at details of the transmission of Euclid's Elements.

In 1988 The Mathematical Intelligencer, a quarterly mathematics journal, carried out a poll to find the most beautiful theorem in mathematics. Twenty-four theorems were listed and readers were invited to award each a 'score for beauty'. While there were many worthy competitors, the winner was 'Euler's equation'. In 2004 Physics World carried out a similar poll of 'greatest equations', and found that among physicists Euler's mathematical result came second only to Maxwell's equations. The Stanford mathematician Keith Devlin reflected the feelings of many in describing it as "like a Shakespearian sonnet that captures the very essence of love, or a painting which brings out the beauty of the human form that is far more than just skin deep, Euler's equation reaches down into the very depths of existence". What is it that makes Euler's identity, ei + 1 = 0, so special? In Euler's Pioneering Equation Robin Wilson shows how this simple, elegant, and profound formula links together perhaps the five most important numbers in mathematics, each associated with a story in themselves: the number 1, the basis of our counting system; the concept of zero, which was a major development in mathematics, and opened up the idea of negative numbers; an irrational number, the basis for the measurement of circles; the exponential e, associated with exponential growth and logarithms; and the imaginary number i, the square root of -1, the basis of complex numbers. Following a chapter on each of the elements, Robin Wilson discusses how the startling relationship between them was established, including the several near misses to the discovery of the formula.

This is the second volume of a two-volume work that traces the development of series and products from 1380 to 2000 by presenting and explaining the interconnected concepts and results of hundreds of unsung as well as celebrated mathematicians. Some chapters deal with the work of primarily one mathematician on a pivotal topic, and other chapters chronicle the progress over time of a given topic. This updated second edition of Sources in the Development of Mathematics adds extensive context, detail, and primary source material, with many sections rewritten to more clearly reveal the significance of key developments and arguments. Volume 1, accessible even to advanced undergraduate students, discusses the development of the methods in series and products that do not employ complex analytic methods or sophisticated machinery. Volume 2 examines more recent results, including deBranges' resolution of Bieberbach's conjecture and Nevanlinna's theory of meromorphic functions.

This is the first volume of a two-volume work that traces the development of series and products from 1380 to 2000 by presenting and explaining the interconnected concepts and results of hundreds of unsung as well as celebrated mathematicians. Some chapters deal with the work of primarily one mathematician on a pivotal topic, and other chapters chronicle the progress over time of a given topic. This updated second edition of Sources in the Development of Mathematics adds extensive context, detail, and primary source material, with many sections rewritten to more clearly reveal the significance of key developments and arguments. Volume 1, accessible to even advanced undergraduate students, discusses the development of the methods in series and products that do not employ complex analytic methods or sophisticated machinery. Volume 2 treats more recent work, including deBranges' solution of Bieberbach's conjecture, and requires more advanced mathematical knowledge.

Ten amazing curves personally selected by one of today's most important math writers Curves for the Mathematically Curious is a thoughtfully curated collection of ten mathematical curves, selected by Julian Havil for their significance, mathematical interest, and beauty. Each chapter gives an account of the history and definition of one curve, providing a glimpse into the elegant and often surprising mathematics involved in its creation and evolution. In telling the ten stories, Havil introduces many mathematicians and other innovators, some whose fame has withstood the passing of years and others who have slipped into comparative obscurity. You will meet Pierre Bezier, who is known for his ubiquitous and eponymous curves, and Adolphe Quetelet, who trumpeted the ubiquity of the normal curve but whose name now hides behind the modern body mass index. These and other ingenious thinkers engaged with the challenges, incongruities, and insights to be found in these remarkable curves-and now you can share in this adventure. Curves for the Mathematically Curious is a rigorous and enriching mathematical experience for anyone interested in curves, and the book is designed so that readers who choose can follow the details with pencil and paper. Every curve has a story worth telling.

Felix Hausdorff war nicht nur einer der herausragenden Mathematiker des ersten Drittels des 20. Jahrhunderts, sondern unter Pseudonym auch Verfasser eines Aphorismenbandes, eines erkenntniskritischen Buches, eines Gedichtbandes, eines Theaterstucks und zahlreicher literarischer und philosophischer Essays. Der Band enthalt alle Briefe von und an Hausdorff, die bisher in Bibliotheken und Archiven in aller Welt aufgefunden werden konnten. Unter seinen Korrespondenzpartnern sind neben bedeutenden Mathematikern auch Philosophen, Schriftsteller, Kunstler und Feuilletonisten. Die gesamte Korrespondenz ist sorgfaltig kommentiert. Jeder Korrespondenzpartner wird dem Leser mit einer Kurzbiographie vorgestellt.

An innovative, dramatic graphic novel about the treacherous pursuit of the foundations of mathematics.

This exceptional graphic novel recounts the spiritual odyssey of philosopher Bertrand Russell. In his agonized search for absolute truth, Russell crosses paths with legendary thinkers like Gottlob Frege, David Hilbert, and Kurt Godel, and finds a passionate student in the great Ludwig Wittgenstein. But his most ambitious goal--to establish unshakable logical foundations of mathematics--continues to loom before him. Through love and hate, peace and war, Russell persists in the dogged mission that threatens to claim both his career and his personal happiness, finally driving him to the brink of insanity.

This story is at the same time a historical novel and an accessible explication of some of the biggest ideas of mathematics and modern philosophy. With rich characterizations and expressive, atmospheric artwork, the book spins the pursuit of these ideas into a highly satisfying tale. Probing and ingeniously layered, the book throws light on Russell's inner struggles while setting them in the context of the timeless questions he spent his life trying to answer. At its heart, "Logicomix "is a story about the conflict between an ideal rationality and the unchanging, flawed fabric of reality.Apostolos Doxiadis studied mathematics at Columbia University. His international bestseller "Uncle Petros and Goldbach's Conjecture" spearheaded the impressive entrance of mathematics into the world of storytelling. Apart from his work in fiction, Apostolos has also worked in film and theater and is an internationally recognized expert on the relationship of mathematics to narrative. Christos H. Papadimitriou is C . Lester Hogan professor of computer science at the University of California, Berkeley. He was won numerous international awards for his pioneering work in computational complexity and algorithmic game theory. Christos is the author of the novel "Turing: A Novel about Computation." Alecos Papadatos worked for over twenty years in film animation in France and Greece. In 1997, he became a cartoonist for the major Athens daily "To Vima." He lives in Athens with his wife, Annie Di Donna, and their two children. Annie Di Donna studied graphic arts and painting in France and has worked as animator on many productions, among them "Babar" and "Tintin." Since 1991, she has been running an animation studio with her husband, Alecos Papadatos. This innovative graphic novel is based on the early life of the brilliant philosopher Bertrand Russell. Russell and his impassioned pursuit of truth. Haunted by family secrets and unable to quell his youthful curiosity, Russell became obsessed with a Promethean goal: to establish the logical foundation of all mathematics. In his agonized search for absolute truth, Russell crosses paths with legendary thinkers like Gottlob Frege, David Hilbert, and Kurt Godel, and finds a passionate student in the great Ludwig Wittgenstein. But the object of his defining quest continues to loom before him. Through love and hate, peace and war, Russell persists in the dogged mission that threatens to claim both his career and his personal happiness, finally driving him to the brink of insanity. "Logicomix" is at the same time a historical novel and an accessible explication to some of the biggest ideas of mathematics and modern philosophy. With rich characterizations and expressive, atmospheric artwork, the book spins the pursuit of these ideas into a captivating tale. Probing and ingeniously layered, the book throws light on Russell's inner struggles while setting them in the context of the timeless questions he spent his life trying to answer. At its heart, "Logicomix" is a story about the conflict between an ideal rationality and the unchanging, flawed fabric of reality. "At the heart of Logicomix stands Sir Bertrand Russell, a man determined to find a way of arriving at absolutely right answers. It's a tale within a tale, as the two authors and two graphic artists ardently pursue their own search for truth and appear as characters in the book. As one of them assures us, this won't be 'your typical, usual comic book.' Their quest takes shape and revolves around a lecture given by Russell at an unnamed American university in 1939, a lecture that is really, as he himself tells us, the story of his life and of his pursuit of real logical truth. With Proustian ambition and exhilarating artwork, "Logicomix"'s search for truth encounters head-on the horrors of the Second World War and the agonizing question of whether war can ever be the right choice. Russell himself had to confront that question personally: he endured six months in jail for his pacifism. Russell was determined to find the perfect logical method for solving all problems and attempted to remold human nature in his experimental school at Beacon Hill. Despite repeated failures, Russell never stopped being 'a sad little boy desperately seeking ways out of the deadly vortex of uncertainty.' The book is a visual banquet chronicling Russell's lifelong pursuit of 'certainty in total rationality.' As Logic and Mathematics, the last bastions of certainty, fail him, and as Reason proves not absolute, Russell is forced to face the fact that there is no Royal Road to Truth. Authors Dosiadis and Papadimitriou perfectly echo Russell's passion, with a sincere, easily grasped text amplified with breathtaking visual richness, making this the most satisfying graphic novel of 2009, a titanic artistic achievement of more than 300 pages, all of it pure reading joy."--Nick DiMartino, "Shelf Awareness" "This is an extraordinary graphic novel, wildly ambitious in daring to put into words and drawings the life and thought of one of the great philosophers of the last century, Bertrand Russell. The book is a rare intellectual and artistic achievement, which will, I am sure, lead its readers to explore realms of knowledge they thought were forbidden to them."--Howard Zinn "This magnificent book is about ideas, passions, madness, and the fierce struggle between well-defined principle and the larger good. It follows the great mathematicians--Russell, Whitehead, Frege Cantor, Hilbert--as they agonized to make the foundations of mathematics exact, consistent, and complete. And we see the band of artists and researchers--and the all-seeking dog Manga--creating, and participating in, this glorious narrative."--Barry Mazur, Gerhard Gade University Professor at Harvard University, and author of "Imagining Numbers (Particularly the Square Root of Minus Fifteen)" "The lives of ideas (and those who think them) can be as dramatic and unpredicteable as any superhero fantasy. "Logicomix" is witty, engaging, stylish, visually stunning, and full of surprising sound effects, a masterpiece in a genre for which there is as yet no name."--Michael Harris, professor of mathematics at Universite Paris 7 and member of the Institut Universitaire de France

Der Band VIII der Gesammelten Werke Felix Hausdorffs enthält seine literarischen Schriften, die er unter dem Pseudonym Paul Mongré veröffentlicht hat. Dazu gehören der Gedichtband "Ekstasen", 14 Essays, die zumeist in führenden Literaturzeitschriften der damaligen Zeit erschienen sind sowie das Theaterstück "Der Arzt seiner Ehre", welches in mehr als 30 Städten über 300 mal aufgeführt wurde. In einer Einleitung des Herausgebers wird Hausdorffs literarisches Schaffen in die Literatur der Moderne eingeordnet. Ausführliche Kommentare und Erläuterungen erhellen den entstehungsgeschichtlichen Kontext, weisen alle literarischen, historischen, philosophischen und andere Anspielungen und Zitate sorgfältig nach und erklären Begriffe und Sachverhalte, die nicht allgemein geläufig sind.

This book deals with the mathematical sciences in medieval Islam, and focuses on three main themes. The first is that of the translation of texts (from Greek into Arabic, then from Arabic into Latin), and close attention is paid to terminology and comparative vocabulary. The other themes are those of the technology of the sphere and of astronomical instruments, which are treated both from the mechanical and mathematical point of view. Several of the articles combine these themes, for instance the study of the self-rotating sphere of al-Khazini (12th century) or that on the transmission of spherical trigonometry to the West. Four articles also contain substantial texts, with translation and commentary.

The central theme of this volume lies in the medieval consciousness of mathematics, and the variety of strategies adopted to apply it in other areas, notably natural philosophy. In diachromic terms, Dr Molland considers ways in which ancient mathematics (particularly geometry) was assimilated in the Middle Ages, and how it was radically transformed in the 17th century, especially by Descartes. A pervasive concern is with ideas of scientific progress: the author argues that medieval commentatorial and disputational modes encouraged probing attitudes to existing knowledge, aimed at deepening individual understanding, rather than more aggressive endeavours to advance public knowledge characteristic of later periods. What brought about this change is the subject of several studies here; others form more specifically on individual scholars, in particular the important figure of Roger Bacon.

An essential work on the origins of statistics The Rise of Statistical Thinking, 1820-1900 explores the history of statistics from the field's origins in the nineteenth century through to the factors that produced the burst of modern statistical innovation in the early twentieth century. Theodore Porter shows that statistics was not developed by mathematicians and then applied to the sciences and social sciences. Rather, the field came into being through the efforts of social scientists, who saw a need for statistical tools in their examination of society. Pioneering statistical physicists and biologists James Clerk Maxwell, Ludwig Boltzmann, and Francis Galton introduced statistical models to the sciences by pointing to analogies between their disciplines and the social sciences. A new preface by the author looks at how the book has remained relevant since its initial publication, and considers the current place of statistics in scientific research.

This book presents, in his own words, the life of Hugo Steinhaus (1887-1972), noted Polish mathematician of Jewish background, educator, and mathematical popularizer. A student of Hilbert, a pioneer of the foundations of probability and game theory, and a contributor to the development of functional analysis, he was one of those instrumental to the extraordinary flowering of Polish mathematics before and after World War I. In particular, it was he who "discovered" the great Stefan Banach. Exhibiting his great integrity and wit, Steinhaus's personal story of the turbulent times he survived - including two world wars and life postwar under the Soviet heel - cannot but be of consuming interest. His account of the years spent evading Nazi terror is especially moving. The steadfast honesty and natural dignity he maintained while pursuing a life of demanding scientific and intellectual enquiry in the face of encroaching calamity and chaos show him to be truly a mathematician for all seasons. The present work will be of great interest not only to mathematicians wanting to learn some of the details of the mathematical blossoming that occurred in Poland in the first half of the 20th century, but also to anyone wishing to read a first-hand account of the history of those unquiet times in Europe - and indeed world-wide - by someone of uncommon intelligence and forthrightness situated near an eye of the storm.

How music has influenced mathematics, physics, and astronomy from ancient Greece to the twentieth century Music is filled with mathematical elements. The works of Bach are often said to possess a math-like logic, and Arnold Schoenberg, Iannis Xenakis, and Karlheinz Stockhausen wrote music explicitly based on mathematical principles. Yet Eli Maor argues that it is music that has had the greater influence on mathematics, not the other way around. Starting with Pythagoras, proceeding through Schoenberg, and bringing the story up to the present with contemporary string theory, Music by the Numbers tells a fascinating story of composers, scientists, inventors, and eccentrics who have played a role in the age-old relationship between music, mathematics, and the physical sciences. Weaving compelling stories of historical episodes with Maor's personal reflections as a mathematician and lover of classical music, this book will delight anyone who loves math and music.

In seinem Kopf stellte er die mathematische Welt auf den Kopf. Er berechnete Flussigkeitsstromungen, das Tragheitsmoment, entwickelte die Variationsrechnung und die moderne Zahlentheorie. Als Wissenschaftler steht er auf einer Stufe mit Newton und Einstein.

Konstrukteure in aller Welt arbeiten tagtaglich mit seinen Formeln egal ob es um den Schiffsrumpf der "Alinghi" geht oder um die Schwingungen des "Viaduc de Millau," der Welt hochster Autobahnbrucke.

Dabei war er ein Mensch, der burgerliche Behaglichkeit und Ruhe liebte. Nicht ganz einfach zur Grundungszeit von St. Petersburg inmitten russischer Kaisermorde oder im Berlin zur Zeit der schlesischen Kriege. Und erst recht nicht inmitten einer grossen Kinderschar.

Der Comic von Elena Pini (Graphik) und Alice und Andreas K. Heyne (Text) zeichnet das Leben des genialen Baslers nach, der vor 300 Jahren geboren wurde, mit zwanzig Jahren seine Heimatstadt verliess und nie wieder zuruckkehrte."

A mathematical journey through the most fascinating problems of extremes and how to solve them What is the best way to photograph a speeding bullet? How can lost hikers find their way out of a forest? Why does light move through glass in the least amount of time possible? When Least Is Best combines the mathematical history of extrema with contemporary examples to answer these intriguing questions and more. Paul Nahin shows how life often works at the extremes-with values becoming as small (or as large) as possible-and he considers how mathematicians over the centuries, including Descartes, Fermat, and Kepler, have grappled with these problems of minima and maxima. Throughout, Nahin examines entertaining conundrums, such as how to build the shortest bridge possible between two towns, how to vary speed during a race, and how to make the perfect basketball shot. Moving from medieval writings and modern calculus to the field of optimization, the engaging and witty explorations of When Least Is Best will delight math enthusiasts everywhere.