Ada's Legacy illustrates the depth and diversity of writers, thinkers, and makers who have been inspired by Ada Lovelace, the English mathematician and writer. The volume, which commemorates the bicentennial of Ada's birth in December 1815, celebrates Lovelace's many achievements as well as the impact of her life and work, which reverberated widely since the late nineteenth century. In the 21st century we have seen a resurgence in Lovelace scholarship, thanks to the growth of interdisciplinary thinking and the expanding influence of women in science, technology, engineering and mathematics. Ada's Legacy is a unique contribution to this scholarship, thanks to its combination of papers on Ada's collaboration with Charles Babbage, Ada's position in the Victorian and Steampunk literary genres, Ada's representation in and inspiration of contemporary art and comics, and Ada's continued relevance in discussions around gender and technology in the digital age. With the 200th anniversary of Ada Lovelace's birth on December 10, 2015, we believe that the timing is perfect to publish this collection of papers. Because of its broad focus on subjects that reach far beyond the life and work of Ada herself, Ada's Legacy will appeal to readers who are curious about Ada's enduring importance in computing and the wider world.

Kurt Gödel was the most outstanding logician of the 20th century and a giant in the field. This book is part of a five volume set that makes available all of Gödels writings. The first three volumes, already published, consist of the papers and essays of Gödel. The final two volumes of the set deal with Gödel's correspondence with his contemporary mathematicians, this fourth volume consists of material from correspondents from A-G.

This fascinating narrative history of math in America introduces readers to the diverse and vibrant people behind pivotal moments in the nation's mathematical maturation. Once upon a time in America, few knew or cared about math. In Republic of Numbers, David Lindsay Roberts tells the story of how all that changed, as America transformed into a powerhouse of mathematical thinkers. Covering more than 200 years of American history, Roberts recounts the life stories of twenty-three Americans integral to the evolution of mathematics in this country. Beginning with self-taught Salem mathematician Nathaniel Bowditch's unexpected breakthroughs in ocean navigation and closing with the astounding work Nobel laureate John Nash did on game theory, this book is meant to be read cover to cover. Revealing the marvelous ways in which America became mathematically sophisticated, the book introduces readers to Kelly Miller, the first black man to attend Johns Hopkins, who brilliantly melded mathematics and civil rights activism; Izaak Wirszup, a Polish immigrant who survived the Holocaust and proceeded to change the face of American mathematical education; Grace Hopper, the "Machine Whisperer," who pioneered computer programming; and many other relatively unknown but vital figures. As he brings American history and culture to life, Roberts also explains key mathematical concepts, from the method of least squares, propositional logic, quaternions, and the mean-value theorem to differential equations, non-Euclidean geometry, group theory, statistical mechanics, and Fourier analysis. Republic of Numbers will appeal to anyone who is interested in learning how mathematics has intertwined with American history.

Although the Fields Medal does not have the same public recognition as the Nobel Prizes, they share a similar intellectual standing. It is restricted to one field - that of mathematics. The medal is awarded to the best mathematicians who are 40 or younger, every four years.A list of Fields Medallists and their contributions provides a bird's-eye view of the major developments in mathematics over the past 80 years. It highlights the areas in which, at various times, the greatest progress has been made.The third edition of Fields Medallists' Lectures features additional contributions from: John W Milnor (1962), Enrico Bombieri (1974), Gerd Faltings (1986), Andrei Okounkov (2006), Terence Tao (2006), Cedric Villani (2010), Elon Lindenstrauss (2010), Ngo Bao Chau (2010), Stanislav Smirnov (2010).

Although the Fields Medal does not have the same public recognition as the Nobel Prizes, they share a similar intellectual standing. It is restricted to one field - that of mathematics. The medal is awarded to the best mathematicians who are 40 or younger, every four years.A list of Fields Medallists and their contributions provides a bird's-eye view of the major developments in mathematics over the past 80 years. It highlights the areas in which, at various times, the greatest progress has been made.The third edition of Fields Medallists' Lectures features additional contributions from: John W Milnor (1962), Enrico Bombieri (1974), Gerd Faltings (1986), Andrei Okounkov (2006), Terence Tao (2006), Cedric Villani (2010), Elon Lindenstrauss (2010), Ngo Bao Chau (2010), Stanislav Smirnov (2010).

In this book, Dr. Smithies analyzes the process through which Cauchy created the basic structure of complex analysis, describing first the eighteenth century background before proceeding to examine the stages of Cauchy's own work, culminating in the proof of the residue theorem and his work on expansions in power series. Smithies describes how Cauchy overcame difficulties including false starts and contradictions brought about by over-ambitious assumptions, as well as the improvements that came about as the subject developed in Cauchy's hands. Controversies associated with the birth of complex function theory are described in detail. Throughout, new light is thrown on Cauchy's thinking during this watershed period. This book is the first to make use of the whole spectrum of available original sources and will be recognized as the authoritative work on the creation of complex function theory.

Unlike some other reproductions of classic texts (1) We have not used OCR(Optical Character Recognition), as this leads to bad quality books with introduced typos. (2) In books where there are images such as portraits, maps, sketches etc We have endeavoured to keep the quality of these images, so they represent accurately the original artefact. Although occasionally there may be certain imperfections with these old texts, we feel they deserve to be made available for future generations to enjoy.

Twentieth-century China has been caught between a desire to increase its wealth and power in line with other advanced nations, which, by implication, means copying their institutions, practices and values, whilst simultaneously seeking to preserve China's independence and historically formed identity. Over time, Chinese philosophers, writers, artists and politicians have all sought to reconcile these goals and this book shows how this search for a Chinese way penetrated even the most central, least contested area of modernity: science. Reviving Ancient Chinese Mathematics is a study of the life of one of modern China's most admired scientific figures, the mathematician Wu Wen-Tsun. Negotiating the conflict between progress and tradition, he found a path that not only ensured his political and personal survival, but which also brought him renown as a mathematician of international status who claimed that he stood outside the dominant western tradition of mathematics. Wu Wen-Tsun's story highlights crucial developments and contradictions in twentieth -century China, the significance of which extends far beyond the field of mathematics. On one hand lies the appeal of radical scientific modernity, "mechanisation" in all its forms, and competitiveness within the international scientific community. On the other is an anxiety to preserve national traditions and make them part of the modernisation project. Moreover, Wu's intellectual development also reflects the complex relationship between science and Maoist ideology, because his turn to history was powered by his internalisation of certain aspects of Maoist ideology, including its utilitarian philosophy of science. This book traces how Wu managed to combine political success and international scientific eminence, a story that has wider implications for a new century of increasing Chinese activity in the sciences. As such, it will be of great interest to students and scholars of Chinese history, the history of science and the history and philosophy of mathematics.

Unlike some other reproductions of classic texts (1) We have not used OCR(Optical Character Recognition), as this leads to bad quality books with introduced typos. (2) In books where there are images such as portraits, maps, sketches etc We have endeavoured to keep the quality of these images, so they represent accurately the original artefact. Although occasionally there may be certain imperfections with these old texts, we feel they deserve to be made available for future generations to enjoy.

This is a charming and insightful contribution to an understanding of the "Science Wars" between postmodernist humanism and science, driving toward a resolution of the mutual misunderstanding that has driven the controversy. It traces the root of postmodern theory to a debate on the foundations of mathematics, early in the 20th century then compares developments in mathematics to what took place in the arts and humanities, discussing issues as diverse as literary theory, arts, and artificial intelligence. This is a straight forward, easily understood presentation of what can be difficult theoretical concepts and demonstrates that a pattern of misreading mathematics can be seen on both the part of science and on the part of postmodern thinking. This is a humorous, playful yet deeply serious look at the intellectual foundations of mathematics for those in the humanities and is the perfect critical introduction to the bases of modernism and postmodernism for those in the sciences.

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.

Two veteran math educators demonstrate how some "magnificent mistakes" had profound consequences for our understanding of mathematics' key concepts.
In the nineteenth century, English mathematician William Shanks spent fifteen years calculating the value of pi, setting a record for the number of decimal places. Later, his calculation was reproduced using large wooden numerals to decorate the cupola of a hall in the Palais de la Decouverte in Paris. However, in 1946, with the aid of a mechanical desk calculator that ran for seventy hours, it was discovered that there was a mistake in the 528th decimal place. Today, supercomputers have determined the value of pi to trillions of decimal places.
This is just one of the amusing and intriguing stories about mistakes in mathematics in this layperson's guide to mathematical principles. In another example, the authors show that when we "prove" that every triangle is isosceles, we are violating a concept not even known to Euclid - that of "betweenness." And if we disregard the time-honored Pythagorean theorem, this is a misuse of the concept of infinity. Even using correct procedures can sometimes lead to absurd - but enlightening - results.
Requiring no more than high-school-level math competency, this playful excursion through the nuances of math will give you a better grasp of this fundamental, all-important science.

From cells in our bodies to measuring the universe, big numbers are everywhere We all know that numbers go on forever, that you could spend your life counting and never reach the end of the line, so there can't be such a thing as a 'biggest number'. Or can there? To find out, David Darling and Agnijo Banerjee embark on an epic quest, revealing the answers to questions like: are there more grains of sand on Earth or stars in the universe? Is there enough paper on Earth to write out the digits of a googolplex? And what is a googolplex? Then things get serious. Enter the strange realm between the finite and the infinite, and float through a universe where the rules we cling to no longer apply. Encounter the highest number computable and infinite kinds of infinity. At every turn, a cast of wild and wonderful characters threatens the status quo with their ideas, and each time the numbers get larger.

The 16th-Century intellectual Robert Recorde is chiefly remembered for introducing the equals sign into algebra, yet the greater significance and broader scope of his work is often overlooked. This book presents an authoritative and in-depth analysis of the man, his achievements and his historical importance. This scholarly yet accessible work examines the latest evidence on all aspects of Recorde 's life, throwing new light on a character deserving of greater recognition. Topics and features: presents a concise chronology of Recorde 's life; examines his published works; describes Recorde 's professional activities in the minting of money and the mining of silver, as well as his dispute with William Herbert, Earl of Pembroke; investigates Recorde 's work as a physician, his linguistic and antiquarian interests, and his religious beliefs; discusses the influence of Recorde 's publisher, Reyner Wolfe, in his life; reviews his legacy to 17th-Century science, and to modern computer science and mathematics.

Missionaries, and in particular the Portuguese Assistancy of the Society of Jesus, played a fundamental role in the dissemination of Western scientific knowledge in East Asia. They also brought to Europe a deeper knowledge of Asian countries. This volume brings together a series of essays analyzing important new data on this significant scientific and cultural exchange, including several in-depth discussions of new sources relevant to Jesuit scientific activities at the Chinese Emperor's Court. It includes major contributions examining various case studies that range from the work of some individual missionaries (Karel Slavicek, Guillaume Bonjour) in Beijing during the reigns of Kangxi and Yongzheng to the cultural exchange between a Korean envoy and the Beijing Jesuits during the early 18th century. Focusing in particular on the relationship between science and the arts, this volume also features articles pertaining to the historical contributions made by Tomas Pereira and Jean-Joseph-Marie Amiot, to the exchange of musical knowledge between China and Europe.

This volume provides a unique primary source on the history and philosophy of mathematics and the exact sciences in the mediaeval Arab world. The second of five comprehensive volumes, this book offers a detailed exploration of Arabic mathematics in the eleventh century as embodied in the legacy of the celebrated polymath al-Hasan ibn al-Haytham.

Extensive analyses and annotations from the eminent scholar, Roshdi Rashed, support a number of key Arabic texts from Ibn al-Haytham s treatises in infinitesimal mathematics, translated here into English for the first time. Rashed shows how Ibn al-Haytham s works demonstrate a remarkable mathematical competence in mathematical subjects like the quadrature of the circle and of lunes, the calculation of the volumes of paraboloids, the problem of isoperimetric plane figures and solid figures with equal surface areas, along with the extraction of square and cubic roots.

The present text is complemented by the first volume of "A" "History of Arabic Sciences and Mathematics," which focused on founding figures and commentators in the ninth and tenth centuries Archimedean-Apollonian mathematical School of Baghdad . This constellation of works illustrates the historical and epistemological development of infinitesimal mathematics as it became clearly articulated in the oeuvre of Ibn al-Haytham.

Contributing to a more informed and balanced understanding of the internal currents of the history of mathematics and the exact sciences in Islam, and of its adaptive interpretation and assimilation in the European context, this fundamental text will appeal to historians of ideas, epistemologists and mathematicians at the most advanced levels of research.

L.E.J. Brouwer (1881-1966) is best known for his revolutionary ideas on topology and foundations of mathematics (intuitionism). The present collection contains a mixture of letters; university and faculty correspondence has been included, some of which shed light on the student years, and in particular on the exchange of letters with his PhD adviser, Korteweg.
Acting as the natural sequel to the publication of Brouwer's biography, this book provides instrumental reading for those wishing to gain a deeper understanding of Brouwer and his role in the twentieth century. Striking a good balance of biographical and scientific information, the latter deals with innovations in topology (Cantor-Schoenflies style and the new topology) and foundations. The topological period in his research is well represented in correspondence with Hilbert, Schoenflies, Poincare, Blumenthal, Lebesgue, Baire, Koebe, and foundational topics are discussed in letters exchanged with Weyl, Fraenkel, Heyting, van Dantzig and others. There is also a large part of correspondence on matters related to the interbellum scientific politics.
This book will appeal to both graduate students and researchers with an interest in topology, the history of mathematics, the foundations of mathematics, philosophy and general science."

In this unique insight into the history and philosophy of mathematics and science in the mediaeval Arab world, the eminent scholar Roshdi Rashed illuminates the various historical, textual and epistemic threads that underpinned the history of Arabic mathematical and scientific knowledge up to the seventeenth century. The first of five wide-ranging and comprehensive volumes, this book provides a detailed exploration of Arabic mathematics and sciences in the ninth and tenth centuries. Extensive and detailed analyses and annotations support a number of key Arabic texts, which are translated here into English for the first time. In this volume Rashed focuses on the traditions of celebrated polymaths from the ninth and tenth centuries 'School of Baghdad' - such as the Banu Musa, Thabit ibn Qurra, Ibrahim ibn Sinan, Abu Jafar al-Khazin, Abu Sahl Wayjan ibn Rustam al-Quhi - and eleventh-century Andalusian mathematicians like Abu al-Qasim ibn al-Samh, and al-Mu'taman ibn Hud. The Archimedean-Apollonian traditions of these polymaths are thematically explored to illustrate the historical and epistemological development of 'infinitesimal mathematics' as it became more clearly articulated in the eleventh-century influential legacy of al-Hasan ibn al-Haytham ('Alhazen'). Contributing to a more informed and balanced understanding of the internal currents of the history of mathematics and the exact sciences in Islam, and of its adaptive interpretation and assimilation in the European context, this fundamental text will appeal to historians of ideas, epistemologists, mathematicians at the most advanced levels of research.

This book is a detailed study of Gottfried Wilhelm Leibniz's creation of calculus from 1673 to the 1680s. We examine and analyze the mathematics in several of his early manuscripts as well as various articles published in the Acta Eruditorum. It studies some of the other lesser known "calculi" Leibniz created such as the Analysis Situs, delves into aspects of his logic, and gives an overview of his efforts to construct a Universal Characteristic, a goal that has its distant origin in the Ars Magna of the 13th century Catalan philosopher Raymond Llull, whose work enjoyed a renewed popularity in the century and a half prior to Leibniz.This book also touches upon a new look at the priority controversy with Newton and a Kuhnian interpretation of the nature of mathematical change. This book may be the only integrated treatment based on recent research and should be a thought-provoking contribution to the history of mathematics for scholars and students, interested in either Leibniz's mathematical achievement or general issues in the field.

This open access book discusses several didactic traditions in mathematics education in countries across Europe, including France, the Netherlands, Italy, Germany, the Czech and Slovakian Republics, and the Scandinavian states. It shows that while they all share common features both in the practice of learning and teaching at school and in research and development, they each have special features due to specific historical and cultural developments. The book also presents interesting historical facts about these didactic traditions, the theories and examples developed in these countries.

During Edmund Husserl s lifetime, modern logic and mathematics rapidly developed toward their current outlook and Husserl s writings can be fruitfully compared and contrasted with both 19th century figures (Boole, Schroder, Weierstrass) as well as the 20th century characters (Heyting, Zermelo, Godel). Besides the more historical studies, the internal ones on Husserl alone and the external ones attempting to clarify his role in the more general context of the developing mathematics and logic, Husserl s phenomenology offers also a systematically rich but little researched area of investigation. This volume aims to establish the starting point for the development, evaluation and appraisal of the phenomenology of mathematics. It gathers the contributions of the main scholars of this emerging field into one publication for the first time. Combining both historical and systematic studies from various angles, the volume charts answers to the question "What kind of philosophy of mathematics is phenomenology?""

Arthur Lyon Bowley, the founding father of modern statistics, was an important and colorful figure and a leader in cementing the foundations of statistical methodology, including survey methodology, and of the applications of statistics to economical and social issues during the late 19th and early 20th centuries. In many respects, he was ahead of his time. The giants in this field around that time were largely concentrated in the British Isles and Scandinavian countries; among these contributors, Arthur Bowley was one of the most active in revolutionizing statistical methodology and its economic applications. However, Bowley has been vastly undervalued by subsequent commentators ???????????????????????? while hundreds of articles and books have been written on Karl Pearson, those on Arthur Bowley amount to a dozen or less. This book seeks to remedy this and fill in an important omission in the monographical literature on the history of statistics. In particular, the recent resurgence of interest in poverty research has led to a renewed interest in Bowley's legacy.

This anthology, consisting of two volumes, is intended to equip background researchers, practitioners and students of international mathematics education with intimate knowledge of mathematics education in Russia. Volume I, entitled Russian Mathematics Education: History and World Significance, consists of several chapters written by distinguished authorities from Russia, the United States and other nations. It examines the history of mathematics education in Russia and its relevance to mathematics education throughout the world. The second volume, entitled Russian Mathematics Education: Programs and Practices will examine specific Russian programs in mathematics, their impact and methodological innovations. Although Russian mathematics education is highly respected for its achievements and was once very influential internationally, it has never been explored in depth. This publication does just that.

People, problems, and proofs are the lifeblood of theoretical computer science. Behind the computing devices and applications that have transformed our lives are clever algorithms, and for every worthwhile algorithm there is a problem that it solves and a proof that it works. Before this proof there was an open problem: can one create an efficient algorithm to solve the computational problem? And, finally, behind these questions are the people who are excited about these fundamental issues in our computational world.

In this book the authors draw on their outstanding research and teaching experience to showcase some key people and ideas in the domain of theoretical computer science, particularly in computational complexity and algorithms, and related mathematical topics. They show evidence of the considerable scholarship that supports this young field, and they balance an impressive breadth of topics with the depth necessary to reveal the power and the relevance of the work described.

Beyond this, the authors discuss the sustained effort of their community, revealing much about the culture of their field. A career in theoretical computer science at the top level is a vocation: the work is hard, and in addition to the obvious requirements such as intellect and training, the vignettes in this book demonstrate the importance of human factors such as personality, instinct, creativity, ambition, tenacity, and luck.

The authors' style is characterized by personal observations, enthusiasm, and humor, and this book will be a source of inspiration and guidance for graduate students and researchers engaged with or planning careers in theoretical computer science.

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.