Greenwich has been a centre for scientific computing since the foundation of the Royal Observatory in 1675. Early Astronomers Royal gathered astronomical data with the purpose of enabling navigators to compute their longitude at sea. Nevil Maskelyne in the 18th century organised the work of computing tables for the Nautical Almanac, anticipating later methods used in safety-critical computing systems. The 19th century saw influential critiques of Charles Babbage's mechanical calculating engines, and in the 20th century Leslie Comrie and others pioneered the automation of computation. The arrival of the Royal Naval College in 1873 and the University of Greenwich in 1999 has brought more mathematicians and different kinds of mathematics to Greenwich. In the 21st century computational mathematics has found many new applications. This book presents an account of the mathematicians who worked at Greenwich and their achievements. Features A scholarly but accessible history of mathematics at Greenwich, from the seventeenth century to the present day, with each chapter written by an expert in the field The book will appeal to astronomical and naval historians as well as historians of mathematics and scientific computing.

Tantrasangraha, composed by the renowned Kerala astronomer N lakantha Somay j (c.1444-1545 AD) ranks along with ryabhat ya of ryabhata and Siddh nta iromani of Bh skar c rya as one of the major works which significantly influenced further work on astronomy in India. One of the distinguishing features is the introduction of a major revision of the traditional Indian planetary model. N lakantha arrived at a unified theory of planetary latitudes and a better formulation of the equation of centre for the interior planets (Mercury and Venus) than was previously available.

In preparing the translation and explanatory notes, K. Ramasubramanian and M. S. Sriram have used authentic Sanskrit editions of Tantrasangraha by Surand Kunjan Pillai and K V Sarma. All verses have been translated into English, which have been supplemented with detailed explanations including all necessary mathematical relations, illustrative examples, figures and tables using modern mathematical notation.

Winner of the Mathematics Association of America's 2021 Euler Book Prize, this is an inclusive vision of mathematics—its beauty, its humanity, and its power to build virtues that help us all flourish   “This is perhaps the most important mathematics book of our time. Francis Su shows mathematics is an experience of the mind and, most important, of the heart.�—James Tanton, Global Math Project   “A good book is an entertaining read. A great book holds up a mirror that allows us to more clearly see ourselves and the world we live in. Francis Su’s Mathematics for Human Flourishing is both a good book and a great book.�—MAA Reviews   For mathematician Francis Su, a society without mathematical affection is like a city without concerts, parks, or museums. To miss out on mathematics is to live without experiencing some of humanity’s most beautiful ideas.   In this profound book, written for a wide audience but especially for those disenchanted by their past experiences, an award‑winning mathematician and educator weaves parables, puzzles, and personal reflections to show how mathematics meets basic human desires—such as for play, beauty, freedom, justice, and love—and cultivates virtues essential for human flourishing. These desires and virtues, and the stories told here, reveal how mathematics is intimately tied to being human. Some lessons emerge from those who have struggled, including philosopher Simone Weil, whose own mathematical contributions were overshadowed by her brother’s, and Christopher Jackson, who discovered mathematics as an inmate in a federal prison. Christopher’s letters to the author appear throughout the book and show how this intellectual pursuit can—and must—be open to all.

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.

Theory of Conics, Geometrical Constructions and Practical Geometry: A History of Arabic Sciences and Mathematics Volume 3, provides a unique primary source on the history and philosophy of mathematics and science from the mediaeval Arab world. The present text is complemented by two preceding volumes of A History of Arabic Sciences and Mathematics, which focused on founding figures and commentators in the ninth and tenth centuries, and the historical and epistemological development of 'infinitesimal mathematics' as it became clearly articulated in the oeuvre of Ibn al-Haytham. This volume examines the increasing tendency, after the ninth century, to explain mathematical problems inherited from Greek times using the theory of conics. Roshdi Rashed argues that Ibn al-Haytham completes the transformation of this 'area of activity,' into a part of geometry concerned with geometrical constructions, dealing not only with the metrical properties of conic sections but with ways of drawing them and properties of their position and shape. Including extensive commentary from one of world's foremost authorities on the subject, this book contributes 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.

This volume provides a unique primary source on the history and philosophy of mathematics and science from the mediaeval Arab world. The fourth volume of A History of Arabic Sciences and Mathematics is complemented by three preceding volumes which focused on infinitesimal determinations and other chapters of classical mathematics. This book includes five main works of the polymath Ibn al-Haytham (Alhazen) on astronomy, spherical geometry and trigonometry, plane trigonometry and studies of astronomical instruments on hour lines, horizontal sundials and compasses for great circles. In particular, volume four examines: the increasing tendency to mathematize the inherited astronomy from Greek sources, namely Ptolemy's Almagest; the development of celestial kinematics; new research in spherical geometry and trigonometry required by the new kinematical theory; the study on astronomical instruments and its impact on mathematical research. These new historical materials and their mathematical and historical commentaries contribute to rewriting the history of mathematical astronomy and mathematics from the 11th century on. Including extensive commentary from one of the world's foremost authorities on the subject, this fundamental text is essential reading for historians and mathematicians at the most advanced levels of research.

The Riemann hypothesis (RH) is perhaps the most important outstanding problem in mathematics. This two-volume text presents the main known equivalents to RH using analytic and computational methods. The book is gentle on the reader with definitions repeated, proofs split into logical sections, and graphical descriptions of the relations between different results. It also includes extensive tables, supplementary computational tools, and open problems suitable for research. Accompanying software is free to download. These books will interest mathematicians who wish to update their knowledge, graduate and senior undergraduate students seeking accessible research problems in number theory, and others who want to explore and extend results computationally. Each volume can be read independently. Volume 1 presents classical and modern arithmetic equivalents to RH, with some analytic methods. Volume 2 covers equivalences with a strong analytic orientation, supported by an extensive set of appendices containing fully developed proofs.

This brilliantly illustrated tale of reason, insanity, love and truth recounts the story of Bertrand Russell's life. Raised by his paternal grandparents, young Russell was never told the whereabouts of his parents. Driven by a desire for knowledge of his own history, he attempted to force the world to yield to his yearnings: for truth, clarity and resolve. As he grew older, and increasingly sophisticated as a philosopher and mathematician, Russell strove to create an objective language with which to describe the world - one free of the biases and slippages of the written word. At the same time, he began courting his first wife, teasing her with riddles and leaning on her during the darker days, when his quest was bogged down by paradoxes, frustrations and the ghosts of his family's secrets. Ultimately, he found considerable success - but his career was stalled when he was outmatched by an intellectual rival: his young, strident, brilliantly original student, Ludwig Wittgenstein. An insightful and complexly layered narrative, Logicomix reveals both Russell's inner struggle and the quest for the foundations of logic. Narration by an older, wiser Russell, as well as asides from the author himself, make sense of the story's heady and powerful ideas. At its heart, Logicomix is a story about the conflict between pure reason and the persistent flaws of reality, a narrative populated by great and august thinkers, young lovers, ghosts and insanity.

This book celebrates the life and work of twelve mathematicians who were either born in Wales or who worked in Wales. When the Welsh national anthem was composed in 1856, Wales was at the centre of the industrial revolution, the country was transformed by engineering and technology, and scientific societies flourished across the length and breadth of the land. By 1859, Charles Darwin had published his On the Origin of Species, and one of its outcomes in Wales was a growing tension between religion and science, which influenced peoples' perceptions of their Welshness. By the end of the nineteenth century, that perception had narrowed to include its poetry, music, religion and little else. Following the popularity of his book Count Us In, the author adopts a similar style inviting us to take pride in our mathematicians and demonstrating how the tide has turned.

A History of Mathematics, Third Edition, provides students with a solid background in the history of mathematics and focuses on the most important topics for today's elementary, high school, and college curricula. Students will gain a deeper understanding of mathematical concepts in their historical context, and future teachers will find this book a valuable resource in developing lesson plans based on the history of each topic. This book is ideal for a junior or senior level course in the history of mathematics for mathematics majors intending to become teachers.

Few people have changed the world like the Nobel Prize winners. Their breakthrough discoveries have revolutionised medicine, chemistry, physics and economics. Nobel Life consists of original interviews with twenty-four Nobel Prize winners. Each of them has a unique story to tell. They recall their eureka moments and the challenges they overcame along the way, give advice to inspire future generations and discuss what remains to be discovered. Engaging and thought-provoking, Nobel Life provides an insight into life behind the Nobel Prize winners. A call from Stockholm turned a group of twenty-four academics into Nobel Prize winners. This is their call to the next generations worldwide.

Is anything truly random? Does infinity actually exist? Could we ever see into other dimensions?

In this delightful journey of discovery, David Darling and extraordinary child prodigy Agnijo Banerjee draw connections between the cutting edge of modern maths and life as we understand it, delving into the strange would we like alien music? and venturing out on quests to consider the existence of free will and the fantastical future of quantum computers. Packed with puzzles and paradoxes, mind-bending concepts and surprising solutions, this is for anyone who wants life s questions answered even those you never thought to ask.

A lively and engaging look at logic puzzles and their role in mathematics, philosophy, and recreation Logic puzzles were first introduced to the public by Lewis Carroll in the late nineteenth century and have been popular ever since. Games like Sudoku and Mastermind are fun and engrossing recreational activities, but they also share deep foundations in mathematical logic and are worthy of serious intellectual inquiry. Games for Your Mind explores the history and future of logic puzzles while enabling you to test your skill against a variety of puzzles yourself. In this informative and entertaining book, Jason Rosenhouse begins by introducing readers to logic and logic puzzles and goes on to reveal the rich history of these puzzles. He shows how Carroll's puzzles presented Aristotelian logic as a game for children, yet also informed his scholarly work on logic. He reveals how another pioneer of logic puzzles, Raymond Smullyan, drew on classic puzzles about liars and truthtellers to illustrate Kurt Goedel's theorems and illuminate profound questions in mathematical logic. Rosenhouse then presents a new vision for the future of logic puzzles based on nonclassical logic, which is used today in computer science and automated reasoning to manipulate large and sometimes contradictory sets of data. Featuring a wealth of sample puzzles ranging from simple to extremely challenging, this lively and engaging book brings together many of the most ingenious puzzles ever devised, including the "Hardest Logic Puzzle Ever," metapuzzles, paradoxes, and the logic puzzles in detective stories.

First published in 2004. Routledge is an imprint of Taylor & Francis, an informa company.

Nearly a century before Mondrian made geometrical red, yellow, and blue lines famous, 19th-century mathematician Oliver Byrne employed the color scheme for his 1847 edition of Euclid's mathematical and geometric treatise Elements. Byrne's idea was to use color to make learning easier and "diffuse permanent knowledge." The result has been described as one of the oddest and most beautiful books of the 19th century. The facsimile of Byrne's vivid publication is now available in a beautiful new edition. A masterwork of art and science, it is as beautiful in the boldness of its red, yellow, and blue figures and diagrams as it is in the mathematical precision of its theories. In the simplicity of forms and colors, the pages anticipate the vigor of De Stijl and Bauhaus design. In making complex information at once accessible and aesthetically engaging, this work is a forerunner to the information graphics that today define much of our data consumption.

A foundational work on historical and social studies of quantification What accounts for the prestige of quantitative methods? The usual answer is that quantification is desirable in social investigation as a result of its successes in science. Trust in Numbers questions whether such success in the study of stars, molecules, or cells should be an attractive model for research on human societies, and examines why the natural sciences are highly quantitative in the first place. Theodore Porter argues that a better understanding of the attractions of quantification in business, government, and social research brings a fresh perspective to its role in psychology, physics, and medicine. Quantitative rigor is not inherent in science but arises from political and social pressures, and objectivity derives its impetus from cultural contexts. In a new preface, the author sheds light on the current infatuation with quantitative methods, particularly at the intersection of science and bureaucracy.

The Development of Mathematics in Medieval Europe complements the previous collection of articles by Menso Folkerts, Essays on Early Medieval Mathematics, and deals with the development of mathematics in Europe from the 12th century to about 1500. In the 12th century European learning was greatly transformed by translations from Arabic into Latin. Such translations in the field of mathematics and their influence are here described and analysed, notably al-Khwarizmi's "Arithmetic" -- through which Europe became acquainted with the Hindu-Arabic numerals -- and Euclid's "Elements". Five articles are dedicated to Johannes Regiomontanus, perhaps the most original mathematician of the 15th century, and to his discoveries in trigonometry, algebra and other fields. The knowledge and application of Euclid's "Elements" in 13th- and 15th-century Italy are discussed in three studies, while the last article treats the development of algebra in South Germany around 1500, where much of the modern symbolism used in algebra was developed.

An interdisciplinary history of trigonometry from the mid-sixteenth century to the early twentieth The Doctrine of Triangles offers an interdisciplinary history of trigonometry that spans four centuries, starting in 1550 and concluding in the 1900s. Glen Van Brummelen tells the story of trigonometry as it evolved from an instrument for understanding the heavens to a practical tool, used in fields such as surveying and navigation. In Europe, China, and America, trigonometry aided and was itself transformed by concurrent mathematical revolutions, as well as the rise of science and technology. Following its uses in mid-sixteenth-century Europe as the "foot of the ladder to the stars" and the mathematical helpmate of astronomy, trigonometry became a ubiquitous tool for modeling various phenomena, including animal populations and sound waves. In the late sixteenth century, trigonometry increasingly entered the physical world through the practical disciplines, and its societal reach expanded with the invention of logarithms. Calculus shifted mathematical reasoning from geometric to algebraic patterns of thought, and trigonometry's participation in this new mathematical analysis grew, encouraging such innovations as complex numbers and non-Euclidean geometry. Meanwhile in China, trigonometry was evolving rapidly too, sometimes merging with indigenous forms of knowledge, and with Western discoveries. In the nineteenth century, trigonometry became even more integral to science and industry as a fundamental part of the science and engineering toolbox, and a staple subject in high school classrooms. A masterful combination of scholarly rigor and compelling narrative, The Doctrine of Triangles brings trigonometry's rich historical past full circle into the modern era.

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.

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.

When George Shoobridge Carr (1837-1914) wrote his Synopsis of Elementary Results he intended it as an aid to students preparing for degree-level examinations such as the Cambridge Mathematical Tripos, for which he provided private tuition. He would have been startled to see the two volumes, first published in 1880 and 1886 respectively, reissued more than a century later. Notably, in 1903 the work fell into the hands of the Indian prodigy Srinivasa Ramanujan (1887-1920) and greatly influenced his mathematical education. It is the interaction between a methodical teaching aid and the soaring spirit of a self-taught genius which gives this reissue its interest. Volume 1 contains sections on mathematical tables, algebra, the theory of equations, plane trigonometry, spherical trigonometry, elementary geometry and geometrical conics. Volume 2 covers differential calculus, integral calculus, calculus of variations, differential equations, calculus of finite differences, plane coordinate geometry and solid coordinate geometry.

"Inspiring and informative...deserves to be widely read." -Wall Street Journal "This fun book offers a philosophical take on number systems and revels in the beauty of math." -Science News Because we have ten fingers, grouping by ten seems natural, but twelve would be better for divisibility, and eight is well suited to repeated halving. Grouping by two, as in binary code, has turned out to have its own remarkable advantages. Paul Lockhart presents arithmetic not as rote manipulation of numbers-a practical if mundane branch of knowledge best suited for filling out tax forms-but as a fascinating, sometimes surprising intellectual craft that arises from our desire to add, divide, and multiply important things. Passionate and entertaining, Arithmetic invites us to experience the beauty of mathematics through the eyes of a beguiling teacher. "A nuanced understanding of working with numbers, gently connecting procedures that we once learned by rote with intuitions long since muddled by education... Lockhart presents arithmetic as a pleasurable pastime, and describes it as a craft like knitting." -Jonathon Keats, New Scientist "What are numbers, how did they arise, why did our ancestors invent them, and how did they represent them? They are, after all, one of humankind's most brilliant inventions, arguably having greater impact on our lives than the wheel. Lockhart recounts their fascinating story... A wonderful book." -Keith Devlin, author of Finding Fibonacci

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.

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.