Robin Wilson

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, eip + 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; p 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.

The History of Mathematics: A Source-Based Approach is a comprehensive history of the development of mathematics. This, the first volume of the two-volume set, takes readers from the beginning of counting in prehistory to 1600 and the threshold of the discovery of calculus. It is notable for the extensive engagement with original—primary and secondary—source material. The coverage is worldwide, and embraces developments, including education, in Egypt, Mesopotamia, Greece, China, India, the Islamic world and Europe. The emphasis on astronomy and its historical relationship to mathematics is new, and the presentation of every topic is informed by the most recent scholarship in the field. The two-volume set was designed as a textbook for the authors' acclaimed year-long course at the Open University. It is, in addition to being an innovative and insightful textbook, an invaluable resource for students and scholars of the history of mathematics. The authors, each among the most distinguished mathematical historians in the world, have produced over fifty books and earned scholarly and expository prizes from the major mathematical societies of the English-speaking world.

Europe has talked itself into a refugee and security crisis. There is, however, a misrecognition of the real challenge facing Europe: the challenge of managing the relationship between Europeans and the currently stigmatized 'others' which it has attracted. Making the case against a 'Europe of walls', Robin Wilson instead proposes a refounding of Europe built on the power of diversity and an ethos of hospitality rather than an institutional thicket serving the market. Providing a robust critique of the moral panic surrounding migrants and security dominating the European public sphere, this book explains why old models for managing cultural diversity in Europe no longer work, and why their obsolescence has led to morbid symptoms. Incorporating discussion of the eurozone crisis and the associated insecurity and the rise of xenophobic populists, Wilson provides an insider account of how the Council of Europe has, over a decade and a half, developed a new paradigm of intercultural integration. He builds theory into this model, drawing on work on cosmopolitanism in the social sciences, also emphasizing the empirical validity of the approach. With its handling of critical issues currently facing Europe, this book is of interest not only to academics across the social sciences, undergraduate students of politics and sociology and postgraduate students of cultural and European studies, but also to policy-makers and NGO practitioners.

The third edition of the Collins Cambridge IGCSE® English Teacher’s Guide supports the Student’s Book, giving teachers everything they need to teach the Cambridge IGCSE® and IGCSE® (9–1) First Language English syllabuses 0500 and 0990. This Teacher’s Guide supports the new syllabuses for first examination in 2020. Exam Board: Cambridge Assessment International Education Level & Subject: IGCSE First Language English (0500), IGCSE (9–1) First Language English (0990) First teaching: September 2018 First examination: June 2020 This title has been endorsed by Cambridge Assessment International Education. Revised and updated to support the 2020 syllabuses and examination formats. Support student progress with teaching sequences that follow the structure of the Student Book, moving from building the key reading and writing skills to applying these skills to specific exam questions and coursework tasks. Save time on planning and preparation with expert support from Julia Burchell, an experienced examiner and trainer. The Teacher Guide includes a two-year scheme of work, differentiated lesson plans, worksheets and PowerPoints for every two- or four-page section of the Student Book, plus extension activities for students aiming for the highest grades. Adapt the resources to the needs of your classes with printable PDFs and editable Word and PowerPoint files. Detailed guidance and annotated sample answers in the Teacher Guide help you and your classes to make the most of the practice examination papers in the Student Book.

Image, Text, Architecture brings a radical and detailed analysis of the modern and contemporary architectural media, addressing issues of architectural criticism, architectural photography and the role of journal editors. It covers examples as diverse as an article by British artist Paul Nash in The Architectural Review, 1940, an early project by French architects Lacaton & Vassal published in the journal 2G, 2001, and recent photography by Hisao Suzuki for the Spanish journal El Croquis. At the intersection of image and text the book also reveals the role of the utopian impulse within the architectural media, drawing on theories of utopian discourse from the work of the French semiotician and art theorist Louis Marin, and the American Marxist critic Fredric Jameson. Through this it builds a fresh theoretical approach to journal studies, revealing a hitherto unexplored dimension of "latent" or "unconscious" discourse within the media portrait of architecture. The purpose of this enquiry is to highlight moments where a different type of critical voice emerges on the architectural journal page, indicating the possibility of a more progressive engagement with the media as a platform for critical and speculative thinking about architecture, and to rethink the journals’ role within architectural history.

Alan Turing has long proved a subject of fascination, but following the centenary of his birth in 2012, the code-breaker, computer pioneer, mathematician (and much more) has become even more celebrated with much media coverage, and several meetings, conferences and books raising public awareness of Turing's life and work. This volume will bring together contributions from some of the leading experts on Alan Turing to create a comprehensive guide to Turing that will serve as a useful resource for researchers in the area as well as the increasingly interested general reader. The book will cover aspects of Turing's life and the wide range of his intellectual activities, including mathematics, code-breaking, computer science, logic, artificial intelligence and mathematical biology, as well as his subsequent influence.

Alan Turing has long proved a subject of fascination, but following the centenary of his birth in 2012, the code-breaker, computer pioneer, mathematician (and much more) has become even more celebrated with much media coverage, and several meetings, conferences and books raising public awareness of Turing's life and work. This volume will bring together contributions from some of the leading experts on Alan Turing to create a comprehensive guide to Turing that will serve as a useful resource for researchers in the area as well as the increasingly interested general reader. The book will cover aspects of Turing's life and the wide range of his intellectual activities, including mathematics, code-breaking, computer science, logic, artificial intelligence and mathematical biology, as well as his subsequent influence.

How many possible sudoku puzzles are there? In the lottery, what is the chance that two winning balls have consecutive numbers? Who invented Pascal's triangle? (it was not Pascal) Combinatorics, the branch of mathematics concerned with selecting, arranging, and listing or counting collections of objects, works to answer all these questions. Dating back some 3000 years, and initially consisting mainly of the study of permutations and combinations, its scope has broadened to include topics such as graph theory, partitions of numbers, block designs, design of codes, and latin squares. In this Very Short Introduction Robin Wilson gives an overview of the field and its applications in mathematics and computer theory, considering problems from the shortest routes covering certain stops to the minimum number of colours needed to colour a map with different colours for neighbouring countries. ABOUT THE SERIES: The Very Short Introductions series from Oxford University Press contains hundreds of titles in almost every subject area. These pocket-sized books are the perfect way to get ahead in a new subject quickly. Our expert authors combine facts, analysis, perspective, new ideas, and enthusiasm to make interesting and challenging topics highly readable.

Image, Text, Architecture brings a radical and detailed analysis of the modern and contemporary architectural media, addressing issues of architectural criticism, architectural photography and the role of journal editors. It covers examples as diverse as an article by British artist Paul Nash in The Architectural Review, 1940, an early project by French architects Lacaton & Vassal published in the journal 2G, 2001, and recent photography by Hisao Suzuki for the Spanish journal El Croquis. At the intersection of image and text the book also reveals the role of the utopian impulse within the architectural media, drawing on theories of utopian discourse from the work of the French semiotician and art theorist Louis Marin, and the American Marxist critic Fredric Jameson. Through this it builds a fresh theoretical approach to journal studies, revealing a hitherto unexplored dimension of "latent" or "unconscious" discourse within the media portrait of architecture. The purpose of this enquiry is to highlight moments where a different type of critical voice emerges on the architectural journal page, indicating the possibility of a more progressive engagement with the media as a platform for critical and speculative thinking about architecture, and to rethink the journals’ role within architectural history.

On October 23, 1852, Professor Augustus De Morgan wrote a letter to a colleague, unaware that he was launching one of the most famous mathematical conundrums in history--one that would confound thousands of puzzlers for more than a century. This is the amazing story of how the "map problem" was solved. The problem posed in the letter came from a former student: What is the least possible number of colors needed to fill in any map (real or invented) so that neighboring counties are always colored differently? This deceptively simple question was of minimal interest to cartographers, who saw little need to limit how many colors they used. But the problem set off a frenzy among professional mathematicians and amateur problem solvers, among them Lewis Carroll, an astronomer, a botanist, an obsessive golfer, the Bishop of London, a man who set his watch only once a year, a California traffic cop, and a bridegroom who spent his honeymoon coloring maps. In their pursuit of the solution, mathematicians painted maps on doughnuts and horseshoes and played with patterned soccer balls and the great rhombicuboctahedron. It would be more than one hundred years (and countless colored maps) later before the result was finally established. Even then, difficult questions remained, and the intricate solution--which involved no fewer than 1,200 hours of computer time--was greeted with as much dismay as enthusiasm. Providing a clear and elegant explanation of the problem and the proof, Robin Wilson tells how a seemingly innocuous question baffled great minds and stimulated exciting mathematics with far-flung applications. This is the entertaining story of those who failed to prove, and those who ultimately did prove, that four colors do indeed suffice to color any map. This new edition features many color illustrations. It also includes a new foreword by Ian Stewart on the importance of the map problem and how it was solved.

Approximately fifty articles that were published in The Mathematical Intelligencer during its first eighteen years. The selection demonstrates the wide variety of attractive articles that have appeared over the years, ranging from general interest articles of a historical nature to lucid expositions of important current discoveries. Each article is introduced by the editors. "... The Mathematical Intelligencer publishes stylish, well-illustrated articles, rich in ideas and usually short on proofs... Many, but not all articles fall within the reach of the advanced undergraduate mathematics major... This book makes a nice addition to any undergraduate mathematics collection that does not already sport back issues of The Mathematical Intelligencer." D. V. Feldman, University of New Hamphire, CHOICE Reviews, June 2001.

The Northern Ireland Experience of Conflict and Agreement presents a salutary warning to the international community against the fashionable view that there is an ‘Irish model’ which can be exported to cauterise ethnic troubles around the globe. The book draws on extensive archive research in London and Dublin on the 1970s power-sharing experiment, and on interviews with senior officials and political figures from the two capitals—as well as reconciliation practitioners—about the negotiation and chequered implementation of the Belfast agreement. It shows how stereotyped conceptions of the problem as a product of ‘ancient hatreds’, allied to solutions based on Realpolitik, have failed to transform Northern Ireland from a fragile peace, following the exhaustion of protracted paramilitary campaigns, to genuine reconciliation. The book concludes with practical proposals for constitutional reforms which would favour genuine power-sharing—rather than merely sharing power out—and set Northern Ireland on the road to the ‘normal’, civic society its long-suffering residents desire. It will be essential reading not only for academics and postgraduates interested in ethnic conflict but also for policy-makers who confront it in practice.

In the tradition of Sylvia Nasar's A Beautiful Mind, this penetrating work explores the amazing imagination and mathematical genius of the man who wrote Alice's Adventures in Wonderland. 100 illustrations.

Lewis Carroll's books have delighted children and adults for generations, but behind their exuberant fantasy and delightful nonsense was the mind of a brilliant mathematician. Now his forgotten achievements in the world of numbers are brought to light by acclaimed author and mathematician Robin Wilson. Here he explores the curious imagination of a man whose pioneering work at Oxford University included investigations into voting patterns and tennis seeding, who dreamt up numerical conundrums in bed at night and who filled his writings with problems, paradoxes, puzzles and teasing games of logic. Taking us into a world of mock turtles and maps, gryphons and gravity, Lewis Carroll in Numberland reveals the singular mind of a genius.

This book picks up the history of mathematics from where Sherlock Holmes in Babylon left it. The 40 articles of Who Gave You the Epsilon? continue the story of the development of mathematics into the nineteenth and twentieth centuries. The articles have all been published in the Mathematical Association of America journals and are in many cases written by distinguished mathematicians such as G. H. Hardy and B. van der Waerden. The articles are arranged thematically to show the development of analysis, geometry, algebra and number theory through this period of time. Each chapter is preceded by a foreword, giving the historical background and setting and the scene, and is followed by an afterword, reporting on advances in our historical knowledge and understanding since the articles first appeared. This book is ideal for anyone wanting to explore the history of mathematics.

From Ancient Greek times, music has been seen as a mathematical art, and the relationship between mathematics and music has fascinated generations. This collection of wide ranging, comprehensive and fully-illustrated papers, authored by leading scholars, presents the link between these two subjects in a lucid manner that is suitable for students of both subjects, as well as the general reader with an interest in music. Physical, theoretical, physiological, acoustic, compositional, and analytical relationships between mathematics and music are unfolded and explored with focus on tuning and temperament, the mathematics of sound, bell-ringing and modern compositional techniques.

Approximately fifty articles that were published in The Mathematical Intelligencer during its first eighteen years. The selection demonstrates the wide variety of attractive articles that have appeared over the years, ranging from general interest articles of a historical nature to lucid expositions of important current discoveries. Each article is introduced by the editors. "... The Mathematical Intelligencer publishes stylish, well-illustrated articles, rich in ideas and usually short on proofs... Many, but not all articles fall within the reach of the advanced undergraduate mathematics major... This book makes a nice addition to any undergraduate mathematics collection that does not already sport back issues of The Mathematical Intelligencer." D. V. Feldman, University of New Hamphire, CHOICE Reviews, June 2001.