Search results for ""Author Ian Stewart""

Mathematician Ian Stewart tells readers what he wishes he had known when he was a student. He takes up subjects ranging from the philosophical to the practical-what mathematics is and why it's worth doing, the relationship between logic and proof, the role of beauty in mathematical thinking, the future of mathematics, how to deal with the peculiarities of the mathematical community, and many others.

Read more less

Flatland is a unique, delightful satire that has charmed readers for over a century. Published in 1884 by the English clergyman and headmaster Edwin A. Abbott, it is the fanciful tale of A. Square, a two-dimensional being who is whisked away by a mysterious visitor to The Land of Three Dimensions, an experience that forever alters his worldview. Like the original, Ian Stewart's commentary takes readers on a strange and wonderful journey. With clarity and wit, Stewart illuminates Abbott's numerous Victorian references and touches on such diverse topics as ancient Babylon, Karl Marx, Mary Shelley's Frankenstein , Mt. Everest, H.G. Wells, and phrenology. The Annotated Flatland makes fascinating connections between Flatland and Abbott's era, resulting in a classic to rival Abbott's own, and a book that will inspire and delight curious readers for generations to come.

Read more less

Imagina un número tan largo que, si lo escribieras, ocuparía todo el universo. Aquí lo vas a encontrar, junto a todo tipo de números reales, imaginarios, racionales, irracionales, positivos, negativos, simples y complejos. Ian Stewart explora las asombrosas propiedades de números que van del cero al infinito y nos enseña cómo han cambiado a lo largo de la historia. El Profesor Stewart nos guía en el descubrimiento de los códigos matemáticos, los sudoku, el cubo de Rubik, la escala musical y cómo un tipo de infinito puede ser mayor que otro. Asimismo, descubre que vivimos en un espacio en once dimensiones. Números increíbles maravillará a los fanáticos de los números y convertirá a aquellos que creen no serlo.

Read more less

New to the Fourth Edition Reorganised and revised chapter seven and thirteen New exercises and examples Expanded, updated references Further historical material on figures besides Galois: Omar Khayyam, Vandermonde, Ruffini, and Abel A new final chapter discussing other directions in which Galois Theory has developed: the inverse Galois problem, differential Galois theory, and a (very) brief introduction to p-adic Galois representations.

Read more less

Most people are familiar with history's great equations: Newton's Law of Gravity, for instance, or Einstein's theory of relativity. But the way these mathematical breakthroughs have contributed to human progress is seldom appreciated. In In Pursuit of the Unknown, celebrated mathematician Ian Stewart untangles the roots of our most important mathematical statements to show that equations have long been a driving force behind nearly every aspect of our lives. Using seventeen of our most crucial equations--including the Wave Equation that allowed engineers to measure a building's response to earthquakes, saving countless lives, and the Black-Scholes model, used by bankers to track the price of financial derivatives over time--Stewart illustrates that many of the advances we now take for granted were made possible by mathematical discoveries. An approachable, lively, and informative guide to the mathematical building blocks of modern life, In Pursuit of the Unknown is a penetrating exploration of how we have also used equations to make sense of, and in turn influence, our world.

Read more less

A retitled and revised edition of Ian Stewart's The Problem of Mathematics, this is the perfect guide to today's mathematics. Read about the latest discoveries, including Andrew Wile's amazing proof of Fermat's Last Theorem, the newest advances in knot theory, the Four Colour Theorem, Chaos Theory, and fake four-dimensial spaces. See how simple concepts from probability theory shed light on the National Lottery and tell you how to maximize your winnings. Discover how infinitesimals become respectable, why there are different kinds of infinity, and how to square the circle with the mathematical equivalent of a pair of scissors.

Read more less

?Las ecuaciones, esos conjuntos de números y símbolos separados por el signo igual, son el alma de las matemáticas, la ciencia y la tecnología. Sin ellas, nuestro mundo no existiría en su forma actual: escondidas para muchos, han constituido una fuerza motriz en la civilización humana durante miles de años, abriendo nuevas perspectivas en campos tan variados como las comunicaciones, la tecnología espacial o la física nuclear. Que así es, es algo que se encarga de demostrar, con su maestría habitual, el distinguido matemático y reputado divulgador Ian Stewart. Para ello ha seleccionado 17 ecuaciones, pertenecientes a dos grupos diferentes. Uno es el de las ecuaciones que revelan regularidades matemáticas, como el teorema de Pitágoras, que nos dice cómo están relacionados los tres lados de un triángulo rectángulo, mientras que el otro es el de las ecuaciones que expresan leyes de la naturaleza, como la ley de gravitación universal de Newton, las ecuaciones del electromagnetismo de Maxwel

Read more less

At its heart, mathematics is about numbers, our fundamental tools for understanding the world. In Professor Stewart's Incredible Numbers, Ian Stewart offers a delightful introduction to the numbers that surround us, from the common (Pi and 2) to the uncommon but no less consequential (1.059463 and 43,252,003,274,489,856,000). Along the way, Stewart takes us through prime numbers, cubic equations, the concept of zero, the possible positions on the Rubik's Cube, the role of numbers in human history, and beyond! An unfailingly genial guide, Stewart brings his characteristic wit and erudition to bear on these incredible numbers, offering an engaging primer on the principles and power of math.

Read more less

In the 1800s mathematicians introduced a formal theory of symmetry: group theory. Now a branch of abstract algebra, this subject first arose in the theory of equations. Symmetry is an immensely important concept in mathematics and throughout the sciences, and its applications range across the entire subject. Symmetry governs the structure of crystals, innumerable types of pattern formation, how systems change their state as parameters vary; and fundamental physics is governed by symmetries in the laws of nature. It is highly visual, with applications that include animal markings, locomotion, evolutionary biology, elastic buckling, waves, the shape of the Earth, and the form of galaxies. In this Very Short Introduction, Ian Stewart demonstrates its deep implications, and shows how it plays a major role in the current search to unify relativity and quantum theory. 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.

Read more less

Eye of the Tiger is the story of one of the most legendary figures in Glasgow Rangers' rich history, a man who epitomised what it meant to be a Ranger. Jock Shaw was a no-nonsense full-back whose fierce, uncompromising tackling earned him the nickname 'Tiger' from club supporters. He joined the Gers from Airdrie in 1938 for GBP2,000 and was a key figure in the Ibrox defence in the immediate post-war years. That defence was dubbed the 'Iron Curtain' because it seemed as unyielding as the barrier that divided Europe at the time. The book charts Jock's extraordinary journey from the coal pit at Bedlay (Annathill) to becoming Rangers' first treble-winning captain. His signing for Rangers started a remarkable association with the club, which lasted over 40 years and saw him serve as team captain, third-team coach and groundsman. He also captained Scotland and shared the distinction of beating England with his brother David. Ian Stewart worked with Tiger Shaw's family to bring you the inside track on his life and career.

Read more less

From ancient Babylon to the last great unsolved problems, Ian Stewart brings us his definitive history of mathematics. In his famous straightforward style, Professor Stewart explains each major development - from the first number systems to chaos theory - and considers how each affected society and changed everyday life forever. Maintaining a personal touch, he introduces all of the outstanding mathematicians of history, from the key Babylonians, Greeks and Egyptians, via Newton and Descartes, to Fermat, Babbage and Godel, and demystifies maths' key concepts without recourse to complicated formulae. Written to provide a captivating historic narrative for the non-mathematician, Taming the Infinite: The Story of Mathematics is packed with fascinating nuggets and quirky asides, and contains 100 illustrations and diagrams to illuminate and aid understanding of a subject many dread, but which has made our world what it is today.

Read more less

Infinity is an intriguing topic, with connections to religion, philosophy, metaphysics, logic, and physics as well as mathematics. Its history goes back to ancient times, with especially important contributions from Euclid, Aristotle, Eudoxus, and Archimedes. The infinitely large (infinite) is intimately related to the infinitely small (infinitesimal). Cosmologists consider sweeping questions about whether space and time are infinite. Philosophers and mathematicians ranging from Zeno to Russell have posed numerous paradoxes about infinity and infinitesimals. Many vital areas of mathematics rest upon some version of infinity. The most obvious, and the first context in which major new techniques depended on formulating infinite processes, is calculus. But there are many others, for example Fourier analysis and fractals. In this Very Short Introduction, Ian Stewart discusses infinity in mathematics while also drawing in the various other aspects of infinity and explaining some of the major problems and insights arising from this concept. He argues that working with infinity is not just an abstract, intellectual exercise but that it is instead a concept with important practical everyday applications, and considers how mathematicians use infinity and infinitesimals to answer questions or supply techniques that do not appear to involve the infinite. 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.

Read more less

A lavishly illustrated practical guide for understanding bridges, with case studies of the world's most famous bridges. How to Read Bridges is a practical introduction to looking at the structure and purpose of bridges and a guide to reading the structural clues embedded in every bridge which allows you to appreciate their variety and ingenuity. Small enough to carry in your pocket and serious enough to provide real answers, this comprehensive guide analyses and explores all types of bridges from around the world from the first millennium to the present day and features the Brooklyn Bridge, Sydney Harbour Bridge, Golden Gate Bridge, Ponte Vecchio, Millau Viaduct and Pont des Arts. The book also explores fundamental concepts of bridge design, key materials and engineering techniques whilst providing an accessible visual guide with intelligent text, using detailed illustrations and cross-sections of technical features.

Read more less

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.

Read more less

Bill Struth is the most celebrated Manager in the history of Rangers Football Club. In his 34 year tenure, he led the club to 30 major trophies and nurtured many of the club's greatest players. To them, he was simply 'Mr. Struth' - a father figure who guided them with the principle that, '... to be a Ranger is to sense the sacred trust of upholding all that such a name means in this shrine of football.'If these words set the ideals for his players to attain, his own personal life was clouded by moments of indiscretion which were to influence the course of his life and career. Drawing on family accounts and Rangers archives, the book explores his early life in Edinburgh and Fife, as well as his celebrated years in Glasgow. It recounts his career in professional athletics and in football with Heart of Midlothian, Clyde and ultimately, Rangers. It reflects on the legacy of the Struth era and his influences that remain at Ibrox today.

Read more less

From Newton's Law of Gravity to the Black-Scholes model used by bankers to predict the markets, equations, are everywhere -- and they are fundamental to everyday life.Seventeen Equations that Changed the World examines seventeen ground-breaking equations that have altered the course of human history. He explores how Pythagoras's Theorem led to GPS and Satnav; how logarithms are applied in architecture; why imaginary numbers were important in the development of the digital camera, and what is really going on with Schrödinger's cat. Entertaining, surprising and vastly informative, Seventeen Equations that Changed the World is a highly original exploration -- and explanation -- of life on earth.

Read more less

The transition from school mathematics to university mathematics is seldom straightforward. Students are faced with a disconnect between the algorithmic and informal attitude to mathematics at school, versus a new emphasis on proof, based on logic, and a more abstract development of general concepts, based on set theory. The authors have many years' experience of the potential difficulties involved, through teaching first-year undergraduates and researching the ways in which students and mathematicians think. The book explains the motivation behind abstract foundational material based on students' experiences of school mathematics, and explicitly suggests ways students can make sense of formal ideas. This second edition takes a significant step forward by not only making the transition from intuitive to formal methods, but also by reversing the process- using structure theorems to prove that formal systems have visual and symbolic interpretations that enhance mathematical thinking. This is exemplified by a new chapter on the theory of groups. While the first edition extended counting to infinite cardinal numbers, the second also extends the real numbers rigorously to larger ordered fields. This links intuitive ideas in calculus to the formal epsilon-delta methods of analysis. The approach here is not the conventional one of 'nonstandard analysis', but a simpler, graphically based treatment which makes the notion of an infinitesimal natural and straightforward. This allows a further vision of the wider world of mathematical thinking in which formal definitions and proof lead to amazing new ways of defining, proving, visualising and symbolising mathematics beyond previous expectations.

Read more less

To Infinity and Beyond explores the idea of infinity in mathematics and art. Eli Maor examines the role of infinity, as well as its cultural impact on the arts and sciences. He evokes the profound intellectual impact the infinite has exercised on the human mind--from the "horror infiniti" of the Greeks to the works of M. C. Escher; from the ornamental designs of the Moslems, to the sage Giordano Bruno, whose belief in an infinite universe led to his death at the hands of the Inquisition. But above all, the book describes the mathematician's fascination with infinity--a fascination mingled with puzzlement.

Read more less

A critically introduced and edited collection of new letters and an essay by the philosopher Adam Ferguson Includes 36 new letters and one essay published for the first time and contextualised within Ferguson's oeuvre Helps to fill in large gaps in Ferguson's biography Presents new angles on major areas of study including the East India Company, the Regency Crisis, Scottish reactions to the French Revolution, and contemporary perceptions of Adam Smith's Political Economy, among others Reveals the political influence that the Moderates of the Scottish Enlightenment, such as Ferguson, Hugh Blair (1718-1800), and Alexander Carlyle (1722-1805), attempted to exert on British foreign policy in the late 1790s This volume will publish for the first time thirty-six, until now, unpublished letters, as well as a new essay on the French Revolution, by the moral philosopher, historian and man-of-letters Adam Ferguson (1723-1816). A major figure in the Scottish Enlightenment, Ferguson has been one of the principal beneficiaries of the refocus of scholarly attention beyond the towering figures of David Hume (1711-1776) and Adam Smith (1723-1790) and toward their larger intellectual network. Penned during the last decades of his life, they were all addressed to his close friend Sir John Macpherson. They concern major topics of the day such as Enlightenment, Empire, and the French Revolution, as well as various illuminating details about Ferguson's final decades. They add considerably to our knowledge of the late Scottish Enlightenment. Located in a recent acquisition at the British Library, these previously unnoticed letters add considerably to our knowledge of Ferguson, his ideas - philosophical, historical, and political - and his intellectual milieu from 1784 to 1815. A substantial introductory essay presents the main findings, while critical apparatus will assist specialists and students alike in understanding this key Enlightenment thinker.

Read more less

Selecting a leader is a momentous and defining choice for a politicalparty. Leaders symbolize their party and are a primary factor inelection outcomes. While much is known about the selection of nationalparty leaders, less is known about the provincial selection process,particularly in the Maritimes. Breaking new ground, ConventionalChoices examines twenty-five different leadership elections inthree maritime provinces. The analysis draws on an extraordinarily richdata set spanning thirty-two years to explore the backgrounds,attitudes, and motivations of those who select party leaders. It is animpressive study that offers fresh insights into leadership selectionand Maritime party politics.

Read more less

Selecting a leader is a momentous and defining choice for a politicalparty. Leaders symbolize their party and are a primary factor inelection outcomes. While much is known about the selection of nationalparty leaders, less is known about the provincial selection process,particularly in the Maritimes. Breaking new ground, ConventionalChoices examines twenty-five different leadership elections inthree maritime provinces. The analysis draws on an extraordinarily richdata set spanning thirty-two years to explore the backgrounds,attitudes, and motivations of those who select party leaders. It is animpressive study that offers fresh insights into leadership selectionand Maritime party politics.

Read more less

Used today in spheres of life as diverse as business strategy, creative writing, medicine, computer science, and theoretical physics, Venn diagrams possess fascinating properties. The basic Venn diagram is both elegantly simple-three overlapping circles that intersect to create eight distinct areas-and conceptually innovative. Devised by English logician John Venn (1834-1923) to visually represent complex logical propositions and algebraic statements, the diagrams drew the excited interest of both scholars and the general public. In Cogwheels of the Mind, statistician and geneticist A. W. F. Edwards provides an accessible and engaging history of the Venn diagram, its reception and evolution, and its presence in such objects and images as Christian iconography, tennis balls, and flags which provide a rich source of Venn diagrams for Edwards, including those of Switzerland, Poland, and Japan (all one-set Venn diagrams), Greenland (a two-set Venn diagram), and Maryland (a three-set device). Edwards begins with a sketch of Venn's life, his discovery of the three-circle design while developing a series of lectures on symbolic logic at Cambridge University, and the publication of his find in an 1880 paper, and, more influentially, his 1881 book, Symbolic Logic. Edwards discusses the rival diagrammatic scheme invented by Charles Dodgson, better known as Lewis Carroll, who also developed a board game based on his design. The author also recreates famous Venn diagrams from history, including Winston Churchill's of 1948 depicting the mutual interests of the British Empire, a united Europe, and the English-speaking world, with the United Kingdom located at the intersection. Edwards goes on to show how different shapes can be linked together to form artistically beautiful and mathematically important, multi-set Venn diagrams, including the author's own influential Adelaide variation. And he delineates the possibilities for expanding the analytic power of these diagrams far beyond those first appreciated by Venn. Edwards even tells readers how to draw complex Venn diagrams on a spherical surface to create "Vennis balls." For anyone interested in mathematics or its history, Cogwheels of the Mind is invaluable and compelling reading.

Read more less

The self plays an integral role in human motivation, cognition, and social identity. A must-have addition to any acceptance and commitment therapy (ACT) practitioner's library, The Self in Practice translates the ACT model's most difficult-yet essential-process into easy-to-apply steps and user-friendly language. Every client who partakes in ACT must identify a self as part of their treatment, and clinicians often report that observing the self is the most difficult of all six core ACT processes. This is because it's so hard for people to shed preconceived notions of "who they really are," and negative perceptions of the self can lead to feelings of low self-worth that stand in the way of treatment.Problems with the self arise when clients orient themselves in the world and learn to relate to others, but these problems can vary considerably. For example, some clients may have deficits in developing a strong sense of self in the first place-particularly if they are diagnosed with autism spectrum conditions (ASC). Depressed clients or those with borderline personality disorder (BPD) may develop a skewed, negative sense of self, and those with narcissistic personality disorder (NPD) may develop an inflated sense of self.With this unique road map, you will learn to apply the complex theory of the self into everyday practice, and help all clients develop empathy, compassion, and flexible perspective taking-leading to better treatment outcomes and better lives for clients.

Read more less

The fantastic first book in the Sunday Times bestselling Science of Discworld seriesWhen a wizardly experiment goes adrift, the wizards of Unseen University find themselves with a pocket universe on their hands: Roundworld, where neither magic nor common sense seems to stand a chance against logic. The Universe, of course, is our own. And Roundworld is Earth. As the wizards watch their accidental creation grow, we follow the story of our universe from the primal singularity of the Big Bang to the internet and beyond. Through this original Terry Pratchett story (with intervening chapters from Cohen and Stewart) we discover how puny and insignificant individual lives are against a cosmic backdrop of creation and disaster. Yet, paradoxically, we see how the richness of a universe based on rules, has led to a complex world and at least one species that tried to get a grip of what was going on. Terry Pratchett is the acclaimed creator of the global bestselling Discworld series, the first of which, The Colour of Magic, was published in 1983. Raising Steam is his fortieth Discworld novel. His books have been widely adapted for stage and screen, and he is the winner of multiple prizes, including the Carnegie Medal, as well as being awarded a knighthood for services to literature. After falling out with his keyboard he now talks to his computer. Occasionally, these days, it answers back.www.terrypratchett.co.uk@terryandrob Professor Ian Stewart is the author of many popular science books. He is the mathematics consultant for New Scientist and a Professor of Mathematics at the University of Warwick. He was awarded the Michael Faraday Prize for furthering the public understanding of science, and in 2001 became a Fellow of the Royal Society. Dr Jack Cohen is an internationally-known reproductive biologist, and lives in Newent, Gloucestershire. Jack has a laboratory in his kitchen, helps couples get pregnant by referring them to colleagues, invents biologically realistic aliens for science fiction writers and, in his spare time, throws boomerangs. Jack, who has more letters to his name than can be repeated here, writes, lectures, talks and campaigns to promote public awareness of science, particularly biology. He is mostly retired.

Read more less

Acclaimed The Science of Discworld centred around an original Pratchett story about the wizards of Discworld. In it they accidentally witnessed the creation and evolution of our universe, a plot which was interleaved with a Cohen & Stewart non-fiction narrative about Big Science. In The Science of Discworld II: The Globe our authors join forces again to see just what happens when the wizards meddle with history in a battle against the elves for the future of humanity on Earth. London is replaced by a dozy Neanderthal village. The Renaissance is given a push. The role of fat women in art is developed. And one very famous playwright gets born and writes The Play. Weaving together a fast-paced Discworld novelette with cutting-edge scientific commentary on the evolution and development of the human mind, culture, language, art, and science, The Globe presents a fascinating and brilliantly original view of the world we live in. The scene of the final epic battle is the first production of A Midsummer's Night Dream at the Globe Theatre.

Read more less

The fourth book in the Science of Discworld series, and this time around dealing with THE REALLY BIG QUESTIONS, Terry Pratchett’s brilliant new Discworld story Judgement Day is annotated with very big footnotes (the interleaving chapters) by mathematician Ian Stewart and biologist Jack Cohen, to bring you a mind-mangling combination of fiction, cutting-edge science and philosophy.Marjorie Daw is a librarian, and takes her job – and indeed the truth of words – very seriously. She doesn’t know it, but her world and ours – Roundworld – is in big trouble. On Discworld, a colossal row is brewing…The Wizards of Unseen University feel responsible for Roundworld (as one would for a pet gerbil). After all, they brought it into existence by bungling an experiment in Quantum ThaumoDynamics. But legal action is being brought against them by Omnians, who say that the Wizards’ god-like actions make a mockery of their noble religion.As the finest legal brains in Discworld (a zombie and a priest) gird their loins to do battle – and when the Great Big Thing in the High Energy Magic Laboratory is switched on – Marjorie Daw finds herself thrown across the multiverse and right in the middle of the whole explosive affair. As God, the Universe and, frankly, Everything Else is investigated by the trio, you can expect world-bearing elephants, quantum gravity in the Escher-verse, evolutionary design, eternal inflation, dark matter, disbelief systems – and an in-depth study of how to invent a better mousetrap.

Read more less

For more than two thousand years a familiarity with mathematics has been regarded as an indispensable part of the intellectual equipment of every cultured person. Today, unfortunately, the traditional place of mathematics in education is in grave danger. The teaching and learning of mathematics has degenerated into the realm of rote memorization, the outcome of which leads to satisfactory formal ability but does not lead to real understanding or to greater intellectual independence. This new edition of Richard Courant's and Herbert Robbins's classic work seeks to address this problem. Its goal is to put the meaning back into mathematics. Written for beginners and scholars, for students and teachers, for philosophers and engineers, What is Mathematics?, Second Edition is a sparkling collection of mathematical gems that offers an entertaining and accessible portrait of the mathematical world. Covering everything from natural numbers and the number system to geometrical constructions and projective geometry, from topology and calculus to matters of principle and the Continuum Hypothesis, this fascinating survey allows readers to delve into mathematics as an organic whole rather than an empty drill in problem solving. With chapters largely independent of one another and sections that lead upward from basic to more advanced discussions, readers can easily pick and choose areas of particular interest without impairing their understanding of subsequent parts. Brought up to date with a new chapter by Ian Stewart, What is Mathematics?, Second Edition offers new insights into recent mathematical developments and describes proofs of the Four-Color Theorem and Fermat's Last Theorem, problems that were still open when Courant and Robbins wrote this masterpiece, but ones that have since been solved. Formal mathematics is like spelling and grammar--a matter of the correct application of local rules. Meaningful mathematics is like journalism--it tells an interesting story. But unlike some journalism, the story has to be true. The best mathematics is like literature--it brings a story to life before your eyes and involves you in it, intellectually and emotionally. What is Mathematics is like a fine piece of literature--it opens a window onto the world of mathematics for anyone interested to view.

Read more less