Matematikens historia

George Dyson's fascinating account of the early years of computers: Turing's Cathedral is the story behind how the PC, ipod, smartphone and almost every aspect of modern life came into being.In 1945 a small group of brilliant engineers and mathematicians gathered at the Institute for Advanced Study in Princeton, determined to build a computer that would make Alan Turing's theory of a 'universal machine' reality. Led by the polymath émigré John von Neumann, they created the numerical framework that underpins almost all modern computing - and ensured that the world would never be the same again.George Dyson is a historian of technology whose interests include the development (and redevelopment) of the Aleut kayak. He is the author of Baidarka; Project Orion; and Darwin Among the Machines.'Unusual, wonderful, visionary' Francis Spufford, Guardian'Fascinating . . . the story Dyson tells is intensely human . . . a gripping account of ideas and inventionFascinating . . . the story Dyson tells is intensely human . . . a gripping account of ideas and invention' Jenny Uglow'Glorious . . . as much a story of the personalities involved as of the discoveries they made, and you do not need any knowledge of computers or mathematics to enjoy the ride . . . a ripping yarn' John Gribbin, Literary Review

**The First Ever Maths Book to be a No.1 Bestseller**'Wonderful ... superb' Daily MailWhat makes a bridge wobble when it's not meant to? Billions of dollars mysteriously vanish into thin air? A building rock when its resonant frequency matches a gym class leaping to Snap's 1990 hit I've Got The Power? The answer is maths. Or, to be precise, what happens when maths goes wrong in the real world.As Matt Parker shows us, our modern lives are built on maths: computer programmes, finance, engineering. And most of the time this maths works quietly behind the scenes, until ... it doesn't. Exploring and explaining a litany of glitches, near-misses and mishaps involving the internet, big data, elections, street signs, lotteries, the Roman empire and a hapless Olympic shooting team, Matt Parker shows us the bizarre ways maths trips us up, and what this reveals about its essential place in our world.Mathematics doesn't have good 'people skills', but we would all be better off, he argues, if we saw it as a practical ally. This book shows how, by making maths our friend, we can learn from its pitfalls. It also contains puzzles, challenges, geometric socks, jokes about binary code and three deliberate mistakes. Getting it wrong has never been more fun.

"Det är något så sällsamt som en spränglärd bok som inte nödvändigtvis vill lära oss något, utan som låter reflektioner över tillvarons beskaffenhet vara ett självändamål. Läs den!"Svenska Dagbladet

"Det är poetiskt och vackert på ett sätt som få kanske trodde att matematik kunde vara."BTJ"Bättre blir det när Ravanis, som har en lätt och ledig stil, lämnar kategorierna och prövar att skriva skönlitterärt. "Göteborgs Posten

"Ravanis presenterar teoremet på ett djupare och mer nyanserat sätt, där hennes pedagogiska och tillgängliga språk ger läsaren en fullständig och klar förståelse"Kultmagasin

”Det är en rik, underbar bok, fylld av mänsklig värme i ett svalnande universum.”Göran Greider, Aftonbladet om Skönheten i Kaos.

Emmy Noether var en av 1900-talets mest framstående matematiker. Hennes viktigaste teorem bidrog till att vända på en världsbild som varit sann ända sedan Newtons dagar. Idag är hon i stort sett bortglömd. Det här är en bok om hennes liv, hennes arv och drömmen om ett liv bortom kroppens begränsningar.Som judisk kvinna född i Tyskland 1882 blev Emmy Noether gång på gång utestängd från matematikens viktigaste rum. Hon, som bara förväntades ägna sig åt värdsliga ting, vigde trots detta sitt liv åt matematisk abstraktion. Medan hon kämpade för att få ta plats på universitetet i Göttingen, arbetade hon frenetiskt på det teorem som förklarar vad det innebär att inte vara förankrad i någon plats eller någon tid alls. Kanske hänger alltihop samman?Vetenskapshistorikern och fysikern Julia Ravanis söker i Emmys teorem efter det som formar våra idéer och gör oss till de vi är. Själva teoremet vägleder berättelsen om vad som ger oss energi att ta oss någonstans, hur vi väljer riktning och håller balansen i tillvaron. Om platserna och tiderna som vi nog aldrig helt kan frigöra oss från.

"Julia Ravanis tecknar Noethers gärning med ett språk som gnistrar av skärpa."Svenska Dagbladet

A New York Times Science BestsellerWhat if you had to take an art class in which you were only taught how to paint a fence? What if you were never shown the paintings of van Gogh and Picasso, weren't even told they existed? Alas, this is how math is taught, and so for most of us it becomes the intellectual equivalent of watching paint dry.In Love and Math , renowned mathematician Edward Frenkel reveals a side of math we've never seen, suffused with all the beauty and elegance of a work of art. In this heartfelt and passionate book, Frenkel shows that mathematics, far from occupying a specialist niche, goes to the heart of all matter, uniting us across cultures, time, and space. Love and Math tells two intertwined stories: of the wonders of mathematics and of one young man's journey learning and living it. Having braved a discriminatory educational system to become one of the twenty-first century's leading mathematicians, Frenkel now works on one of the biggest ideas to come out of math in the last 50 years: the Langlands Program.Considered by many to be a Grand Unified Theory of mathematics, the Langlands Program enables researchers to translate findings from one field to another so that they can solve problems, such as Fermat's last theorem, that had seemed intractable before.At its core, Love and Math is a story about accessing a new way of thinking, which can enrich our lives and empower us to better understand the world and our place in it. It is an invitation to discover the magic hidden universe of mathematics.

En liten räknebok skriven av Christopher Polhem trycktes år 1716. Han kallade den Wishetens andra grundwahl. I boken fanns 57 läxor som handlade om tal, geometri och algebra. Polhems pedagogiska tanke var att ungdomen skulle lära sig en läxa utantill varje dag för att senare som vuxna kunna få både nytta och nöje av sina kunskaper. Wishetens andra grundwahl är nu utgiven på nytt i Polhems lilla räknebok. Matematikhistorikern Staffan Rodhe har lagt kommentarer och problem till bokens läxor så att det blir lättare att förstå Polhems sätt att räkna. Polhems lilla räknebok handlar också om Polhems liv, hans uppfinningar och hans intresse för matematik. En del i denna historia berättar om hur Emanuel Swedenborg såg till att Wishetens andra grundwahl till slut blev en tryckt bok. Polhems lilla räknebok är en bok för de flesta, som gillar att lösa problem och vill lära sig mer om gamla matematiska metoder och måttenheter. Ser du förresten att det är en text om algebra på bokens framsida? Den kan du läsa mer om i Polhems lilla räknebok. Välkommen att träda in i 1700-talets matematiska värld och låt Polhem vara din lärare!

A fascinating look into how the transformative joys of mathematical experience are available to everyone, not just specialists  Math has a reputation for being inaccessible. People think that it requires a special gift or that comprehension is a matter of genes. Yet the greatest mathematicians throughout history, from René Descartes to Alexander Grothendieck, have insisted that this is not the case. Like Albert Einstein, who famously claimed to have “no special talent,” they said that they had accomplished what they did using ordinary human doubts, weaknesses, curiosity, and imagination.  David Bessis guides us on an illuminating path toward deeper mathematical comprehension, reconnecting us with the mental plasticity we experienced as children. With simple, concrete examples, Bessis shows how mathematical comprehension is integral to the great learning milestones of life, such as learning to see, to speak, to walk, and to eat with a spoon.  Focusing on the deeply human roots of mathematics, Bessis dispels the myths of mathematical genius. He offers an engaging initiation into the experience of math not as a series of discouragingly incomprehensible logic problems but as a physical activity akin to yoga, meditation, or a martial art. This perspective will change the way you think not only about math but also about intelligence, intuition, and everything that goes on inside your head.

'Fascinating and immensely readable' Ian Stewart 'A charming tour through the realm of the very, very, very numerous, from the ancient world through to the distant future' Jordan Ellenberg, author of How Not to Be WrongWhat if, every time you wanted to write down 1,000,000, you had to draw a picture of a god? And what if that number were the biggest you had a symbol for? In ancient Egypt, those were the rules: anything bigger broke maths. Writing down some numbers is still beyond us today: try it with all the zeroes in a googolplex, or an outrageous alien number like FISH 7. Even harnessing every particle in the universe, you wouldn't come close. But that hasn't stopped us from hunting down these mind-bendingly big numbers and studying them.In Huge Numbers, mathematician and Numberphile presenter Richard Elwes shows how counting has shaped human thought. Whether recorded with notches carved on a tally stick, beads on an abacus, or electrical signals carrying binary code, it allows us to test the limits of mathematics over and over, breaking it down and putting it back together again.Come on a fascinating tour that spans continents and millennia, from the Mayan calendar to today's chatbots. You'll see that huge numbers are everywhere, expanding our horizons and powering our modern world.

A lively, accessible history of mathematics throughout the ages and across the globe  Mathematics is fundamental to our daily lives. Science, computing, economics—all aspects of modern life rely on some kind of maths. But how did our ancestors think about numbers? How did they use mathematics to explain and understand the world around them? Where do numbers even come from?  In this Little History, Snezana Lawrence traces the fascinating history of mathematics, from the Egyptians and Babylonians to Renaissance masters and enigma codebreakers. Like literature, music, or philosophy, mathematics has a rich history of breakthroughs, creativity and experimentation. And its story is a global one. We see Chinese Mathematical Art from 200 BCE, the invention of algebra in Baghdad’s House of Wisdom, and sangaku geometrical theorems at Japanese shrines. Lawrence goes beyond the familiar names of Newton and Pascal, exploring the prominent role women have played in the history of maths, including Emmy Noether and Maryam Mirzakhani.

This book provides the first detailed account of Riemann's life along with analysis of his major works and their reception. These themes are presented in a chronological flow that takes into account numerous others who played important roles in Riemann's brief life and career. Among the more prominent figures who influenced Riemann's work were Gauss, Dirichlet, and Jacobi, but several others, including the physicist Wilhelm Weber, also played a major part. Special attention is given to the last four years of Riemann's life, which he and his wife Elise mainly spent in Italy, where he died. Her role in supporting Richard Dedekind and Heinrich Weber, the editors of Riemann's posthumous papers, is one of the many new aspects covered in this book.Drawing on family letters and other archival documents, the biographical chapters bring the reader into Riemann's often tumultuous personal life. Money and other mundane problems were a constant cause of concern, but even more serious were the health problems he suffered all his life. Socially awkward, he often withdrew from his peers while seeking solace in his work or that of others. Riemann was a voracious reader, but the present account offers a detailed picture of what he read and when. Plenty of mysteries still remain, but here for the first time one gains a sense of the extraordinary intellectual adventure that dominated Riemann's life.To help orient the reader, the book begins with an Introduction describing the landscape of German mathematics before Riemann arrived on the scene and ending with a chronological list of key events in his life. The remainder of the book has a three-part structure. Part I tells the story of Riemann's life in four chapters, corresponding to four distinct phases in his career. Part II delves into his better-known mathematical works, treated at first chronologically in Chapters 5 to 8. These are followed by an examination of Riemann's work on physical topics in Chapter 9, and closing with Chapter 10, which discusses Gaussian themes and their connections with Riemann's work. Part III deals with aspects of Riemann's legacy in two chapters. Chapter 11 traces the activities of seven important pupils and followers of Riemann up until the early 1880s. Chapter 12 then picks up the story told in the final section of Chapter 4, which describes the initial plans to publish Riemann's Collected Works. How that project was eventually brought to fruition by Dedekind and Weber forms part of the remarkable story of their lifelong friendship.The biographical parts of this book – Chapters 1 to 4 and 12 – are intended for the general reader. They are not totally "jargon-free", but will interest anyone with a taste for intellectual history. The remaining parts of the book aim to describe Riemann's work in the language of his time, which often means quoting him directly. A short section on "Reading Riemann" appears at the end of Chapter 5. For a serious historical account, one should always keep the author's voice in mind, even if, as in Riemann's case, the meaning of his words was at times unclear.

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 seminal publication is now available in a beautiful new edition. A masterwork of art and science, it is as remarkable 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.

In the mid-eighteenth century, Swiss-born mathematician Leonhard Euler developed a formula so innovative and complex that it continues to inspire research, discussion, and even the occasional limerick. Dr. Euler's Fabulous Formula shares the fascinating story of this groundbreaking formula--long regarded as the gold standard for mathematical beauty--and shows why it still lies at the heart of complex number theory. In some ways a sequel to Nahin's An Imaginary Tale, this book examines the many applications of complex numbers alongside intriguing stories from the history of mathematics. Dr. Euler's Fabulous Formula is accessible to any reader familiar with calculus and differential equations, and promises to inspire mathematicians for years to come.

Number theory is the branch of mathematics that is primarily concerned with the counting numbers. Of particular importance are the prime numbers, the 'building blocks' of our number system. The subject is an old one, dating back over two millennia to the ancient Greeks, and for many years has been studied for its intrinsic beauty and elegance, not least because several of its challenges are so easy to state that everyone can understand them, and yet no-one has ever been able to resolve them. But number theory has also recently become of great practical importance - in the area of cryptography, where the security of your credit card, and indeed of the nation's defence, depends on a result concerning prime numbers that dates back to the 18th century. Recent years have witnessed other spectacular developments, such as Andrew Wiles's proof of 'Fermat's last theorem' (unproved for over 250 years) and some exciting work on prime numbers. In this Very Short Introduction Robin Wilson introduces the main areas of classical number theory, both ancient and modern. Drawing on the work of many of the greatest mathematicians of the past, such as Euclid, Fermat, Euler, and Gauss, he situates some of the most interesting and creative problems in the area in their historical context.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.

Best Books of 2024, The Economist From the codebreakers and problem solvers, to the engineers, mathematicians and other problem-solvers – what the secret world can teach us about performance and creativity How do you hire smart people who can work together to prevent terrorist attacks and decode encrypted technology?How do you come up with creative, counterintuitive solutions to solve major global problems?How do you provide the right environment for these people to thrive and work at their best when under immense pressure?Written by Robert Hannigan, the former Director of GCHQ, this book explores the role of the counter-intelligence services in history and today’s world – from the codebreakers and problem solvers, to innovation and creativity, secrecy and transparency and the global tech community. It will trace the history of counter-intelligence – from the early days of Bletchley Park, to the ongoing work of GCHQ – while reflecting on some of the unique characteristics of the engineers, mathematicians and other problem-solvers that make up the world’s intelligence community.An exhaustive and authoritative account of the history of counter-intelligence from Bletchley Park to modern day GCHQ, this brilliant and unique book will appeal to business readers, history readers and fans of smart thinking and big ideas around the world.

We all played tag when we were kids. What most of us don't realize is that this simple chase game is in fact an application of pursuit theory, and that the same principles of games like tag, dodgeball, and hide-and-seek are also at play in military strategy, high-seas chases by the Coast Guard, and even romantic pursuits. In Chases and Escapes, Paul Nahin gives us the first complete history of this fascinating area of mathematics, from its classical analytical beginnings to the present day. Drawing on game theory, geometry, linear algebra, target-tracking algorithms, and much more, Nahin also offers an array of challenging puzzles with their historical background and broader applications. Chases and Escapes includes solutions to all problems and provides computer programs that readers can use for their own cutting-edge analysis. Now with a gripping new preface on how the Enola Gay escaped the shock wave from the atomic bomb dropped on Hiroshima, this book will appeal to anyone interested in the mathematics that underlie pursuit and evasion.

The official book behind the Academy Award-winning film The Imitation Game, starring Benedict Cumberbatch and Keira Knightley Alan Turing was the mathematician whose cipher-cracking transformed the Second World War. Taken on by British Intelligence in 1938, as a shy young Cambridge don, he combined brilliant logic with a flair for engineering. In 1940 his machines were breaking the Enigma-enciphered messages of Nazi Germany’s air force. He then headed the penetration of the super-secure U-boat communications. But his vision went far beyond this achievement. Before the war he had invented the concept of the universal machine, and in 1945 he turned this into the first design for a digital computer.Turing's far-sighted plans for the digital era forged ahead into a vision for Artificial Intelligence. However, in 1952 his homosexuality rendered him a criminal and he was subjected to humiliating treatment. In 1954, aged 41, Alan Turing took his own life.

In this scientific tour de force, world-class physicist Frank Wilczek argues that beauty is at the heart of the logic of the universe, a principle that has guided his pioneering work in quantum physics. As this book demonstrates, the human quest to find the beauty embodied in the universe connects all scientific pursuit from Pythagoras and Plato on to Galileo and Newton, Maxwell and Einstein. Indeed, Wilczek shows us just how deeply intertwined our ideas about beauty and art are with our scientific understanding of the cosmos. Gorgeously illustrated, A Beautiful Question is the culmination of Wilczek's life work and a mind-expanding book that combines the age-old human quest for beauty and the age-old human quest for truth.

How the computer revolution shaped our conception of rationality—and why human problems require solutions rooted in human intuition, morality, and judgmentIn the 1940s, mathematicians set out to design computers that could act as ideal rational agents in the face of uncertainty. The Irrational Decision tells the story of how they settled on a peculiar mathematical definition of rationality in which every decision is a statistical question of risk. Benjamin Recht traces how this quantitative standard came to define our understanding of rationality, looking at the history of optimization, game theory, statistical testing, and machine learning. He explains why, now more than ever, we need to resist efforts by powerful tech interests to drive public policy and essentially rule our lives.While mathematical rationality has proven valuable in accelerating computers, regulating pharmaceuticals, and deploying electronic commerce, it fails to solve messy human problems and has given rise to a view of a rational world that is not only overquantified but surprisingly limited. Recht shows how these mathematical methods emerged from wartime research and influenced fields ranging from economics to health care, drawing on illuminating examples ranging from diet planning to chess to self-driving cars.Highlighting both the power and limitations of mathematical rationality, The Irrational Decision reveals why only humans can resolve fundamentally political or value-based questions and proposes a more expansive approach to decision making that is appropriately supported by computational tools yet firmly rooted in human intuition, morality, and judgment.

This textbook provides an accessible account of the history of abstract algebra, tracing a range of topics in modern algebra and number theory back to their modest presence in the seventeenth and eighteenth centuries, and exploring the impact of ideas on the development of the subject.Beginning with Gauss’s theory of numbers and Galois’s ideas, the book progresses to Dedekind and Kronecker, Jordan and Klein, Steinitz, Hilbert, and Emmy Noether. Approaching mathematical topics from a historical perspective, the author explores quadratic forms, quadratic reciprocity, Fermat’s Last Theorem, cyclotomy, quintic equations, Galois theory, commutative rings, abstract fields, ideal theory, invariant theory, and group theory. Readers will learn what Galois accomplished, how difficult the proofs of his theorems were, and how important Camille Jordan and Felix Klein were in the eventual acceptance of Galois’s approach to the solution of equations. The book also describes the relationshipbetween Kummer’s ideal numbers and Dedekind’s ideals, and discusses why Dedekind felt his solution to the divisor problem was better than Kummer’s. Designed for a course in the history of modern algebra, this book is aimed at undergraduate students with an introductory background in algebra but will also appeal to researchers with a general interest in the topic. With exercises at the end of each chapter and appendices providing material difficult to find elsewhere, this book is self-contained and therefore suitable for self-study.

A fascinating exploration of how cartography shapes our world and the impact of maps on our everyday lives.‘If you have ever wondered why an airliner bound from London to Los Angeles flies over Greenland, how we know what lies inside the Earth, or how computers correct errors, then this book is for you’ – John Gribbin, author of In Search of Schrodinger's Cat'An expansive journey through time and place' – The Observer'Entertaining, illuminating . . . An engaging look at a fascinating subject' – New ScientistHow does a delivery driver distribute hundreds of packages in a single day?Why can maps influence elections?Where should we look for serial killers?The answers lie in the connection between maps and maths.Mathematician Dr Paulina Rowinska explores the mathematical foundations of maps and cartography's impact on mathematics. From sixteenth-century maps which we still use on our phones to public transport maps that both guide and mislead, she uncovers how maps and maths shape our sense of space and time, and our worldview.Through engaging stories, unforgettable characters and real-world examples, Mapmatics reveals the mathematical techniques behind maps and how they help us better understand - and care for - the world around us.

The Science of Secrecy from Ancient Egypt to Quantum CryptographyFrom the best-selling author of Fermat’s Last Theorem, The Code Book is a history of man’s urge to uncover the secrets of codes, from Egyptian puzzles to modern day computer encryptions.As in Fermat’s Last Theorem, Simon Singh brings life to an anstonishing story of puzzles, codes, languages and riddles that reveals man’s continual pursuit to disguise and uncover, and to work out the secret languages of others.Codes have influenced events throughout history, both in the stories of those who make them and those who break them. The betrayal of Mary Queen of Scots and the cracking of the enigma code that helped the Allies in World War II are major episodes in a continuing history of cryptography. In addition to stories of intrigue and warfare, Simon Singh also investigates other codes, the unravelling of genes and the rediscovery of ancient languages and most tantalisingly, the Beale ciphers, an unbroken code that could hold the key to a $20 million treasure.Note that it has not been possible to include the same picture content that appeared in the original print version.

'An invaluable companion for anyone who wants a deep understanding of what’s under the hood of often inscrutable machines' Melanie Mitchell A rich, narrative explanation of the mathematics that has brought us machine learning and the ongoing explosion of artificial intelligenceMachine-learning systems are making life-altering decisions for us: approving mortgage loans, determining whether a tumour is cancerous, or deciding whether someone gets bail. They now influence discoveries in chemistry, biology and physics - the study of genomes, extra-solar planets, even the intricacies of quantum systems.We are living through a revolution in artificial intelligence that is not slowing down. This major shift is based on simple mathematics, some of which goes back centuries: linear algebra and calculus, the stuff of eighteenth-century mathematics. Indeed by the mid-1850s, a lot of the groundwork was all done. It took the development of computer science and the kindling of 1990s computer chips designed for video games to ignite the explosion of AI that we see all around us today. In this enlightening book, Anil Ananthaswamy explains the fundamental maths behind AI, which suggests that the basics of natural and artificial intelligence might follow the same mathematical rules.As Ananthaswamy resonantly concludes, to make the most of our most wondrous technologies we need to understand their profound limitations - the clues lie in the maths that makes AI possible.

Can one prove that 1 + 1 = 2? How long is the coastline of Britain? Which US president proved Pythagoras' theorem on right-angled triangles? Who originated the quadratic equation we learned at school? In how many ways can you tile your bathroom? Is there a formula for prime numbers? How often are two winning lottery numbers consecutive? Who was the witch of Agnesi? What is 'the most important theorem in mathematics'? Who scratched mathematical equations on a Dublin bridge? What is a 'space-filling curve'? Must all infinities be the same size? These and many other questions are answered in this book which presents eighteen 'Stories' featuring famous mathematical equations and their historical development. The equations arise from geometry, arithmetic, algebra, calculus, combinatorics, number theory, and mathematical logic, and range over 4,000 years from early counting and circle measurement via Renaissance algebra to fractal geometry, and from the geometry of the ancient Greeks via the development of calculus to Boolean algebra and computing. The Stories are well illustrated with historical artefacts and explanatory diagrams.Presented in a straightforward, intelligible, and entertaining manner, Sum Stories is written for general readers of all ages with an interest in mathematics and its historical development.