Matematikens historia

**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.

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

A celebration of the seemingly simple idea that allowed us to imagine the world in new dimensions—sparking both controversy and discovery.   The stars of this book, vectors and tensors, are unlikely celebrities. If you ever took a physics course, the word “vector” might remind you of the mathematics needed to determine forces on an amusement park ride, a turbine, or a projectile. You might also remember that a vector is a quantity that has magnitude and (this is the key) direction. In fact, vectors are examples of tensors, which can represent even more data. It sounds simple enough—and yet, as award-winning science writer Robyn Arianrhod shows in this riveting story, the idea of a single symbol expressing more than one thing at once was millennia in the making. And without that idea, we wouldn’t have such a deep understanding of our world.Vector and tensor calculus offers an elegant language for expressing the way things behave in space and time, and Arianrhod shows how this enabled physicists and mathematicians to think in a brand-new way. These include James Clerk Maxwell when he ushered in the wireless electromagnetic age; Einstein when he predicted the curving of space-time and the existence of gravitational waves; Paul Dirac, when he created quantum field theory; and Emmy Noether, when she connected mathematical symmetry and the conservation of energy. For it turned out that it’s not just physical quantities and dimensions that vectors and tensors can represent, but other dimensions and other kinds of information, too. This is why physicists and mathematicians can speak of four-dimensional space-time and other higher-dimensional “spaces,” and why you’re likely relying on vectors or tensors whenever you use digital applications such as search engines, GPS, or your mobile phone.In exploring the evolution of vectors and tensors—and introducing the fascinating people who gave them to us—Arianrhod takes readers on an extraordinary, five-thousand-year journey through the human imagination. She shows the genius required to reimagine the world—and how a clever mathematical construct can dramatically change discovery’s direction.

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.

"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

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.

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!

'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.

Very Short Introductions: Brilliant, Sharp, Inspiring Kurt Gödel first published his celebrated theorem, showing that no axiomatization can determine the whole truth and nothing but the truth concerning arithmetic, nearly a century ago. The theorem challenged prevalent presuppositions about the nature of mathematics and was consequently of considerable mathematical interest, while also raising various deep philosophical questions. Gödel's Theorem has since established itself as a landmark intellectual achievement, having a profound impact on today's mathematical ideas. Gödel and his theorem have attracted something of a cult following, though his theorem is often misunderstood.This Very Short Introduction places the theorem in its intellectual and historical context, and explains the key concepts as well as common misunderstandings of what it actually states. A. W. Moore provides a clear statement of the theorem, presenting two proofs, each of which has something distinctive to teach about its content. Moore also discusses the most important philosophical implications of the theorem. In particular, Moore addresses the famous question of whether the theorem shows the human mind to have mathematical powers beyond those of any possible computerABOUT 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.

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.

Does the universe embody beautiful ideas?   Artists as well as scientists throughout human history have pondered this “beautiful question.” With Nobel laureate Frank Wilczek as your guide, embark on a voyage of related discoveries, from Plato and Pythagoras up to the present. Wilczek’s groundbreaking work in quantum physics was inspired by his intuition to look for a deeper order of beauty in nature. This is the deep logic of the universe—and it is no accident that it is also at the heart of what we find aesthetically pleasing and inspiring.   Wilczek is hardly alone among great scientists in charting his course using beauty as his compass. As he reveals in A Beautiful Question, this has been the heart of scientific pursuit from Pythagoras and the ancient belief in the music of the spheres to Galileo, Newton, Maxwell, Einstein, and into the deep waters of twentieth-century physics. Wilczek brings us right to the edge of knowledge today, where the core insights of even the craziest quantum ideas apply principles we all understand. The equations for atoms and light are almost the same ones that govern musical instruments and sound; the subatomic particles that are responsible for most of our mass are determined by simple geometric symmetries.   Gorgeously illustrated, A Beautiful Question is a mind-shifting book that braids the age-old quest for beauty and the age-old quest for truth into a thrilling synthesis. It is a dazzling and important work from one of our best thinkers, whose humor and infectious sense of wonder animate every page. Yes: The world is a work of art, and its deepest truths are ones we already feel, as if they were somehow written in our souls.

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.

Shortlisted for the Royal Society Science Book Prize 2019A magisterial history of calculus (and the people behind it) from one of the world's foremost mathematicians.This is the captivating story of mathematics' greatest ever idea: calculus. Without it, there would be no computers, no microwave ovens, no GPS, and no space travel. But before it gave modern man almost infinite powers, calculus was behind centuries of controversy, competition, and even death. Taking us on a thrilling journey through three millennia, professor Steven Strogatz charts the development of this seminal achievement from the days of Archimedes to today's breakthroughs in chaos theory and artificial intelligence. Filled with idiosyncratic characters from Pythagoras to Fourier, Infinite Powers is a compelling human drama that reveals the legacy of calculus on nearly every aspect of modern civilisation, including science, politics, medicine, philosophy, and much besides.

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.

Between inventing the concept of a universal computer in 1936 and breaking the German Enigma code during World War II, Alan Turing (1912-1954), the British founder of computer science and artificial intelligence, came to Princeton University to study mathematical logic. Some of the greatest logicians in the world--including Alonzo Church, Kurt Godel, John von Neumann, and Stephen Kleene--were at Princeton in the 1930s, and they were working on ideas that would lay the groundwork for what would become known as computer science. This book presents a facsimile of the original typescript of Turing's fascinating and influential 1938 Princeton PhD thesis, one of the key documents in the history of mathematics and computer science. The book also features essays by Andrew Appel and Solomon Feferman that explain the still-unfolding significance of the ideas Turing developed at Princeton. A work of philosophy as well as mathematics, Turing's thesis envisions a practical goal--a logical system to formalize mathematical proofs so they can be checked mechanically. If every step of a theorem could be verified mechanically, the burden on intuition would be limited to the axioms.Turing's point, as Appel writes, is that "mathematical reasoning can be done, and should be done, in mechanizable formal logic." Turing's vision of "constructive systems of logic for practical use" has become reality: in the twenty-first century, automated "formal methods" are now routine. Presented here in its original form, this fascinating thesis is one of the key documents in the history of mathematics and computer science.

I am very pleased that my books about David Hilbert, published in 1970, and Richard Courant, published in 1976, are now being issued by Springer­ Verlag in a single volume. I have always felt that they belonged together, Courant being, as I have written, the natural and necessary sequel to Hilbert­ the rest of the story. To make the two volumes more compatible when published as one, we have combined and brought up to date the indexes of names and dates. U nfortu­ nately we have had to omit Hermann Weyl's article on "David Hilbert and his mathematical work," but the interested reader can always find it in the hard­ back edition of Hilbert and in Weyl's collected papers. At the request of a number of readers we have included a listing of all of Hilbert's famous Paris problems. It was, of course, inevitable that we would give the resulting joint volume the title Hilbert-Courant.

How can we be sure that Pythagoras's theorem is really true? Why is the 'angle in a semicircle' always 90 degrees? And how can tangents help determine the speed of a bullet?David Acheson takes the reader on a highly illustrated tour through the history of geometry, from ancient Greece to the present day. He emphasizes throughout elegant deduction and practical applications, and argues that geometry can offer the quickest route to the whole spirit of mathematics at its best. Along the way, we encounter the quirky and the unexpected, meet the great personalities involved, and uncover some of the loveliest surprises in mathematics.

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.

The legendary Renaissance math duel that ushered in the modern age of algebraThe Secret Formula tells the story of two Renaissance mathematicians whose jealousies, intrigues, and contentious debates led to the discovery of a formula for the solution of the cubic equation. Niccolò Tartaglia was a talented and ambitious teacher who possessed a secret formula—the key to unlocking a seemingly unsolvable, two-thousand-year-old mathematical problem. He wrote it down in the form of a poem to prevent other mathematicians from stealing it. Gerolamo Cardano was a physician, gifted scholar, and notorious gambler who would not hesitate to use flattery and even trickery to learn Tartaglia's secret.Set against the backdrop of sixteenth-century Italy, The Secret Formula provides new and compelling insights into the peculiarities of Renaissance mathematics while bringing a turbulent and culturally vibrant age to life. It was an era when mathematicians challenged each other in intellectual duels held outdoors before enthusiastic crowds. Success not only enhanced the winner's reputation, but could result in prize money and professional acclaim. After hearing of Tartaglia's spectacular victory in one such contest in Venice, Cardano invited him to Milan, determined to obtain his secret by whatever means necessary. Cardano's intrigues paid off. In 1545, he was the first to publish a general solution of the cubic equation. Tartaglia, eager to take his revenge by establishing his superiority as the most brilliant mathematician of the age, challenged Cardano to the ultimate mathematical duel.A lively account of genius, betrayal, and all-too-human failings, The Secret Formula reveals the epic rivalry behind one of the fundamental ideas of modern algebra.

Heavenly Mathematics traces the rich history of spherical trigonometry, revealing how the cultures of classical Greece, medieval Islam, and the modern West used this forgotten art to chart the heavens and the Earth. Once at the heart of astronomy and ocean-going navigation for two millennia, the discipline was also a mainstay of mathematics education for centuries and taught widely until the 1950s. Glen Van Brummelen explores this exquisite branch of mathematics and its role in ancient astronomy, geography, and cartography; Islamic religious rituals; celestial navigation; polyhedra; stereographic projection; and more. He conveys the sheer beauty of spherical trigonometry, providing readers with a new appreciation of its elegant proofs and often surprising conclusions. Heavenly Mathematics is illustrated throughout with stunning historical images and informative drawings and diagrams. This unique compendium also features easy-to-use appendixes as well as exercises that originally appeared in textbooks from the eighteenth to the early twentieth centuries.

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.

A revisionist, completely accessible and radically inclusive history of maths'Lively, satisfying, good at explaining difficult concepts' The Sunday TimesMathematics shapes almost everything we do. But despite its reputation as the study of fundamental truths, the stories we have been told about it are wrong. In The Secret Lives of Numbers, historian Kate Kitagawa and journalist Timothy Revell introduce readers to the mathematical boundary-smashers who have been erased by history because of their race, gender or nationality.From the brilliant Arabic scholars of the ninth-century House of Wisdom, and the pioneering African American mathematicians of the twentieth century, to the 'lady computers' around the world who revolutionised our knowledge of the night sky, we meet these fascinating trailblazers and see how they contributed to our global knowledge today.This revisionist, completely accessible and radically inclusive history of mathematics is as entertaining as it is important.

A New York Times Book Review Editor’s Choice: A vivid account of the generations-long dispute over Bayes’ rule, one of the greatest breakthroughs in the history of applied mathematics and statistics  “An intellectual romp touching on, among other topics, military ingenuity, the origins of modern epidemiology, and the theological foundation of modern mathematics.”—Michael Washburn, Boston Globe  “To have crafted a page-turner out of the history of statistics is an impressive feat. If only lectures at university had been this racy.”—David Robson, New Scientist  Bayes’ rule appears to be a straightforward, one-line theorem: by updating our initial beliefs with objective new information, we get a new and improved belief. To its adherents, it is an elegant statement about learning from experience. To its opponents, it is subjectivity run amok.  In the first-ever account of Bayes’ rule for general readers, Sharon Bertsch McGrayne explores this controversial theorem and the human obsessions surrounding it. She traces its discovery by an amateur mathematician in the 1740s through its development into roughly its modern form by French scientist Pierre Simon Laplace. She reveals why respected statisticians rendered it professionally taboo for 150 years—at the same time that practitioners relied on it to solve crises involving great uncertainty and scanty information (Alan Turing’s role in breaking Germany’s Enigma code during World War II), and explains how the advent of off-the-shelf computer technology in the 1980s proved to be a game-changer. Today, Bayes’ rule is used everywhere from DNA de-coding to Homeland Security.  Drawing on primary source material and interviews with statisticians and other scientists, The Theory That Would Not Die is the riveting account of how a seemingly simple theorem ignited one of the greatest controversies of all time.

Big Think's Best Science Book of 2024A theoretical physicist takes readers on an awe-inspiring journey to discover how the universe generates everything from nothing at all: "If you want to know what's really going on in the realms of relativity and particle physics, read this book" (Sean Carroll, author of The Biggest Ideas in the Universe) In Waves in an Impossible Sea, physicist Matt Strassler tells a startling tale of elementary particles, human experience, and empty space. He begins with a simple mystery of motion-our planet hurtles through the cosmos at 150 miles per second, and yet we feel nothing of it. How can our voyage be so tranquil? The reason, Strassler reveals, is that empty space is a sea, albeit a paradoxical one. Much like water and air, it ripples in various ways, and we ourselves, made from its ripples, can move through space as effortlessly as waves crossing an ocean. Deftly weaving together daily experience and fundamental physics-the musical universe, the enigmatic quantum, cosmic fields, and the Higgs boson-Strassler shows us how all things, familiar and unfamiliar, emerge from what seems like nothing at all. Accessible and profound, Waves in an Impossible Sea is the ultimate guide to our place in the universe.