Matematikens filosofi

*A Financial Times and Waterstones Book of the Year 2025* Many artists are unaware of the mathematics that bubble beneath their craft, while some consciously use it for inspiration. Our instincts might tell us that these two subjects are incompatible forces with nothing in common, but what if we’re wrong? Marcus du Sautoy, acclaimed mathematician and Simonyi Professor for the Public Understanding of Science at the University of Oxford, looks to art, music, design and literature to uncover the key mathematical structures that underpin both human creativity and the natural world.Blueprints takes us from the earliest stone circles to the modernist architecture of Le Corbusier, from Bach’s circular compositions to Radiohead’s disruptive soundscapes, and from Shakespeare’s hidden numerical clues to the Dada artists who embraced randomness. Instead of polar opposites we find a complementary relationship that spans a vast historical and geographic landscape.Whether we are searching for meaning in an abstract painting or deciphering poetry, there are blueprints everywhere: prime numbers, symmetry, fractals and the weirder worlds of Hamiltonian cycles and hyperbolic geometry. Nature similarly exploits these structures to achieve the wonders of our universe.In this innovative and delightfully bold exploration of creativity, Marcus explains how we make art, why a creative mindset is vital for discovering new mathematics and how a fundamental connection to the natural world intrinsically links these two subjects.‘Blueprints is an extraordinary book which shows us how mathematics and art are connected through structures. Du Sautoy shows us how to bridge the divide of science and the humanities and proves that we can only face and solve the big challenges of the twenty-first century if we go beyond the fear of pooling knowledge’ Hans Ulrich Obrist, Artistic Director, Serpentine Galleries

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.

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.

Ludwig Wittgenstein was one of the greatest philosophers of the modern era, while his pupil and friend Elizabeth Anscombe is increasingly recognized as being an important philosopher in her own right. Over a number of years, Anscombe kept a series of notebooks labeled "Anecdotes about Wittgenstein," documents which are uniquely valuable for their ability to shed light on the intellectual and personal character of Wittgenstein, as well as Anscombe's own views on a wide range of topics--cultural, historical and psychological. While the original manuscript was divided into sections of varying lengths and jumped around among topics, Anscombe on Wittgenstein reorders them thematically so that readers might more vividly perceive the contours of her subjects. Between 1946-1947, Anscombe, Wittgenstein, and Wasfi Hijab routinely had philosophical conversations, which Anscombe wrote down immediately afterward while they were still fresh in her mind. Transcribed here as they were originally written--similar to a play, with the voices of the participants indicated by their initials--readers can experience these philosophers grappling with topics such as rule-following, necessity, and the notion of the indefinite, all subjects that were at the heart of Wittgenstein's later philosophy. This book also offers a previously unpublished essay by Anscombe, as well as two essays by the book's editors, leading scholars on Anscombe, and biographies of the characters mentioned in the manuscripts. What emerges from these accounts is not only a picture of Wittgenstein, the man and philosopher, but also a memoir of a close friendship between two of the most significant philosophers of the twentieth century.

How do you begin to understand the concept of nothing? Where does it begin and where does it end?From the zeros of the mathematician to the void of the philosophers, from Shakespeare to the empty set, from the ether to the quantum vacuum, from being and nothingness to creatio ex nihilo, there is much ado about nothing at the heart of things. Recent exciting discoveries in astronomy are shown to shed new light on the nature of the vacuum and its dramatic effect upon the explanation of the Universe. This remarkable book ranges over every nook and cranny of nothingness to reveal how the human mind has had to make something of nothing in every field of human enquiry.

A marvelous compendium of mathematical symbols and their fascinating historiesGalileo famously wrote that the book of nature is written in mathematical language. The Language of Mathematics is a wide-ranging and beautifully illustrated collection of short, colorful histories of the most commonly used symbols in mathematics, providing readers with an engaging introduction to the origins, evolution, and conceptual meaning of each one.In dozens of lively and informative entries, Raúl Rojas shows how today’s mathematics stands on the shoulders of giants, mathematicians from around the world who developed mathematical notation through centuries of collective effort. He tells the stories of such figures as al-Khwārizmī, René Descartes, Joseph-Louis Lagrange, Carl Friedrich Gauss, Augustin-Louis Cauchy, Karl Weierstrass, Sofia Kovalevskaya, David Hilbert, and Kenneth Iverson. Topics range from numbers and variables to sets and functions, constants, and combinatorics. Rojas describes the mathematical problems associated with different symbols and reveals how mathematical notation has sometimes been an accidental process. The entries are self-contained and can be read in any order, each one examining one or two symbols, their history, and the variants they may have had over time.An essential companion for math enthusiasts, The Language of Mathematics shows how mathematics is a living and evolving entity, forever searching for the best symbolism to express relationships between abstract concepts and to convey meaning.

SHORTLISTED FOR THE BRITISH SOCIETY FOR THE HISTORY OF SCIENCE PRIZE 2025 SHORTLISTED FOR THE NEUMANN PRIZE 2025 WHAT DOES IT MEAN TO COUNT? WHY ARE HUMANS THE ONLY SPECIES ON EARTH THAT CAN DO IT? WHERE DID COUNTING COME FROM? HOW HAS IT SHAPED SOCIETIES ALONG THE WAY? AND WHY DOES IT MATTER? Counting is an innovative, erudite, world-wrapping journey through humanity’s marvellous ability to impose numbers on things. Acclaimed historian and mathematician Benjamin Wardhaugh draws on stories from the Stone Age to cyberspace in pursuit of the elusive, fascinating, endlessly diverse history of human counting.Starting with the roots of counting in human brains, bodies and environments, Wardhaugh tours us around the world and through time while exploring the different flavours of counting that have developed over millennia. We meet the makers of bead necklaces in ancient South Africa, the inventors of writing in the world ’ s first metropolis, and the ‘counter culture’ of classical Athens. We see counting used – and changed – by Indian scholars, Chinese peasants and Papuan shopkeepers; we meet the distinctive numerate agendas of Mayan kings, US governments and Korean vloggers.Weaving these stories together, Wardhaugh shows how cultures have shaped counting, and how counting has shaped culture, in a rich tapestry spanning thousands of years. This is the vast story of human attempts to find some order in an unruly world; or, perhaps, to impose on a reluctant world the order that humans find within themselves. It is a history as wide, deep and tangled as that of humanity itself

'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.

THE INTERNATIONAL BESTSELLER'An entertaining tour that will change how you see the world' Sean Carroll, author of Something Deeply HiddenIs there a secret formula for improving your life? For making something a viral hit? For deciding how long to stick with your current job, Netflix series, or even relationship?This book is all about the equations that make our world go round. Ten of them, in fact. They are integral to everything from investment banking to betting companies and social media giants. And they can help you to increase your chance of success, guard against financial loss, live more healthily and see through scaremongering. They are known only by mathematicians - until now.With wit and clarity, mathematician David Sumpter shows that it isn't the technical details which make these formulas so successful. It is the way they allow mathematicians to view problems from a different angle - a way of seeing the world that anyone can learn.Empowering and illuminating, The Ten Equations that Rule the World shows how maths really can change your life.

'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 Financial Times and Waterstones Book of the Year 2025* Many artists are unaware of the mathematics that bubble beneath their craft, while some consciously use it for inspiration. Our instincts might tell us that these two subjects are incompatible forces with nothing in common, but what if we’re wrong? Marcus du Sautoy, acclaimed mathematician and Simonyi Professor for the Public Understanding of Science at the University of Oxford, looks to art, music, design and literature to uncover the key mathematical structures that underpin both human creativity and the natural world.Blueprints takes us from the earliest stone circles to the modernist architecture of Le Corbusier, from Bach’s circular compositions to Radiohead’s disruptive soundscapes, and from Shakespeare’s hidden numerical clues to the Dada artists who embraced randomness. Instead of polar opposites we find a complementary relationship that spans a vast historical and geographic landscape.Whether we are searching for meaning in an abstract painting or deciphering poetry, there are blueprints everywhere: prime numbers, symmetry, fractals and the weirder worlds of Hamiltonian cycles and hyperbolic geometry. Nature similarly exploits these structures to achieve the wonders of our universe.In this innovative and delightfully bold exploration of creativity, Marcus explains how we make art, why a creative mindset is vital for discovering new mathematics and how a fundamental connection to the natural world intrinsically links these two subjects.‘Blueprints is an extraordinary book which shows us how mathematics and art are connected through structures. Du Sautoy shows us how to bridge the divide of science and the humanities and proves that we can only face and solve the big challenges of the twenty-first century if we go beyond the fear of pooling knowledge’ Hans Ulrich Obrist, Artistic Director, Serpentine Galleries

The twentieth century has witnessed an unprecedented 'crisis in the foundations of mathematics', featuring a world-famous paradox (Russell's Paradox), a challenge to 'classical' mathematics from a world-famous mathematician (the 'mathematical intuitionism' of Brouwer), a new foundational school (Hilbert's Formalism), and the profound incompleteness results of Kurt Gödel. In the same period, the cross-fertilization of mathematics and philosophy resulted in a new sort of 'mathematical philosophy', associated most notably (but in different ways) with Bertrand Russell, W. V. Quine, and Gödel himself, and which remains at the focus of Anglo-Saxon philosophical discussion. The present collection brings together in a convenient form the seminal articles in the philosophy of mathematics by these and other major thinkers. It is a substantially revised version of the edition first published in 1964 and includes a revised bibliography. The volume will be welcomed as a major work of reference at this level in the field.

_______________'Beguiling ... I was riveted. Olsson is evocative on curiosity as an appetite of the mind, on the pleasure of glutting oneself on knowledge' - New York Times'A wonderful book ... Reading it is akin to kicking a can along the road of higher learning' - Patti Smith'A remarkable tour de force' - Standpoint_______________Simone Weil: philosopher, political activist, mystic – and sister to André, one of the most influential mathematicians of the twentieth century. These two extraordinary siblings formed an obsession for Karen Olsson, who studied mathematics at Harvard, only to turn to writing as a vocation.When Olsson got hold of the 1940 letters between the siblings, she found they shared a curiosity about the inception of creative thought – that flash of insight – that Olsson experienced as both a mathematics student, and later, a novelist. Following this thread of connections, The Weil Conjectures explores the lives of Simone and André, the lore and allure of mathematics, and its significance in Olsson’s own life.

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

I Wish They'd Taught Me That: Overlooked and Omitted Topics in Mathematics concerns the topics which every undergraduate mathematics student "should" know but has probably never encountered. These topics are not the ones which dominate every syllabus, but those magnificent secrets that are beautiful, useful and accessible but which are inexplicably hidden away from the mainstream curriculum.Each chapter of this book concerns a different topic which students will almost certainly be unfamiliar with. Written in a lively, conversational style, by the end of each section the reader should feel equipped with the knowledge to explore the area more fully elsewhere.FeaturesTopics from a variety of areas of mathematics, including geometry, logic, analysis, algebra, numerical analysis, and topologyNumerous examples, diagrams, and exercisesCollections of resources where an interested reader can learn more about each topicNontechnical introductions to each chapter.For a full list of errata, maintained by the authors, please visit: https://juliangould.github.io/pages/IWTTMT_corrections.html

A "fascinating romp" (Johnjoe McFadden) and stirring account of the mathematicians who went looking for the bedrock philosophical foundations of their field and witnessed a house of cards collapse instead As the nineteenth century ended, mathematicians were celebrating a century of triumphs that-surprisingly-made clear how little they knew: What is the nature of infinity? Is math free from self-contradiction? And what does math have to do with reality? This was the Foundational Crisis in mathematics. In The Great Math War, Jason Socrates Bardi tells the story of three competing efforts by mathematicians to resolve it-and the firefight that ensued. Bertrand Russell thought we could achieve certainty if we treated math as an extension of logic. David Hilbert believed redemption lay in accepting mathematics as a formal game of arbitrary rules, no different from the moves and pieces in chess. And L. E. J. Brouwer argued math is entirely rooted in human intuition-and that math is not based on logic but rather logic is based on math. It was a bitter struggle, intellectually and personally, as the three vied to set the course for mathematics in the twentieth century. Set against the backdrop of international warfare unfolding alongside it, The Great Math War brings the Foundational Crisis to radiant life-and shows how it indelibly shaped twentieth-century intellectual life.

A NEW SCIENTIST BOOK OF THE YEAR'Clear, clever and friendly...even at her most whimsical, she is rigorous and insightful' ALEX BELLOS'Eugenia Cheng has humour, grace and a natural gift' DANIEL LEVITIN'Playful and deeply serious ... shows how exploring equality in maths may help the real world' NEW SCIENTISTWhen we see an equals sign, we usually see something clear cut: problem on one side, solution on the other. We might need to shuffle some things around - balance the equation - to get there, but it's all pretty clear cut...isn't it?As it turns out, between those parallel lines lies something far more exciting than questions and answers. An equals sign is an invitation to a mathematical playground of choice and abstraction. By opening your mind to different mathematical choices and perspectives, you can unlock far greater insight than you could have dreamed.Eugenia Cheng explores the rich and rewarding interplay between sameness and difference, and offers us a new way to see the world based on the choices and interpretations we make. A glorious celebration of mathematics, Unequal will change the way you think - in maths, and in life.

Think of a number between one and ten.No, hang on, let's make this interesting. Between zero and infinity. Even if you stick to the whole numbers, there are a lot to choose from - an infinite number in fact. Throw in decimal fractions and infinity suddenly gets an awful lot bigger (is that even possible?) And then there are the negative numbers, the imaginary numbers, the irrational numbers like pi which never end. It literally never ends.The world of numbers is indeed strange and beautiful. Among its inhabitants are some really notable characters - pi, e, the "imaginary" number i and the famous golden ratio to name just a few. Prime numbers occupy a special status. Zero is very odd indeed: is it a number, or isn't it?How Numbers Work takes a tour of this mind-blowing but beautiful realm of numbers and the mathematical rules that connect them. Not only that, but take a crash course on the biggest unsolved problems that keep mathematicians up at night, find out about the strange and unexpected ways mathematics influences our everyday lives, and discover the incredible connection between numbers and reality itself.ABOUT THE SERIESNew Scientist Instant Expert books are definitive and accessible entry points to the most important subjects in science; subjects that challenge, attract debate, invite controversy and engage the most enquiring minds. Designed for curious readers who want to know how things work and why, the Instant Expert series explores the topics that really matter and their impact on individuals, society, and the planet, translating the scientific complexities around us into language that's open to everyone, and putting new ideas and discoveries into perspective and context.

This Element aims to present an outline of mathematics and its history, with particular emphasis on events that shook up its philosophy. It ranges from the discovery of irrational numbers in ancient Greece to the nineteenth- and twentieth-century discoveries on the nature of infinity and proof. Recurring themes are intuition and logic, meaning and existence, and the discrete and the continuous. These themes have evolved under the influence of new mathematical discoveries and the story of their evolution is, to a large extent, the story of philosophy of mathematics.

In this third installment of his classic 'Foundations' trilogy, Michel Serres takes on the history of geometry and mathematics. Even more broadly, Geometry is the beginnings of things and also how these beginnings have shaped how we continue to think philosophically and critically. Serres rejects a traditional history of mathematics which unfolds in a linear manner, and argues for the need to delve into the past of maths and identify a series of ruptures which can help shed light on how this discipline has developed and how, in turn, the way we think has been shaped and formed.This meticulous and lyrical translation marks the first ever English translation of this key text in the history of ideas.

A WATERSTONES BEST BOOK OF 2023A NEW SCIENTIST BEST BOOK OF 2023WINNER OF THE LA TIMES SCIENCE & TECHNOLOGY 2023 BOOK PRIZE'A generous tour of mathematics for anyone whose instincts tend less towards "Just tell me the answer" and more towards "Wait, but why?"' JORDAN ELLENBERGTo many, maths feels like an unmapped wilderness. Between abstract concepts like imaginary numbers and infinity, it can sometimes feel like a lot of maths is just made up. Why, for example, is 1 not a prime? Why do two negatives cancel each other out? Where does trigonometry come from? Is maths even real? Abstract mathematician Eugenia Cheng shows that curiosity is the best teacher. Is Maths Real? takes us on a scintillating tour of the simple questions that provoke mathematics' deepest insights. 'Intriguing...celebrates the dizziness and disorientation engendered by childlike questions that hint at the deep mysteries beneath'NEW SCIENTIST'Masterfully uncovers what's simply profound in the profoundly simple'FRANCIS SU'Discover what it feels like to be a real mathematician'DAILY TELEGRAPH