Symmetry is all around us. Of fundamental significance to the way we interpret the world, this unique, pervasive phenomenon indicates a dynamic relationship between objects. Combining a rich historical narrative with his own personal journey as a mathematician, Marcus du Sautoy takes a unique look into the mathematical mind as he explores deep conjectures about symmetry and brings us face-to-face with the oddball mathematicians, both past and present, who have battled to understand symmetry's elusive qualities.

How do you remember more and forget less? How can you earn more and become more creative just by moving house? And how do you pack a car boot most efficiently? This is your shortcut to the art of the shortcut. Mathematics is full of better ways of thinking, and with over 2,000 years of knowledge to draw on, Oxford mathematician Marcus du Sautoy interrogates his passion for shortcuts in this fresh and fascinating guide. After all, shortcuts have enabled so much of human progress, whether in constructing the first cities around the Euphrates 5,000 years ago, using calculus to determine the scale of the universe or in writing today's algorithms that help us find a new life partner. As well as looking at the most useful shortcuts in history - such as measuring the circumference of the earth in 240 BC to diagrams that illustrate how modern GPS works - Marcus also looks at how you can use shortcuts in investing or how to learn a musical instrument to memory techniques. He talks to, among many, the writer Robert MacFarlane, cellist Natalie Clein and the psychologist Suzie Orbach, asking whether shortcuts are always the best idea and, if so, when they use them. With engaging puzzles and conundrums throughout to illustrate the shortcut's ability to find solutions with speed, Thinking Better offers many clever strategies for daily complex problems.

Why do some games seem to be universal while others have a particular connection to the culture of the people playing them? Around the World in 80 Games is about the mathematics of chance, game theory, gamification, gaming strategies and computer games. Traversing the globe, Marcus du Sautoy looks at the genesis of games new and old, explores how to invent a good game and explains the fascination of a popular lockdown game. From the secrets of whist to hopscotch, Scrabble to Wordle. The most simple games endure: board games, card games and dice games have captivated us for centuries and the acclaimed mathematician and author of The Creativity Code (among many others) will once again bring mathematics to the fore with insight and aplomb in Around the World in 80 Games.

The paperback of the critically-acclaimed popular science book by a writer who is fast becoming a celebrity mathematician. Prime numbers are the very atoms of arithmetic. They also embody one of the most tantalising enigmas in the pursuit of human knowledge. How can one predict when the next prime number will occur? Is there a formula which could generate primes? These apparently simple questions have confounded mathematicians ever since the Ancient Greeks. In 1859, the brilliant German mathematician Bernard Riemann put forward an idea which finally seemed to reveal a magical harmony at work in the numerical landscape. The promise that these eternal, unchanging numbers would finally reveal their secret thrilled mathematicians around the world. Yet Riemann, a hypochondriac and a troubled perfectionist, never publicly provided a proof for his hypothesis and his housekeeper burnt all his personal papers on his death. Whoever cracks Riemann's hypothesis will go down in history, for it has implications far beyond mathematics. In business, it is the lynchpin for security and e-commerce. In science, it has critical ramifications in Quantum Mechanics, Chaos Theory, and the future of comput

A pro-p group is the inverse limit of some system of finite p-groups, that is, of groups of prime-power order where the prime - conventionally denoted p - is fixed. Thus from one point of view, to study a pro-p group is the same as studying an infinite family of finite groups; but a pro-p group is also a compact topological group, and the compactness works its usual magic to bring 'infinite' problems down to manageable proportions. The p-adic integers appeared about a century ago, but the systematic study of pro-p groups in general is a fairly recent development. Although much has been dis covered, many avenues remain to be explored; the purpose of this book is to present a coherent account of the considerable achievements of the last several years, and to point the way forward. Thus our aim is both to stimulate research and to provide the comprehensive background on which that research must be based. The chapters cover a wide range. In order to ensure the most authoritative account, we have arranged for each chapter to be written by a leading contributor (or contributors) to the topic in question. Pro-p groups appear in several different, though sometimes overlapping, contexts."

'Du Sautoy's discussion of computer creativity is fascinating' Observer CAN MACHINES BE CREATIVE? In The Creativity Code, Marcus du Sautoy examines the nature of creativity, asking how much of our emotional response to art is a product of our brains reacting to pattern and structure, and exactly what it is to be creative in mathematics, art, language and music. Exploring how long it might be before machines compose a symphony or paint a masterpiece, and whether they might jolt us into being more imaginative in turn, The Creativity Code is a fascinating and very different exploration into the essence of what it means to be human.

Alone in a cube that's glowing in the darkness, X is content within its little universe of infinite thought. This solitude is disturbed by the appearance of Y, who insists on exposing X to the richness of the physical world. Each begins to long for what the other has, luring them into a strange loop. In this play for two variables, Marcus du Sautoy and Victoria Gould use mathematics and theatre to navigate the furthest reaches of our world. Through a series of surreal episodes, X and Y tackle some of life's greatest questions: where did the universe come from, does time have an end, do we have free will? I is a Strange Loop was first performed by the authors at the Barbican Pit, London, in March 2019. 'I is a Strange Loop is a play that plays with ideas, concepts, abstractions and relationships that are, usually, hidden from the sight of ordinary mortals, articulating the ineffable, incarnating the incorporeal, revealing the inconceivable. It makes us feel we know a great deal more than we do. It is also very funny, utterly compelling and marvellously human.' Simon McBurney

A pro-p group is the inverse limit of some system of finite p-groups, that is, of groups of prime-power order where the prime - conventionally denoted p - is fixed. Thus from one point of view, to study a pro-p group is the same as studying an infinite family of finite groups; but a pro-p group is also a compact topological group, and the compactness works its usual magic to bring 'infinite' problems down to manageable proportions. The p-adic integers appeared about a century ago, but the systematic study of pro-p groups in general is a fairly recent development. Although much has been dis covered, many avenues remain to be explored; the purpose of this book is to present a coherent account of the considerable achievements of the last several years, and to point the way forward. Thus our aim is both to stimulate research and to provide the comprehensive background on which that research must be based. The chapters cover a wide range. In order to ensure the most authoritative account, we have arranged for each chapter to be written by a leading contributor (or contributors) to the topic in question. Pro-p groups appear in several different, though sometimes overlapping, contexts."

Zeta functions have been a powerful tool in mathematics over the last two centuries. This book considers a new class of non-commutative zeta functions which encode the structure of the subgroup lattice in infinite groups. It explores the analytic behavior of these functions together with an investigation of functional equations. The book examines many important examples of zeta functions, providing an important database of explicit examples and methods for calculation.

This new book from the author of 'The Music of the Primes' combines a personal insight into the mind of a working mathematician with the story of one of the biggest adventures in mathematics: the search for symmetry. This is the story of how humankind has come to its understanding of the bizarre world of symmetry - a subject of fundamental significance to the way we interpret the world around us. Our eyes and minds are drawn to symmetrical objects, from the sphere to the swastika, the pyramid to the pentagon. Symmetry indicates a dynamic relationship or connection between objects, and it is all-pervasive: in chemistry and physics the concept of symmetry explains the structure of crystals or the theory of fundamental particles; in evolutionary biology, the natural world exploits symmetry in the fight for survival; symmetry and the breaking of symmetry are central to ideas in art, architecture and music; the mathematics of symmetry is even exploited in industry, for example to find efficient ways to store more music on a CD or to keep your mobile phone conversation from cracking up through interference. Marcus du Sautoy constantly strives to push his own boundaries to find ways in which to share the excitement of mathematics with a broader audience; this book charts his own personal quest to master one of the most innate and intangible concepts, and to demonstrate the intricacy and beauty of the world around us.

"Cosmos" offers new approaches on the stunning art works of Eduardo Terrazas (* 1936). Four well known authors present a multidisciplinary vision on the artists ongoing series "Possibilities of a Structure". Which suggests at once a curiosity in the fabric of our universe and a profoundly human hope for an underlying rationality behind the chaos of the world. Eduardo Terrazas has explored a lifetime’s worth of questions about the nature of the universe through the microcosm of his images. He derives his visual reflections with a basic geometric structure and a technique that is inspired by the Huichol tablas from Mexican indigenous tribes. His highly colourful and playful series "Possibilities of a Structure" – of which Cosmos is a subseries – has been an ongoing project since 1974 and comprises over 650 works until today: an artistic exploration of the boundaries of the infinite.

From the author of 'The Music of the Primes' and 'Finding Moonshine' comes a short, lively book on five mathematical problems that just refuse be solved - and on how many everyday problems can be solved by maths. Every time we download a song from Itunes, take a flight across the Atlantic or talk on our mobile phones, we are relying on great mathematical inventions. Maths may fail to provide answers to various of its own problems, but it can provide answers to problems that don't seem to be its own - how prime numbers are the key to Real Madrid's success, to secrets on the Internet and to the survival of insects in the forests of North America. In 'The Number Mysteries', Marcus du Sautoy explains how to fake a Jackson Pollock; how to work out whether or not the universe has a hole in the middle of it; how to make the world's roundest football. He shows us how to see shapes in four dimensions - and how maths makes you a better gambler. He tells us about the quest to predict the future - from the flight of asteroids to an impending storm, from bending a ball like Beckham to predicting population growth. It's a book to dip in to; a book to challenge and puzzle - and a book that gives us answers.

Cosmos: Silence and Infinite offers new approaches on the stunning art works of Eduardo Terrazas's (1936) art works. Four well known authors present a multidisciplinary vision on the artists ongoing series Possibilities of a Structure. Which suggests at once a curiosity in the fabric of our universe and a profoundly human hope for an underlying rationality behind the chaos of the world. Eduardo Terrazas's has explored a lifetime's worth of questions about the nature of the universe through the microcosm of his images. He derives his visual reflections with a basic geometric structure and a technique that is inspired by the Huichol "tablas" from Mexican indigenous tribes. His highly colourful and playful series Possibilities of a Structure - of which Cosmos is a subseries - is ongoing since 1974 and holds over 650 works until today: an artistic exploration of the boundaries of the infinite.

In 1859, German mathematician Bernhard Riemann presented a paper to the Berlin Academy that would forever change mathematics. The subject was the mystery of prime numbers. At the heart of the presentation was an idea that Riemann had not yet proved--one that baffles mathematicians to this day.

Solving the Riemann Hypothesis could change the way we do business, since prime numbers are the lynchpin for security in banking and e-commerce. It would also have a profound impact on the cutting edge of science, affecting quantum mechanics, chaos theory, and the future of computing. Leaders in math and science are trying to crack the elusive code, and a prize of $1 million has been offered to the winner. In this engaging book, Marcus du Sautoy reveals the extraordinary history behind the holy grail of mathematics and the ongoing quest to capture it.

How do you remember more and forget less? How can you earn more and become more creative just by moving house? And how do you pack a car boot most efficiently? This is your shortcut to the art of the shortcut. Mathematics is full of better ways of thinking, and with over 2,000 years of knowledge to draw on, Oxford mathematician Marcus du Sautoy interrogates his passion for shortcuts in this fresh and fascinating guide. After all, shortcuts have enabled so much of human progress, whether in constructing the first cities around the Euphrates 5,000 years ago, using calculus to determine the scale of the universe or in writing today's algorithms that help us find a new life partner. As well as looking at the most useful shortcuts in history - such as measuring the circumference of the earth in 240 BC to diagrams that illustrate how modern GPS works - Marcus also looks at how you can use shortcuts in investing or how to learn a musical instrument to memory techniques. He talks to, among many, the writer Robert MacFarlane, cellist Natalie Clein and the psychologist Suzie Orbach, asking whether shortcuts are always the best idea and, if so, when they use them. With engaging puzzles and conundrums throughout to illustrate the shortcut's ability to find solutions with speed, Thinking Better offers many clever strategies for daily complex problems.

Will a computer ever compose a symphony, write a prize-winning novel, or paint a masterpiece? And if so, would we be able to tell the difference?

As humans, we have an extraordinary ability to create works of art that elevate, expand and transform what it means to be alive.

Yet in many other areas, new developments in AI are shaking up the status quo, as we find out how many of the tasks humans engage in can be done equally well, if not better, by machines. But can machines be creative? Will they soon be able to learn from the art that moves us, and understand what distinguishes it from the mundane?

In The Creativity Code, Marcus du Sautoy examines the nature of creativity, as well as providing an essential guide into how algorithms work, and the mathematical rules underpinning them. He asks how much of our emotional response to art is a product of our brains reacting to pattern and structure, and exactly what it is to be creative in mathematics, art, language and music.

Marcus finds out how long it might be before machines come up with something creative, and whether they might jolt us into being more imaginative in turn. The result is a fascinating and very different exploration into both AI and the essence of what it means to be human.

"Every time we download music, take a flight across the Atlantic or talk on our cell phones, we are relying on great mathematical inventions. In The Number Mysteries, one of our generations foremost mathematicians Marcus du Sautoy offers a playful and accessible examination of numbers and how, despite efforts of the greatest minds, the most fundamental puzzles of nature remain unsolved. Du Sautoy tells about the quest to predict the future from the flight of asteroids to an impending storm, from bending a ball like Beckham to forecasting population growth. He brings to life the beauty behind five mathematical puzzles that have contributed to our understanding of the world around us and have helped develop the technology to cope with it. With loads of games to play and puzzles to solve, this is a math book for everyone"--Provided by publisher.

'Brilliant and fascinating. No one is better at making the recondite accessible and exciting' Bill Bryson Britain's most famous mathematician takes us to the edge of knowledge to show us what we cannot know. Is the universe infinite? Do we know what happened before the Big Bang? Where is human consciousness located in the brain? And are there more undiscovered particles out there, beyond the Higgs boson? In the modern world, science is king: weekly headlines proclaim the latest scientific breakthroughs and numerous mathematical problems, once indecipherable, have now been solved. But are there limits to what we can discover about our physical universe? In this very personal journey to the edges of knowledge, Marcus du Sautoy investigates how leading experts in fields from quantum physics and cosmology, to sensory perception and neuroscience, have articulated the current lie of the land. In doing so, he travels to the very boundaries of understanding, questioning contradictory stories and consulting cutting edge data. Is it possible that we will one day know everything? Or are there fields of research that will always lie beyond the bounds of human comprehension? And if so, how do we cope with living in a universe where there are things that will forever transcend our understanding? In What We Cannot Know, Marcus du Sautoy leads us on a thought-provoking expedition to the furthest reaches of modern science. Prepare to be taken to the edge of knowledge to find out if there's anything we truly cannot know.

"A brilliant travel guide to the coming world of AI." -Jeanette Winterson What does it mean to be creative? Can creativity be trained? Is it uniquely human, or could AI be considered creative? Mathematical genius and exuberant polymath Marcus du Sautoy plunges us into the world of artificial intelligence and algorithmic learning in this essential guide to the future of creativity. He considers the role of pattern and imitation in the creative process and sets out to investigate the programs and programmers-from Deep Mind and the Flow Machine to Botnik and WHIM-who are seeking to rival or surpass human innovation in gaming, music, art, and language. A thrilling tour of the landscape of invention, The Creativity Code explores the new face of creativity and the mysteries of the human code. "As machines outsmart us in ever more domains, we can at least comfort ourselves that one area will remain sacrosanct and uncomputable: human creativity. Or can we?...In his fascinating exploration of the nature of creativity, Marcus du Sautoy questions many of those assumptions." -Financial Times "Fascinating...If all the experiences, hopes, dreams, visions, lusts, loves, and hatreds that shape the human imagination amount to nothing more than a 'code,' then sooner or later a machine will crack it. Indeed, du Sautoy assembles an eclectic array of evidence to show how that's happening even now." -The Times