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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.... and is also very funny, utterly compelling and marvellously human.' Simon McBurney.
(source: Nielsen Book Data)

• The Lovelace Test
• Three types of creativity
• Ready steady go
• Algorithms, the secret to modern life
• From top-down to bottom-up
• Algorithmic evolution
• Painting by numbers
• Learning from the masters
• The art of mathematics
• The mathematician's telescope
• Music : the process of sounding mathematics
• The song-writing formula
• DeepMathematics
• Language games
• Let AI tell you a story
• Why we create : a meeting of minds.

The award-winning author of The Music of the Primes explores the future of creativity and how machine learning will disrupt, enrich, and transform our understanding of what it means to be human. Can a well-programmed machine do anything a human can-only better? Complex algorithms are buying our groceries, picking our partners, and driving our investments. They can navigate more data than a doctor or lawyer and act with greater precision. For many years we've taken solace in the notion that they can't create. But now that algorithms can learn and adapt, does the future of creativity belong to machines too? It is hard to imagine a better guide to the bewildering world of artificial intelligence than Marcus du Sautoy, a celebrated Oxford mathematician whose work on symmetry in the ninth dimension has taken him to the vertiginous edge of mathematical understanding. In The Creativity Code he considers what machine learning means for the future of creativity. Programs like Deep Dream produce drip paintings that could fool students of Jackson Pollock; Deep Jazz composes music in the style of Duke Ellington. But do these programs just mimic, or do they have what it takes to create? Du Sautoy argues that to answer this question, we need to understand how the algorithms that drive them work-and this brings him back to his own subject of mathematics, with its puzzles, constraints, and enticing possibilities. Where most recent books on AI focus on the future of work, The Creativity Code moves us to the forefront of creative new technologies and offers a more positive and unexpected vision of our future cohabitation with machines.
(source: Nielsen Book Data)

• The Lovelace Test
• Three types of creativity
• Ready steady go
• Algorithms, the secret to modern life
• From top-down to bottom-up
• Algorithmic evolution
• Painting by numbers
• Learning from the masters
• The art of mathematics
• The mathematician's telescope
• Music: the process of sounding mathematics
• The song-writing formula
• Deepmathematics
• Language games
• Let AI tell you a story
• Why we create: a meeting of minds.

Most books on AI focus on the future of work. But now that algorithms can learn and adapt, does the future of creativity also belong to well-programmed machines? To answer this question, Marcus du Sautoy takes us to the forefront of creative new technologies and offers a more positive and unexpected vision of our future cohabitation with machines.-- Provided by publisher.

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.
(source: Nielsen Book Data)

Do something amazing and learn a new skill thanks to the Little Ways to Live a Big Life books! Birds do it, bees do it, even educated fleas do it... Not falling in love, but counting. Animals and humans have been using numbers to navigate their way through the jungle of life ever since we all evolved on this planet. But this book will help you to do something that humans have only recently understood how to do: to count to regions that no animal has ever reached. By the end of this book you'll be able to count to infinity...and beyond.On our way to infinity we'll discover how the ancient Babylonians used their bodies to count to 60 (which gave us 60 minutes in the hour), how the number zero was only discovered in the 7th century by Indian mathematicians contemplating the void, why in China going into the red meant your numbers had gone negative and why numbers might be our best language for communicating with alien life.But for millennia contemplating infinity has sent even the greatest minds into a spin. Then at the end of the nineteenth century mathematicians discovered a way to think about infinity that revealed that it is a number that we can count. Not only that. They found that there are an infinite number of infinities, some bigger than others. Just using the finite neurons in your brain and the finite pages in this book, you'll have your mind blown discovering the secret of how to count to infinity.
(source: Nielsen Book Data)

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.
(source: Nielsen Book Data)

"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.

• Introduction.- Nilpotent Groups: Explicit Examples.- Soluble Lie Rings.- Local Functional Equations.- Natural Boundaries I: Theory.- Natural boundaries II: Algebraic groups.- Natural boundaries III: Nilpotent groups.- Large polynomials.- Factorisation of polynomials associated to classical groups.- References.- Index.
• (source: Nielsen Book Data)

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. The book explores the analytic behaviour of these functions together with an investigation of functional equations. Many important examples of zeta functions are calculated and recorded providing an important data base of explicit examples and methods for calculation.
(source: Nielsen Book Data)

• Lie methods in the theory of pro-p groups, A. Shalev
• on the classification of prop-p groups and finite p-groups, C.R. Leedham-Green, S. McKay
• prop-p trees and applications, L. Ribes, P. Zalesskii
• just infinite branch groups, R. I. Grigorchuk
• on just infinite abstract and profinite groups, J.S. Wilson
• the Nottingham group, R. Camina
• on groups satisfying the Golod-Shafarevich condition, E. Zelmanov
• sub-group growth in prop-p groups, A. Mann
• zeta functions of groups, M. du Sautoy, D. Segal
• where the wild things are - ramification groups and the Nottingham group, M. du Sautoy, I. Fesenko
• p-adic Galois representations and prop-p Galois groups, N. Boston
• the cohomology of p-adic analytic groups, P. Symonds, T. Weigel. Appendix: further problems.
• (source: Nielsen Book Data)

The impetus for current research in pro-p groups comes from four main directions: from new applications in number theory, which continue to be a source of deep and challenging problems; from the traditional problem of classifying finite p-groups; from questions arising in infinite group theory; and finally, from the younger subject of 'profinite group theory'. A correspondingly diverse range of mathematical techniques is being successfully applied, leading to new results and pointing to exciting new directions of research. In this work important theoretical developments are carefully presented by leading mathematicians in the field, bringing the reader to the cutting edge of current research. With a systematic emphasis on the construction and examination of many classes of examples, the book presents a clear picture of the rich universe of pro-p groups, in its unity and diversity. Thirty open problems are discussed in the appendix. For graduate students and researchers in group theory, number theory, and algebra, this work will be an indispensable reference text and a rich source of promising avenues for further exploration.
(source: Nielsen Book Data)

• Prelude
• Part I. Pro-p Groups: 1. Profinite groups and pro-p groups
• 2. Powerful p-groups
• 3. Pro-p groups of finite rank
• 4. Uniformly powerful groups
• 5. Automorphism groups
• Interlude A. Fascicule de resultats: pro-p groups of finite rank
• Part II. Analytic Groups: 6. Normed algebras
• 7. The group algebra
• Interlude B. Linearity criteria
• 8. P-adic analytic groups
• Interlude C. Finitely generated groups, p-adic analytic groups and Poincare series
• 9. Lie theory
• Part III. Further Topics: 10. Pro-p groups of finite co-class
• 11. Dimension subgroup methods
• 12. Some graded algebras
• Interlude D. The Golod Shafarevic inequality
• Interlude E. Groups of sub-exponential growth
• 13. Analytic groups over pro-p rings.
• (source: Nielsen Book Data)

The first edition of this book was the indispensable reference for researchers in the theory of pro-p groups. In this second edition the presentation has been improved and important new material has been added. The first part of the book is group-theoretic. It develops the theory of pro-p groups of finite rank, starting from first principles and using elementary methods. Part II introduces p-adic analytic groups: by taking advantage of the theory developed in Part I, it is possible to define these, and derive all the main results of p-adic Lie theory, without having to develop any sophisticated analytic machinery. Part III, consisting of new material, takes the theory further. Among those topics discussed are the theory of pro-p groups of finite coclass, the dimension subgroup series, and its associated graded Lie algebra. The final chapter sketches a theory of analytic groups over pro-p rings other than the p-adic integers.
(source: Nielsen Book Data)

• disc 1. Episode 1: The language of the universe ; Episode 2: The genius of the East
• disc 2. Episode 3: The frontiers of space ; Episode 4: To infinity and beyond
• [disc 3.] Bonus disc: The music of the primes (2005) / written by Marcus du Sautoy ; directed and produced by Robin Dashwood.

In this landmark series of films, University of Oxford Professor Marcus du Sautoy escorts viewers through the history of this most important of all intellectual disciplines. In a journey that takes him through the ages and around the world, he examines the development of key mathematical ideas and shows how, in a multitude of surprising ways, mathematical ideas underpin the science, technology, and culture that shape our world.