'Space is big. Really big. You just won't believe how vastly, hugely, mind-bogglingly big it is. I mean, you may think it's a long way down the street to the chemist, but that's just peanuts to space.' Douglas Adams, Hitch-hiker's Guide to the Galaxy We human beings have trouble with infinity - yet infinity is a surprisingly human subject. Philosophers and mathematicians have gone mad contemplating its nature and complexity - yet it is a concept routinely used by schoolchildren. Exploring the infinite is a journey into paradox. Here is a quantity that turns arithmetic on its head, making it feasible that 1 = 0. Here is a concept that enables us to cram as many extra guests as we like into an already full hotel. Most bizarrely of all, it is quite easy to show that there must be something bigger than infinity - when it surely should be the biggest thing that could possibly be. Brian Clegg takes us on a fascinating tour of that borderland between the extremely large and the ultimate that takes us from Archimedes, counting the grains of sand that would fill the universe, to the latest theories on the physical reality of the infinite. Full of unexpected delights, whether St Augustine contemplating the nature of creation, Newton and Leibniz battling over ownership of calculus, or Cantor struggling to publicise his vision of the transfinite, infinity's fascination is in the way it brings together the everyday and the extraordinary, prosaic daily life and the esoteric. Whether your interest in infinity is mathematical, philosophical, spiritual or just plain curious, this accessible book offers a stimulating and entertaining read.

Infinity is a concept that fascinates everyone from a seven-year-old child to a maths professor. An exploration of the most mind-boggling feature of maths and physics, this work examines amazing paradoxes and looks at many features of this fascinating concept.

In A Brief History of Infinity, the infinite in all its forms - viewed from the perspective of mathematicians, philosophers, and theologians - is explored, as Zellini strives to explain this fundamental principle. What is the difference between trueand false infinity? How might we explain away the puzzle of Zeno's paradox? And how is the concept of infinity helping us as we wrestle with the fundamental uncertainties of the quantum world? Paolo Zellini shows that the concept of the infinite is a multifaceted one, and eloquently demonstrates the manner in which humanity has attempted to comprehend that concept for millenia.

Have you ever wondered what humans did before numbers existed? How they organized their lives, traded goods, or kept track of their treasures? What would your life be like without them? Numbers began as simple representations of everyday things, but mathematics rapidly took on a life of its own, occupying a parallel virtual world. In Are Numbers Real? Brian Clegg explores the way that maths has become more and more detached from reality, yet despite this is driving the development of modern physics. From devising a new counting system based on goats, through the weird and wonderful mathematics of imaginary numbers and infinity to the debate over whether mathematics has too much influence on the direction of science, this fascinating and accessible book opens the reader's eyes to the hidden reality of the strange yet familiar world of numbers.

A retitled and revised edition of Ian Stewart's The Problem of Mathematics, this is the perfect guide to today's mathematics. Read about the latest discoveries, including Andrew Wile's amazing proof of Fermat's Last Theorem, the newest advances in knot theory, the Four Colour Theorem, Chaos Theory, and fake four-dimensial spaces. See how simple concepts from probability theory shed light on the National Lottery and tell you how to maximize your winnings. Discover howinfinitesimals become respectable, why there are different kinds of infinity, and how to square the circle with the mathematical equivalent of a pair of scissors.

The infinite! No other question has ever moved so profoundly the spirit of man; no other idea has so fruitfully stimulated his intellect; yet no other concept stands in greater need of clarification than that of the infinite. . . - David Hilbert (1862-1943) Infinity is a fathomless gulf, There is a story attributed to David Hilbert, the preeminent mathe into which all things matician whose quotation appears above. A man walked into a vanish. hotel late one night and asked for a room. "Sorry, we don't have o Marcus Aurelius (121- 180), Roman Emperor any more vacancies," replied the owner, "but let's see, perhaps and philosopher I can find you a room after alL" Leaving his desk, the owner reluctantly awakened his guests and asked them to change their rooms: the occupant of room #1 would move to room #2, the occupant of room #2 would move to room #3, and so on until each occupant had moved one room over. To the utter astonish ment of our latecomer, room #1 suddenly became vacated, and he happily moved in and settled down for the night. But a numbing thought kept him from sleep: How could it be that by merely moving the occupants from one room to another, the first room had become vacated? (Remember, all of the rooms were occupied when he arrived.

An engaging account of the scientists and mathematicians who conceived of the concept of infinity, tracing the history of the idea from its ancient origins to its role in modern-day science and mathematics and profiling the individuals who defined, refined, and explored the paradoxes of infinity. Original.

A modern classic by an accomplished mathematician and best-selling author has been updated to encompass and explain the recent headline-making advances in the field in non-technical terms.

Documents the calculation, numerical value, and use of the ratio from 2000 B.C. to the modern computer age, detailing social conditions in eras when progress was made.

The bestselling author of "Infinite Jest" takes on the 2,000 year-old quest to understand infinity. Wallace brings his considerable talents to the history of one of math's most enduring puzzles: the seemingly paradoxical nature of infinity.

A thrilling journey from empty space all the way to the human mind.

In Infinity and the Mind, Rudy Rucker leads an excursion to that stretch of the universe he calls the "Mindscape," where he explores infinity in all its forms: potential and actual, mathematical and physical, theological and mundane. Rucker acquaints us with Gödel's rotating universe, in which it is theoretically possible to travel into the past, and explains an interpretation of quantum mechanics in which billions of parallel worlds are produced every microsecond. It is in the realm of infinity, he maintains, that mathematics, science, and logic merge with the fantastic. By closely examining the paradoxes that arise from this merging, we can learn a great deal about the human mind, its powers, and its limitations. Using cartoons, puzzles, and quotations to enliven his text, Rucker guides us through such topics as the paradoxes of set theory, the possibilities of physical infinities, and the results of Gödel's incompleteness theorems. His personal encounters with Gödel the mathematician and philosopher provide a rare glimpse at genius and reveal what very few mathematicians have dared to admit: the transcendent implications of Platonic realism.

Among the many constants that appear in mathematics, π, e, and i are the most familiar. Following closely behind is y, or gamma, a constant that arises in many mathematical areas yet maintains a profound sense of mystery. In a tantalizing blend of history and mathematics, Julian Havil takes the reader on a journey through logarithms and the harmonic series, the two defining elements of gamma, toward the first account of gamma's place in mathematics. Introduced by the Swiss mathematician Leonhard Euler (1707-1783), who figures prominently in this book, gamma is defined as the limit of the sum of 1 + 1/2 + 1/3 + . . . Up to 1/n, minus the natural logarithm of n--the numerical value being 0.5772156. . . . But unlike its more celebrated colleagues π and e, the exact nature of gamma remains a mystery--we don't even know if gamma can be expressed as a fraction. Among the numerous topics that arise during this historical odyssey into fundamental mathematical ideas are the Prime Number Theorem and the most important open problem in mathematics today--the Riemann Hypothesis (though no proof of either is offered!). Sure to be popular with not only students and instructors but all math aficionados, Gamma takes us through countries, centuries, lives, and works, unfolding along the way the stories of some remarkable mathematics from some remarkable mathematicians.

Star Trek was right — there is only one final frontier, and that is space... Human beings are natural explorers, and nowhere is this frontier spirit stronger than in the United States of America. It almost defines the character of the US. But the Earth is running out of frontiers fast. In Brian Clegg's The Final Frontier we discover the massive challenges that face explorers, both human and robotic, to uncover the current and future technologies that could take us out into the galaxy and take a voyage of discovery where no one has gone before... but one day someone will. In 2003, General Wesley Clark set the nation a challenge to produce the technology that would enable new pioneers to explore the galaxy. That challenge is tough — the greatest we've ever faced. But taking on the final frontier does not have to be a fantasy. In a time of recession, escapism is always popular — and what greater escape from the everyday can there be than the chance of leaving Earth's bounds and exploring the universe? With a rich popular culture heritage in science fiction movies, books and TV shows, this is a subject that entertains and informs in equal measure.

‘I have a truly marvellous demonstration of this proposition which this margin is too narrow to contain.’

In 2000, the Clay Foundation of Cambridge, Massachusetts, announced a historic competition: Whoever could solve any of seven extraordinarily difficult mathematical problems, and have the solution acknowledged as correct by the experts, would receive $1million in prize money. They encompass many of the most fascinating areas of pure and applied mathematics, from topology and number theory to particle physics, cryptography, computing and even aircraft design. Keith Devlin describes here what the seven problems are, how they came about, and what they mean for mathematics and science. In the hands of Devlin, each Millennium Problem becomes a fascinating window onto the deepest questions in the field.

LONGLISTED FOR THE 2014 WINTON ROYAL SOCIETY PRIZE FOR SCIENCE BOOKSAs troubling as we pattern-seeking humans may find it, modern science has repeatedly shown us that randomness is the underlying heartbeat of nature.In Dice World, acclaimed science writer Brian Clegg takes readers on an incredible trip around our random universe, uncovering the truths and lies behind probability and statistics, explaining how chaotic intervention is behind every great success in business, and demonstrating the possibilities quantum mechanics has given us for creating unbreakable ciphers and undergoing teleportation.He explores how the ‘clockwork universe’ imagined by Newton, in which everything could be predicted given enough data, was disproved bit by bit, to be supplanted by chaos theory and quantum physics. Clegg reveals a world in which not only is accurate forecasting often impossible but probability is the only way for us to understand the fundamental nature of things.Forget the clockwork universe. Welcome to Dice World, a unique portrait of a startlingly complex cosmos, from the bizarre microscopic world of the quantum to the unfathomable mechanics of planetary movements, where very little is as it seems...