He revolutionized the field of topology, which studies properties of geometric configurations that are unchanged by stretching or twisting. The Poincare conjecture lies at the heart of modern geometry and topology, and even pertains to the possible shape of the universe. The conjecture states that there is only one shape possible for a finite universe in which every loop can be contracted to a single point.Poincare's conjecture is one of the seven "millennium problems" that bring a one-million-dollar award for a solution. Grigory Perelman, a Russian mathematician, has offered a proof that is likely to win the Fields Medal, the mathematical equivalent of a Nobel prize, in August 2006. He also will almost certainly share a Clay Institute millennium award.In telling the vibrant story of The Poincare Conjecture, Donal O'Shea makes accessible to general readers for the first time the meaning of the conjecture, and brings alive the field of mathematics and the achievements of generations of mathematicians whose work have led to Perelman's proof of this famous conjecture.

    It engineered a civilization, empowered the world's first democracy, and led a band of ordinary citizens on a voyage of discovery that altered the course of history. With Lords of the Sea, renowned archaeologist John R. Hale presents, for the first time, the definitive history of the epic battles, the fearsome ships, and the men – from extraordinary leaders to seductive rogues – that established Athens's supremacy. With a scholar's insight and a storyteller's flair, Hale takes us on an unforgettable voyage with these heroes, their turbulent careers, and far-flung expeditions, bringing back to light a forgotten maritime empire and its majestic legacy.

    Encompassing a grand sweep of human history, A History of the World in 100 Objects begins with one of the earliest surviving objects made by human hands, a chopping tool from the Olduvai gorge in Africa, and ends with objects which characterise the world we live in today. Seen through MacGregor's eyes, history is a kaleidoscope - shifting, interconnected, constantly surprising, and shaping our world today in ways that most of us have never imagined. A stone pillar tells us about a great Indian emperor preaching tolerance to his people; Spanish pieces of eight tell us about the beginning of a global currency; and an early Victorian tea-set speaks to us about the impact of empire. An intellectual and visual feast, this is one of the most engrossing and unusual history books published in years. 'Brilliant, engagingly written, deeply researched' Mary Beard, Guardian 'A triumph: hugely popular, and rightly lauded as one of the most effective and intellectually ambitious initiatives in the making of 'public history' for many decades' Sunday Telegraph 'Highly intelligent, delightfully written and utterly absorbing ' Timothy Clifford, Spectator 'This is a story book, vivid and witty, shining with insights, connections, shocks and delights' Gillian Reynolds Daily Telegraph

    Then, attempting to break a Nazi code during World War II, he successfully designed and built one, thus ensuring the Allied victory. Turing became a champion of artificial intelligence, but his work was cut short. As an openly gay man at a time when homosexuality was illegal in England, he was convicted and forced to undergo a humiliating "treatment" that may have led to his suicide.With a novelist's sensitivity, David Leavitt portrays Turing in all his humanity—his eccentricities, his brilliance, his fatal candor—and elegantly explains his work and its implications.

    Through most of its long history, Greece was poor. But in the classical era, Greece was densely populated and highly urbanized. Many surprisingly healthy Greeks lived in remarkably big houses and worked for high wages at specialized occupations. Middle-class spending drove sustained economic growth. Classical wealth produced a stunning cultural efflorescence lasting hundreds of years.Why did Greece reach such heights in the classical period--and why only then? And how, after "the Greek miracle" had endured for centuries, did the Macedonians defeat the Greeks, seemingly bringing an end to their glory? Drawing on a massive body of newly available data and employing novel approaches to evidence, Josiah Ober offers a major new history of classical Greece and an unprecedented account of its rise and fall.Ober argues that Greece's rise was no miracle but rather the result of political breakthroughs and economic development. The extraordinary emergence of citizen-centered city-states transformed Greece into a society that defeated the mighty Persian Empire. Yet Philip and Alexander of Macedon were able to beat the Greeks in the Battle of Chaeronea in 338 BCE, a victory enabled by the Macedonians' appropriation of Greek innovations. After Alexander's death, battle-hardened warlords fought ruthlessly over the remnants of his empire. But Greek cities remained populous and wealthy, their economy and culture surviving to be passed on to the Romans--and to us.A compelling narrative filled with uncanny modern parallels, this is a book for anyone interested in how great civilizations are born and die.This book is based on evidence available on a new interactive website. To learn more, please visit http://polis.stanford.edu/

    Indeed, he sees the fall of Rome as a time of horror and dislocation that destroyed a great civilization, throwing the inhabitants of the West back to a standard of living typical of prehistoric times. Attacking contemporary theories with relish and making use of modern archaeological evidence, he looks at both the wider explanations for the disintegration of the Roman world and also the consequences for the lives of everyday Romans, who were caught in a world of marauding barbarians, and economic collapse.The book recaptures the drama and violence of the last days of the Roman world, and reminds us of the very real terrors of barbarian occupation. Equally important, Ward-Perkins contends that a key problem with the new way of looking at the end of the ancient world is that all difficulty and awkwardness is smoothed out into a steady and positive transformation of society. Nothing ever goes badly wrong in this vision of the past. The evidence shows otherwise.Up-to-date and brilliantly written, combining a lively narrative with the latest research and thirty illustrations, this superb volume reclaims the drama, the violence, and the tragedy of the fall of Rome.From Back Cover:For decades, the dominant view amongst historians has been that the 'fall of Rome' was a largely peaceful transition to Germanic rule, within a period of positive cultural evolution. Now, Bryan Ward-Perkins argues for what you always thought but didn't dare say: the Roman Empire really did fall to violent invasion; the 'transformation' of the Roman world saw a catastrophic collapse of living standards; and the 'Dark Ages' were genuinely sombre.

    But in Art & Physics, Leonard Shlain tracks their breakthroughs side by side throughout history to reveal an astonishing correlation of visions.From teh classical Greek sculptors to Andy Warhol and Jasper Johns, and from Aristotle to Einstein, aritsts have foreshadowed the discoveries of scientists, such as when Money and Cezanne intuited the coming upheaval in physics that Einstein would initiate. In this lively and colorful narrative, Leonard Shlain explores how artistic breakthroughs could have prefigured the visionary insights of physicists on so many occasions throughtout history.Provacative and original, Art & Physics is a seamless integration of the romance of art and the drama of science...and exhilarating history of ideas.

    Evo Devo Evolutionary Developmental Biology is the new science that has finally cracked open the box. Within the pages of his rich and riveting book, Sean B. Carroll explains how we are discovering that complex life is ironically much simpler than anyone ever expected.

    Gödel received public recognition of his work in 1951 when he was awarded the first Albert Einstein Award for achievement in the natural sciences--perhaps the highest award of its kind in the United States. The award committee described his work in mathematical logic as "one of the greatest contributions to the sciences in recent times."However, few mathematicians of the time were equipped to understand the young scholar's complex proof. Ernest Nagel and James Newman provide a readable and accessible explanation to both scholars and non-specialists of the main ideas and broad implications of Gödel's discovery. It offers every educated person with a taste for logic and philosophy the chance to understand a previously difficult and inaccessible subject.New York University Press is proud to publish this special edition of one of its bestselling books. With a new introduction by Douglas R. Hofstadter, this book will appeal students, scholars, and professionals in the fields of mathematics, computer science, logic and philosophy, and science.

    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.

    As politician and diplomat, writer and lover, but above all as a military genius, Julius Caesar is one of the perennially fascinating figures in history -- Boswell called him "the greatest man of any age." Christian Meier's authoritative and accessible biography is the definitive modern account of Caesar's life and career, setting Caesar's life story against the rich political and social background of the Late Roman Republic.

    Polya, How to Solve It will show anyone in any field how to think straight. In lucid and appealing prose, Polya reveals how the mathematical method of demonstrating a proof or finding an unknown can be of help in attacking any problem that can be reasoned out--from building a bridge to winning a game of anagrams. Generations of readers have relished Polya's deft--indeed, brilliant--instructions on stripping away irrelevancies and going straight to the heart of the problem.

    Augustine equate nothingness with the Devil? What tortuous means did 17th-century scientists employ in their attempts to create a vacuum? And why do contemporary quantum physicists believe that the void is actually seething with subatomic activity? You’ll find the answers in this dizzyingly erudite and elegantly explained book by the English cosmologist John D. Barrow.Ranging through mathematics, theology, philosophy, literature, particle physics, and cosmology, The Book of Nothing explores the enduring hold that vacuity has exercised on the human imagination. Combining high-wire speculation with a wealth of reference that takes in Freddy Mercury and Shakespeare alongside Isaac Newton, Albert Einstein, and Stephen Hawking, the result is a fascinating excursion to the vanishing point of our knowledge.

    Coated in red dust, the terrain is bewilderingly empty. And yet multiple spacecraft are circling Mars, sweeping over Terra Sabaea, Syrtis Major, the dunes of Elysium, and Mare Sirenum—on the brink, perhaps, of a staggering find, one that would inspire humankind as much as any discovery in the history of modern science.In this beautifully observed, deeply personal book, Georgetown scientist Sarah Stewart Johnson tells the story of how she and other researchers have scoured Mars for signs of life, transforming the planet from a distant point of light into a world of its own.Johnson’s fascination with Mars began as a child in Kentucky, turning over rocks with her father and looking at planets in the night sky. She now conducts fieldwork in some of Earth’s most hostile environments, such as the Dry Valleys of Antarctica and the salt flats of Western Australia, developing methods for detecting life on other worlds. Here, with poetic precision, she interlaces her own personal journey—as a female scientist and a mother—with tales of other seekers, from Percival Lowell, who was convinced that a utopian society existed on Mars, to Audouin Dollfus, who tried to carry out astronomical observations from a stratospheric balloon. In the process, she shows how the story of Mars is also a story about Earth: This other world has been our mirror, our foil, a telltale reflection of our own anxieties and yearnings.Empathetic and evocative, The Sirens of Mars offers an unlikely natural history of a place where no human has ever set foot, while providing a vivid portrait of our quest to defy our isolation in the cosmos.

    Much of what we know about the beliefs of the Sadducees and Pharisees comes from Josephus. Without Josephus, we would know very little about the Essenes, the ancient Jewish group most frequently associated with the Dead Sea Scrolls.Features include:The War of the Jews—an account of the Jewish revolt against Rome up to the destruction of the temple in JerusalemThe Antiquities of the Jews—a history of the Jews from Creation to the Roman occupation of PalestineThe Life of Flavius Josephus—the autobiography of Josephus, who fought against Rome and later served the empireAgainst Apion—a defense of the origin of Judaism in the face of Greco-Roman slandersDiscourse to the Greeks Concerning Hades—a text Whiston attributed to JosephusIndex of parallels between Josephus’s Antiquities and the Old Testament including the Apocrypha