Beginning millions of years ago with ancient “ant odometers” and moving through time to our modern-day quest for new dimensions, it covers 250 milestones in mathematical history. Among the numerous delights readers will learn about as they dip into this inviting anthology: cicada-generated prime numbers, magic squares from centuries ago, the discovery of pi and calculus, and the butterfly effect. Each topic gets a lavishly illustrated spread with stunning color art, along with formulas and concepts, fascinating facts about scientists’ lives, and real-world applications of the theorems.

    In the paper, Wigner observed that the mathematical structure of a physical theory often points the way to further advances in that theory and even to empirical predictions.

    Using Everett's unpublished papers (recently discovered in his son's basement) and dozens of interviews with his friends, colleagues, and surviving family members, Byrne paints, for the general reader, a detailed portrait of the genius who invented an astonishing way of describing our complex universe from the inside. Everett's mathematical model (called the "universal wave function") treats all possible events as "equally real," and concludes that countless copies of every person and thing exist in all possible configurations spread over an infinity of universes: many worlds. Afflicted by depression and addictions, Everett strove to bring rational order to the professional realms in which he played historically significant roles. In addition to his famous interpretation of quantum mechanics, Everett wrote a classic paper in game theory; created computer algorithms that revolutionized military operations research; and performed pioneering work in artificial intelligence for top secret government projects. He wrote the original software for targeting cities in a nuclear hot war; and he was one of the first scientists to recognize the danger of nuclear winter. As a Cold Warrior, he designed logical systems that modeled "rational" human and machine behaviors, and yet he was largely oblivious to the emotional damage his irrational personal behavior inflicted upon his family, lovers, and business partners. He died young, but left behind a fascinating record of his life, including correspondence with such philosophically inclined physicists as Niels Bohr, Norbert Wiener, and John Wheeler. These remarkable letters illuminate the long and often bitter struggle to explain the paradox of measurement at the heart of quantum physics. In recent years, Everett's solution to this mysterious problem-the existence of a universe of universes-has gained considerable traction in scientific circles, not as science fiction, but as an explanation of physical reality.

    "One of today's best popularizers of science." —Kirkus Reviews.Loyal readers of the monthly "Universe" essays in Natural History magazine have long recognized Neil deGrasse Tyson's talent for guiding them through the mysteries of the cosmos with stunning clarity and almost childlike enthusiasm. Here, Tyson compiles his favorite essays across a myriad of cosmic topics. The title essay introduces readers to the physics of black holes by explaining the gory details of what would happen to your body if you fell into one. "Holy Wars" examines the needless friction between science and religion in the context of historical conflicts. "The Search for Life in the Universe" explores astral life from the frontiers of astrobiology. And "Hollywood Nights" assails the movie industry's feeble efforts to get its night skies right. Known for his ability to blend content, accessibility, and humor, Tyson is a natural teacher who simplifies some of the most complex concepts in astrophysics while simultaneously sharing his infectious excitement about our universe.

    Now he brings his considerable talents to the history of one of math's most enduring puzzles: the seemingly paradoxical nature of infinity.Is infinity a valid mathematical property or a meaningless abstraction? The nineteenth-century mathematical genius Georg Cantor's answer to this question not only surprised him but also shook the very foundations upon which math had been built. Cantor's counterintuitive discovery of a progression of larger and larger infinities created controversy in his time and may have hastened his mental breakdown, but it also helped lead to the development of set theory, analytic philosophy, and even computer technology.Smart, challenging, and thoroughly rewarding, Wallace's tour de force brings immediate and high-profile recognition to the bizarre and fascinating world of higher mathematics.

    From the first time mankind had an inkling of the vast space that surrounds us, those who study the universe have had to struggle against political and religious preconceptions. They have included some of the most charismatic, courageous, and idiosyncratic thinkers of all time. In Coming of Age in the Milky Way, Timothy Ferris uses his unique blend of rigorous research and captivating narrative skill to draw us into the lives and minds of these extraordinary figures, creating a landmark work of scientific history.

    From Hesiod's Chaos, described in his poem about the origins of the Greek gods, Theogony, to today's mind-bending theories of the multiverse, humans have been consumed by the relentless pursuit of an answer to one awe inspiring question: What exactly happened during those first moments?Guido Tonelli, the acclaimed, award-winning particle physicist and a central figure in the discovery of the Higgs boson (the "God particle"), reveals the extraordinary story of our genesis--from the origins of the universe, to the emergence of life on Earth, to the birth of human language with its power to describe the world. Evoking the seven days of biblical creation, Tonelli takes us on a brisk, lively tour through the evolution of our cosmos and considers the incredible challenges scientists face in exploring its mysteries. Genesis both explains the fundamental physics of our universe and marvels at the profound wonder of our existence.

    Michael Guillen, known to millions as the science editor of ABC's Good Morning America, tells the fascinating stories behind five mathematical equations. As a regular contributor to daytime's most popular morning news show and an instructor at Harvard University, Dr. Michael Guillen has earned the respect of millions as a clear and entertaining guide to the exhilarating world of science and mathematics. Now Dr. Guillen unravels the equations that have led to the inventions and events that characterize the modern world, one of which -- Albert Einstein's famous energy equation, E=mc2 -- enabled the creation of the nuclear bomb. Also revealed are the mathematical foundations for the moon landing, airplane travel, the electric generator -- and even life itself. Praised by Publishers Weekly as "a wholly accessible, beautifully written exploration of the potent mathematical imagination," and named a Best Nonfiction Book of 1995, the stories behind The Five Equations That Changed the World, as told by Dr. Guillen, are not only chronicles of science, but also gripping dramas of jealousy, fame, war, and discovery. Dr. Michael Guillen is Instructor of Physics and Mathematics in the Core Curriculum Program at Harvard University.

    Mysteries don't lose their poetry because they are solved: the solution often is more beautiful than the puzzle, uncovering deeper mysteries. With the wit, insight, and spellbinding prose that have made him a best-selling author, Dawkins takes up the most important and compelling topics in modern science, from astronomy and genetics to language and virtual reality, combining them in a landmark statement of the human appetite for wonder. This is the book Richard Dawkins was meant to write: a brilliant assessment of what science is (and isn't), a tribute to science not because it is useful but because it is uplifting.

     The eternal questions of science and religion were profoundly recast by Einstein's theory of relativity and its implications that time can be warped by motion and gravitation, and that it cannot be meaningfully divided into past, present, and future. In About Time, Paul Davies discusses the big bang theory, chaos theory, and the recent discovery that the universe appears to be younger than some of the objects in it, concluding that Einstein's theory provides only an incomplete understanding of the nature of time. Davies explores unanswered questions such as: * Does the universe have a beginning and an end? * Is the passage of time merely an illusion? * Is it possible to travel backward -- or forward -- in time? About Time weaves physics and metaphysics in a provocative contemplation of time and the universe.

    And yet for many years it was equally baffling for scientists themselves. Manjit Kumar gives a dramatic and superbly-written history of this fundamental scientific revolution, and the divisive debate at its heart.For 60 years most physicists believed that quantum theory denied the very existence of reality itself. Yet Kumar shows how the golden age of physics ignited the greatest intellectual debate of the twentieth century.Quantum sets the science in the context of the great upheavals of the modern age. In 1925 the quantum pioneers nearly all hailed from upper-middle-class academic families; most were German; and their average age was 24. But it was their irrational, romantic spirit, formed in reaction to the mechanised slaughter of the First World War that inspired their will to test science to its limits.The essential read for anyone fascinated by this complex and thrilling story and by the band of young men at its heart.

    With his trademark clarity and humor, Holt probes the mysteries of quantum mechanics, the quest for the foundations of mathematics, and the nature of logic and truth. Along the way, he offers intimate biographical sketches of celebrated and neglected thinkers, from the physicist Emmy Noether to the computing pioneer Alan Turing and the discoverer of fractals, Benoit Mandelbrot. Holt offers a painless and playful introduction to many of our most beautiful but least understood ideas, from Einsteinian relativity to string theory, and also invites us to consider why the greatest logician of the twentieth century believed the U.S. Constitution contained a terrible contradiction--and whether the universe truly has a future.

    A meld of history and science, this book is a group portrait of some of the greatest minds who ever lived as they wrestled with nature’s most sweeping mysteries. The answers they uncovered still hold the key to how we understand the world.At the end of the seventeenth century—an age of religious wars, plague, and the Great Fire of London—when most people saw the world as falling apart, these earliest scientists saw a world of perfect order. They declared that, chaotic as it looked, the universe was in fact as intricate and perfectly regulated as a clock. This was the tail end of Shakespeare’s century, when the natural land the supernatural still twined around each other. Disease was a punishment ordained by God, astronomy had not yet broken free from astrology, and the sky was filled with omens. It was a time when little was known and everything was new. These brilliant, ambitious, curious men believed in angels, alchemy, and the devil, and they also believed that the universe followed precise, mathematical laws—-a contradiction that tormented them and changed the course of history.The Clockwork Universe is the fascinating and compelling story of the bewildered geniuses of the Royal Society, the men who made the modern world.

    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.

    It far surpasses any previous explanation of Relativity for laypersons.