This recreational math book takes the reader on a fantastic voyage into the world of natural numbers. From the earliest discoveries of the ancient Greeks to various fundamental characteristics of the natural number sequence, Clawson explains fascinating mathematical mysteries in clear and easy prose. He delves into the heart of number theory to see and understand the exquisite relationships among natural numbers, and ends by exploring the ultimate mystery of mathematics: the Riemann hypothesis, which says that through a point in a plane, no line can be drawn parallel to a given line.While a professional mathematician's treatment of number theory involves the most sophisticated analytical tools, its basic ideas are surprisingly easy to comprehend. By concentrating on the meaning behind various equations and proofs and avoiding technical refinements, Mathematical Mysteries lets the common reader catch a glimpse of this wonderful and exotic world.

    While maintaining that “the letters record the daily life of an ordinary scientist doing ordinary work,” Dyson nonetheless has worked with many of the twentieth century’s most renowned physicists, mathematicians, and intellectuals, so that Maker of Patterns presents not only his personal story but chronicles through firsthand accounts an exciting era of twentieth-century science.Though begun in the dark year of 1941 when Hitler’s armies had already conquered much of Europe, Dyson’s letters to his parents, written at Trinity College, Cambridge, often burst with the curiosity of a precocious seventeen-year-old. Pursuing mathematics and physics with a cast of legendary professors, Dyson thrived in Cambridge’s intellectual ferment, working on, for example, the theory of partitions or reading about Kurt Gödel’s hypotheses, while still finding time for billiards and mountain climbing. After graduating and serving with the Royal Air Force’s Bomber Command operational research section, whose job it was “to demolish German cities and kill as many German civilians as possible,” Dyson visited a war-torn Germany, hoping through his experience to create a “tolerably peaceful world.”Juxtaposing descriptions of scientific breakthroughs with concerns for mankind’s future, Dyson’s postwar letters reflect the quandaries faced by an entire scientific generation that was dealing with the aftereffects of nuclear detonations and concentration camp killings. Arriving in America in 1947 to study with Cornell’s Hans Bethe, Dyson continued to send weekly missives to England that were never technical but written with grace and candor, creating a portrait of a generation that was eager, as Einstein once stated, to solve “deep mysteries that Nature intend[ed] to keep for herself.”We meet, among others, scientists like Richard Feynman, who took Dyson across country on Route 66, Robert Oppenheimer, Eugene Wigner, Niels Bohr, James Watson, and a young Stephen Hawking; and we encounter intellectuals and leaders, among them Reinhold Niebuhr, George Kennan, Arthur C. Clarke, as well as Martin Luther King, Jr.The “patterns of comparable beauty in the dance of electrons jumping around atoms” invariably replicate themselves in this autobiography told through letters, one that combines accounts of wanton arms development with the not-inconsiderable demands of raising six children. As we once again attempt to guide society toward a more hopeful future, these letters, with their reenactment of what, at first, seems like a distant past, reveal invaluable truths about human nature.

    The seeds of this problem were sewn eighty years ago when a dramatic revolution in physics reached a climax at the 1927 Solvay conference in Brussels.It’s the story of a rush to formalize quantum physics, the work of just a handful of men fired by ambition, philosophical conflicts and personal agendas. Sheilla Jones paints an intimate portrait of the ten key figures who wrestled with the mysteries of the new science of the quantum, along with a powerful supporting cast of famous (and not so famous) colleagues.The Brussels conference was the first time so many of the “quantum ten” had been in the same place: Albert Einstein, the lone wolf; Niels Bohr, the obsessive but gentlemanly father figure; Max Born, the anxious hypochondriac; Werner Heisenberg, the intensely ambitious one; Wolfgang Pauli, the sharp-tongued critic with a dark side; Paul Dirac, the silent Englishman; Erwin Schrödinger, the enthusiastic womanizer; Prince Louis de Broglie, the French aristocrat; Pascual Jordan, the ardent Aryan nationalist, who was not invited; and Paul Ehrenfest, who was witness to it all.This is the story of quantum physics that has never been told, an equation-free investigation into the turbulent development of the new science and its very fallible creators, including little-known details of the personal relationship between the deeply troubled Ehrenfest and his dear friend Albert Einstein. Jones weaves together the personal and the scientific in a heartwarming—and heartbreaking—story of the men who struggled to create quantum physics … a story of passion, tragedy, ambition and science.

    From the transistor to the laser, it s hard to find an aspect of modern life that hasn t been touched by Bell Labs. Why did so many transformative ideas come from Bell Labs? In "The Idea Factory," Jon Gertner traces the origins of some of the twentieth century s most important inventions and delivers a riveting and heretofore untold chapter of American history. At its heart this is a story about the life and work of a small group of brilliant and eccentric men Mervin Kelly, Bill Shockley, Claude Shannon, John Pierce, and Bill Baker who spent their careers at Bell Labs. Their job was to research and develop the future of communications. Small-town boys, childhood hobbyists, oddballs: they give the lie to the idea that Bell Labs was a grim cathedral of top-down command and control.Gertner brings to life the powerful alchemy of the forces at work behind Bell Labs inventions, teasing out the intersections between science, business, and society. He distills the lessons that abide: how to recruit and nurture young talent; how to organize and lead fractious employees; how to find solutions to the most stubbornly vexing problems; how to transform a scientific discovery into a marketable product, then make it even better, cheaper, or both. Today, when the drive to invent has become a mantra, Bell Labs offers us a way to enrich our understanding of the challenges and solutions to technological innovation. Here, after all, was where the foundational ideas on the management of innovation were born. "The Idea Factory" is the story of the origins of modern communications and the beginnings of the information age a deeply human story of extraordinary men who were given extraordinary means time, space, funds, and access to one another and edged the world into a new dimension."

    Before this explosive growth into the modern age took place, an all-but-forgotten genius strove for forty years to win acceptance for the atomic theory of matter and an altogether new way of doing physics. Ludwig Boltz-mann battled with philosophers, the scientific establishment, and his own potent demons. His victory led the way to the greatest scientific achievements of the twentieth century. Now acclaimed science writer David Lindley portrays the dramatic story of Boltzmann and his embrace of the atom, while providing a window on the civilized world that gave birth to our scientific era. Boltzmann emerges as an endearingly quixotic character, passionately inspired by Beethoven, who muddled through the practical matters of life in a European gilded age. Boltzmann's story reaches from fin de siecle Vienna, across Germany and Britain, to America. As the Habsburg Empire was crumbling, Germany's intellectual might was growing; Edinburgh in Scotland was one of the most intellectually fertile places on earth; and, in America, brilliant independent minds were beginning to draw on the best ideas of the bureaucratized old world.Boltzmann's nemesis in the field of theoretical physics at home in Austria was Ernst Mach, noted today in the term Mach I, the speed of sound. Mach believed physics should address only that which could be directly observed. How could we know that frisky atoms jiggling about corresponded to heat if we couldn't see them? Why should we bother with theories that only told us what would probably happen, rather than making an absolute prediction? Mach and Boltzmann both believed in the power of science, but their approaches to physics could not have been more opposed. Boltzmann sought to explain the real world, and cast aside any philosophical criteria. Mach, along with many nineteenth-century scientists, wanted to construct an empirical edifice of absolute truths that obeyed strict philosophical rules. Boltzmann did not get on well with authority in any form, and he did his best work at arm's length from it. When at the end of his career he engaged with the philosophical authorities in the Viennese academy, the results were personally disastrous and tragic. Yet Boltzmann's enduring legacy lives on in the new physics and technology of our wired world.Lindley's elegant telling of this tale combines the detailed breadth of the best history, the beauty of theoretical physics, and the psychological insight belonging to the finest of novels.

    Tracing his rise from a pragmatic local official in Kentucky to the leader of the Republican opposition in Washington, the book tracks McConnell’s transformation from a moderate Republican who supported abortion rights and public employee unions to the embodiment of partisan obstructionism and conservative orthodoxy on Capitol Hill. Driven less by a shift in ideological conviction than by a desire to win elections and stay in power at all costs, McConnell’s transformation exemplifies the “permanent campaign” mindset that has come to dominate American government. From his first race for local office in 1977—when the ad crew working on it nicknamed McConnell “love-me-love-me” for his insecurity and desire to please—to his fraught accommodation of the Tea Party, McConnell’s political career is a story of ideological calcification and a vital mirror for understanding this country’s own political development and what is wrought when politicians serve not at the behest of country, but at the behest of party and personal aggrandizement.

    He studied the flight patterns of birds to create some of the first human flying machines; designed military weapons and defenses; studied optics, hydraulics, and the workings of the human circulatory system; and created designs for rebuilding Milan, employing principles still used by city planners today. Perhaps most importantly, Leonardo pioneered an empirical, systematic approach to the observation of nature-what is known today as the scientific method.Drawing on over 6,000 pages of Leonardo's surviving notebooks, acclaimed scientist and bestselling author Fritjof Capra reveals Leonardo's artistic approach to scientific knowledge and his organic and ecological worldview. In this fascinating portrait of a thinker centuries ahead of his time, Leonardo singularly emerges as the unacknowledged “father of modern science.”From the Trade Paperback edition.

    Thorp invented card counting, proving the seemingly impossible: that you could beat the dealer at the blackjack table. As a result he launched a gambling renaissance. His remarkable success--and mathematically unassailable method--caused such an uproar that casinos altered the rules of the game to thwart him and the legions he inspired. They barred him from their premises, even put his life in jeopardy. Nonetheless, gambling was forever changed.Thereafter, Thorp shifted his sights to "the biggest casino in the world" Wall Street. Devising and then deploying mathematical formulas to beat the market, Thorp ushered in the era of quantitative finance we live in today. Along the way, the so-called godfather of the quants played bridge with Warren Buffett, crossed swords with a young Rudy Giuliani, detected the Bernie Madoff scheme, and, to beat the game of roulette, invented, with Claude Shannon, the world's first wearable computer.Here, for the first time, Thorp tells the story of what he did, how he did it, his passions and motivations, and the curiosity that has always driven him to disregard conventional wisdom and devise game-changing solutions to seemingly insoluble problems. An intellectual thrill ride, replete with practical wisdom that can guide us all in uncertain financial waters, A Man for All Markets is an instant classic--a book that challenges its readers to think logically about a seemingly irrational world.Praise for A Man for All Markets"In A Man for All Markets, [Thorp] delightfully recounts his progress (if that is the word) from college teacher to gambler to hedge-fund manager. Along the way we learn important lessons about the functioning of markets and the logic of investment."--The Wall Street Journal"[Thorp] gives a biological summation (think Richard Feynman's Surely You're Joking, Mr. Feynman!) of his quest to prove the aphorism 'the house always wins' is flawed. . . . Illuminating for the mathematically inclined, and cautionary for would-be gamblers and day traders"-- Library Journal

    Now, at a moment when mathematicians are finally moving in on a proof, Dartmouth professor Dan Rockmore tells the riveting history of the hunt for a solution.In 1859 German professor Bernhard Riemann postulated a law capable of describing with an amazing degree of accuracy the occurrence of the prime numbers. Rockmore takes us all the way from Euclid to the mysteries of quantum chaos to show how the Riemann hypothesis lies at the very heart of some of the most cutting-edge research going on today in physics and mathematics.

    Approaching science with a freshness unbound by convention or previous expectations, he produced some of the most original scientific thinking of the nineteenth century - and his discoveries went on to shape the twentieth century.

    The book was based on a course of public lectures delivered by Schrödinger in February 1943 at Trinity College, Dublin. Schrödinger's lecture focused on one important question: "how can the events in space and time which take place within the spatial boundary of a living organism be accounted for by physics and chemistry?" In the book, Schrödinger introduced the idea of an "aperiodic crystal" that contained genetic information in its configuration of covalent chemical bonds. In the 1950s, this idea stimulated enthusiasm for discovering the genetic molecule and would give both Francis Crick and James Watson initial inspiration in their research.

    Five hundred years after Luther’s now famous Ninety-five Theses appeared, Eric Metaxas, acclaimed biographer of the bestselling Bonhoeffer: Pastor, Martyr, Prophet, Spy and Amazing Grace: William Wilberforce and the Heroic Campaign to End Slavery, paints a startling portrait of the wild figure whose adamantine faith cracked the edifice of Western Christendom and dragged medieval Europe into the future. Written in riveting prose and impeccably researched, Martin Luther tells the searing tale of a humble man who, by bringing ugly truths to the highest seats of power, caused the explosion whose sound is still ringing in our ears. Luther’s monumental faith and courage gave birth to the ideals of liberty, equality, and individualism that today lie at the heart of all modern life.

    S. Lewis continues to inspire and fascinate millions. His legacy remains varied and vast. He was a towering intellectual figure, a popular fiction author who inspired a global movie franchise around the world of Narnia, and an atheist-turned-Christian thinker.In C.S. Lewis: A Life, Alister McGrath, prolific author and respected professor at King's College of London, paints a definitive portrait of the life of C. S. Lewis. After thoroughly examining recently published Lewis correspondence, Alister challenges some of the previously held beliefs about the exact timing of Lewis's shift from atheism to theism and then to Christianity. He paints a portrait of an eccentric thinker who became an inspiring, though reluctant, prophet for our times.You won't want to miss this fascinating portrait of a creative genius who inspired generations. (Tyndale House Publishers)

    Admittedly, computers now play chess at the grandmaster level, but do they understand the game as we do? Can a computer eventually do everything a human mind can do? In this absorbing and frequently contentious book, Roger Penrose--eminent physicist and winner, with Stephen Hawking, of the prestigious Wolf prize--puts forward his view that there are some facets of human thinking that can never be emulated by a machine. Penrose examines what physics and mathematics can tell us about how the mind works, what they can't, and what we need to know to understand the physical processes of consciousness. He is among a growing number of physicists who think Einstein wasn't being stubborn when he said his little finger told him that quantum mechanics is incomplete, and he concludes that laws even deeper than quantum mechanics are essential for the operation of a mind. To support this contention, Penrose takes the reader on a dazzling tour that covers such topics as complex numbers, Turing machines, complexity theory, quantum mechanics, formal systems, Godel undecidability, phase spaces, Hilbert spaces, black holes, white holes, Hawking radiation, entropy, quasicrystals, the structure of the brain, and scores of other subjects. The Emperor's New Mind will appeal to anyone with a serious interest in modern physics and its relation to philosophical issues, as well as to physicists, mathematicians, philosophers and those on either side of the AI debate.

    In this compelling memoir, his first wife, Jane Hawking, relates the inside story of their extraordinary marriage. As Stephen's academic renown soared, his body was collapsing under the assaults of a motor neuron disease. Jane's candid account of trying to balance his 24-hour care with the needs of their growing family reveals the inner strength of the author, while the self-evident character and achievements of her husband make for an incredible tale presented with unflinching honesty. Jane's candor is no less apparent when the marriage finally ends in a high-profile meltdown, with Stephen leaving Jane for one of his nurses and Jane marrying an old family friend. In this exceptionally open, moving, and often funny memoir, Jane Hawking confronts not only the acutely complicated and painful dilemmas of her first marriage, but also the relationship's fault lines exposed by the pervasive effects of fame and wealth. The result is a book about optimism, love, and change that will resonate with readers everywhere.