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.

    Whether pondering black holes or predicting discoveries at CERN, physicists believe the best theories are beautiful, natural, and elegant, and this standard separates popular theories from disposable ones. This is why, Sabine Hossenfelder argues, we have not seen a major breakthrough in the foundations of physics for more than four decades. The belief in beauty has become so dogmatic that it now conflicts with scientific objectivity: observation has been unable to confirm mindboggling theories, like supersymmetry or grand unification, invented by physicists based on aesthetic criteria. Worse, these "too good to not be true" theories are actually untestable and they have left the field in a cul-de-sac. To escape, physicists must rethink their methods. Only by embracing reality as it is can science discover the truth.

    In this new major work Abraham Pais, himself an eminent physicist who worked alongside Einstein in the post-war years, traces the development of Einstein's entire oeuvre. This is the first book which deal comprehensively and in depth with Einstein's science, both the successes and the failures.Running through the book is a completely non-scientific biography (identified in the table of contents by italic type) including many letters which appear in English for the first time, as well as other information not published before.Throughout the preparation of this book, Pais has had complete access to the Einstein Archives (now in the possession of the Hebrew University) and the invaluable guidance of the late Helen Dukas--formerly Einstein's private secretary.

    At the time, Watson was only 24, a young scientist hungry to make his mark. His uncompromisingly honest account of the heady days of their thrilling sprint against other world-class researchers to solve one of science's greatest mysteries gives a dazzlingly clear picture of a world of brilliant scientists with great gifts, very human ambitions & bitter rivalries. With humility unspoiled by false modesty, Watson relates his & Crick's desperate efforts to beat Linus Pauling to the Holy Grail of life sciences, the identification of the basic building block of life. Never has a scientist been so truthful in capturing in words the flavor of his work.

    His breaking of the German U-boat Enigma cipher in World War II ensured Allied-American control of the Atlantic. But Turing's vision went far beyond the desperate wartime struggle. Already in the 1930s he had defined the concept of the universal machine, which underpins the computer revolution. In 1945 he was a pioneer of electronic computer design. But Turing's true goal was the scientific understanding of the mind, brought out in the drama and wit of the famous "Turing test" for machine intelligence and in his prophecy for the twenty-first century.Drawn in to the cockpit of world events and the forefront of technological innovation, Alan Turing was also an innocent and unpretentious gay man trying to live in a society that criminalized him. In 1952 he revealed his homosexuality and was forced to participate in a humiliating treatment program, and was ever after regarded as a security risk. His suicide in 1954 remains one of the many enigmas in an astonishing life story.

    Yet Euler's formula is so simple it can be explained to a child. Euler's Gem tells the illuminating story of this indispensable mathematical idea.From ancient Greek geometry to today's cutting-edge research, Euler's Gem celebrates the discovery of Euler's beloved polyhedron formula and its far-reaching impact on topology, the study of shapes. In 1750, Euler observed that any polyhedron composed of V vertices, E edges, and F faces satisfies the equation V-E+F=2. David Richeson tells how the Greeks missed the formula entirely; how Descartes almost discovered it but fell short; how nineteenth-century mathematicians widened the formula's scope in ways that Euler never envisioned by adapting it for use with doughnut shapes, smooth surfaces, and higher dimensional shapes; and how twentieth-century mathematicians discovered that every shape has its own Euler's formula. Using wonderful examples and numerous illustrations, Richeson presents the formula's many elegant and unexpected applications, such as showing why there is always some windless spot on earth, how to measure the acreage of a tree farm by counting trees, and how many crayons are needed to color any map.Filled with a who's who of brilliant mathematicians who questioned, refined, and contributed to a remarkable theorem's development, Euler's Gem will fascinate every mathematics enthusiast.

    He constructed a fleet of customized unicycles and a flamethrowing trumpet, outfoxed Vegas casinos, and built juggling robots. He also wrote the seminal text of the digital revolution, which has been called “the Magna Carta of the Information Age.” His discoveries would lead contemporaries to compare him to Albert Einstein and Isaac Newton. His work anticipated by decades the world we’d be living in today—and gave mathematicians and engineers the tools to bring that world to pass.In this elegantly written, exhaustively researched biography, Jimmy Soni and Rob Goodman reveal Claude Shannon’s full story for the first time. It’s the story of a small-town Michigan boy whose career stretched from the era of room-sized computers powered by gears and string to the age of Apple. It’s the story of the origins of our digital world in the tunnels of MIT and the “idea factory” of Bell Labs, in the “scientists’ war” with Nazi Germany, and in the work of Shannon’s collaborators and rivals, thinkers like Alan Turing, John von Neumann, Vannevar Bush, and Norbert Wiener.And it’s the story of Shannon’s life as an often reclusive, always playful genius. With access to Shannon’s family and friends, A Mind at Play brings this singular innovator and creative genius to life.

    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.

    At the dawn of the Industrial Revolution in eighteenth-century England, standards of measurement were established, giving way to the development of machine tools—machines that make machines. Eventually, the application of precision tools and methods resulted in the creation and mass production of items from guns and glass to mirrors, lenses, and cameras—and eventually gave way to further breakthroughs, including gene splicing, microchips, and the Hadron Collider.Simon Winchester takes us back to origins of the Industrial Age, to England where he introduces the scientific minds that helped usher in modern production: John Wilkinson, Henry Maudslay, Joseph Bramah, Jesse Ramsden, and Joseph Whitworth. It was Thomas Jefferson who later exported their discoveries to the fledgling United States, setting the nation on its course to become a manufacturing titan. Winchester moves forward through time, to today’s cutting-edge developments occurring around the world, from America to Western Europe to Asia.As he introduces the minds and methods that have changed the modern world, Winchester explores fundamental questions. Why is precision important? What are the different tools we use to measure it? Who has invented and perfected it? Has the pursuit of the ultra-precise in so many facets of human life blinded us to other things of equal value, such as an appreciation for the age-old traditions of craftsmanship, art, and high culture? Are we missing something that reflects the world as it is, rather than the world as we think we would wish it to be? And can the precise and the natural co-exist in society?

    Having just completed his masterpiece, The General Theory of Relativity—which provided a brand-new theory of gravity and promised a new perspective on the cosmos as a whole—he set out at once to share his excitement with as wide a public as possible in this popular and accessible book.Here published for the first time as a Penguin Classic, this edition of Relativity features a new introduction by bestselling science author Nigel Calder.

    But ask what it means, and the result will be a brawl. For a century, most physicists have followed Niels Bohr's Copenhagen interpretation and dismissed questions about the reality underlying quantum physics as meaningless. A mishmash of solipsism and poor reasoning, Copenhagen endured, as Bohr's students vigorously protected his legacy, and the physics community favored practical experiments over philosophical arguments. As a result, questioning the status quo long meant professional ruin. And yet, from the 1920s to today, physicists like John Bell, David Bohm, and Hugh Everett persisted in seeking the true meaning of quantum mechanics. What Is Real? is the gripping story of this battle of ideas and of the courageous scientists who dared to stand up for truth.

    Aimed at undergraduate students in mathematics, physics, and engineering, the book's intuitive explanations, lack ofadvanced prerequisites, and consciously user-friendly prose style will help students to master the subject more readily than was previously possible. The key to this is the book's use of new geometric arguments in place of the standard calculational ones. These geometric arguments are communicatedwith the aid of hundreds of diagrams of a standard seldom encountered in mathematical works. A new approach to a classical topic, this work will be of interest to students in mathematics, physics, and engineering, as well as to professionals in these fields.

    This book investigates what cannot be known. Rather than exploring the amazing facts that science, mathematics, and reason have revealed to us, this work studies what science, mathematics, and reason tell us cannot be revealed. In The Outer Limits of Reason, Noson Yanofsky considers what cannot be predicted, described, or known, and what will never be understood. He discusses the limitations of computers, physics, logic, and our own thought processes.Yanofsky describes simple tasks that would take computers trillions of centuries to complete and other problems that computers can never solve; perfectly formed English sentences that make no sense; different levels of infinity; the bizarre world of the quantum; the relevance of relativity theory; the causes of chaos theory; math problems that cannot be solved by normal means; and statements that are true but cannot be proven. He explains the limitations of our intuitions about the world -- our ideas about space, time, and motion, and the complex relationship between the knower and the known.Moving from the concrete to the abstract, from problems of everyday language to straightforward philosophical questions to the formalities of physics and mathematics, Yanofsky demonstrates a myriad of unsolvable problems and paradoxes. Exploring the various limitations of our knowledge, he shows that many of these limitations have a similar pattern and that by investigating these patterns, we can better understand the structure and limitations of reason itself. Yanofsky even attempts to look beyond the borders of reason to see what, if anything, is out there.

    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.

    Based on original material and previously unavailable documents, this acclaimed book is the definitive biography of the man considered by many to be the founding father of modern electrical technology. Among Tesla's creations were the channeling of alternating current, fluorescent and neon lighting, wireless telegraphy, and the giant turbines that harnessed the power of Niagara Falls.