Nearly a hundred years after its publication, Kurt Gödel's famous proof that every mathematical system must contain propositions that are true - yet never provable - continues to unsettle mathematics, philosophy, and computer science. Yet unlike Einstein, with whom he formed a warm and abiding friendship, Gödel has long escaped all but the most casual scrutiny of his life.

Is philosophy obsolete? Are the ancient questions still relevant in the age of cosmology and neuroscience, not to mention crowd-sourcing and cable news? The acclaimed philosopher and novelist Rebecca Newberger Goldstein provides a dazzlingly original plunge into the drama of philosophy, revealing its hidden role in today’s debates on religion, morality, politics, and science.

One of our greatest philosophers and scientists of the mind asks where the self comes from - and how our selves can exist in the minds of others. I Am a Strange Loop argues that the key to understanding selves and consciousness is the "strange loop" - a special kind of abstract feedback loop inhabiting our brains. The most central and complex symbol in your brain is the one called "I". The "I" is the nexus in our brain, one of many symbols seeming to have free will and to have gained the paradoxical ability to push particles around, rather than the reverse.

The smartphones in our pockets and computers like brains. The vagaries of game theory and evolutionary biology. Nuclear weapons and self-replicating spacecrafts. All bear the fingerprints of one remarkable, yet largely overlooked, man: John von Neumann.

Does time exist? What is infinity? Why do mirrors reverse left and right but not up and down? In this scintillating collection, Holt explores the human mind, the cosmos, and the thinkers who’ve tried to encompass the latter with the former. 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.

Aubrey Clayton traces the history of how statistics went astray, beginning with the groundbreaking work of the 17th-century mathematician Jacob Bernoulli and winding through gambling, astronomy, and genetics. Clayton recounts the feuds among rival schools of statistics, exploring the surprisingly human problems that gave rise to the discipline and the all-too-human shortcomings that derailed it.

Philosophical Investigations was published in 1953, two years after the death of its author. In the preface written in Cambridge in 1945 where he was professor of philosophy he states: ‘Four years ago I had occasion to re-read my first book (the Tractatus Logico-Philosophicus) and to explain its ideas to someone. It suddenly seemed to me that I should publish those old thoughts and the new ones together: that the latter could be seen in the right light only by contrast with and against the background of my old way of thinking.’

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.

Ludwig Wittgenstein (1889-1951) was an extraordinarily original thinker, whose influence on 20th-century thinking far outside the bounds of philosophy alone. In this engaging Introduction, A. C. Grayling makes Wittgenstein's thought accessible to the general listener by explaining the nature and impact of Wittgenstein's views. He describes both his early and later philosophy, the differences and connections between them, and gives a fresh assessment of Wittgenstein's continuing influence on contemporary thought.

In the weeks after Japan finally surrendered to the Allies to end World War II, the world turned to the question of how to move on from years of carnage and destruction. For Harry Truman, Douglas MacArthur, Chiang Kai-shek, and their fellow victors, the question of justice seemed clear: Japan’s militaristic leaders needed to be tried and punished for the surprise attack at Pearl Harbor; shocking atrocities against civilians in China, the Philippines, and elsewhere; and rampant abuses of prisoners of war in notorious incidents such as the Bataan death march.

On July 4, 2012, the announcement came that one of the longest-running mysteries in physics had been solved: the Higgs boson, the missing piece in understanding why particles have mass, had finally been discovered. On the rostrum, surrounded by jostling physicists and media, was the particle’s retiring namesake—the only person in history to have an existing single particle named for them. Why Peter Higgs? Drawing on years of conversations with Higgs and others, Close illuminates how an unprolific man became one of the world’s most famous scientists.

Argentine poet Jorge Luis Borges was madly in love when his life was shattered by painful heartbreak. But the breakdown that followed illuminated an incontrovertible truth—that love is necessarily imbued with loss, that the one doesn’t exist without the other. German physicist Werner Heisenberg was fighting with the scientific establishment on the meaning of the quantum realm’s absurdity when he had his own epiphany—that there is no such thing as a complete, perfect description of reality.

In Significant Figures, acclaimed mathematician Ian Stewart introduces the visionaries of mathematics throughout history. Delving into the lives of twenty-five great mathematicians, Stewart examines the roles they played in creating, inventing, and discovering the mathematics we use today. Through these short biographies, we get acquainted with the history of mathematics.

Conjectures and Refutations is one of Karl Popper’s most wide-ranging and popular works, notable not only for its acute insights into the way scientific knowledge grows, but also for applying those insights to politics and to history. It provides one of the clearest and most accessible statements of the fundamental idea that guided his work: not only our knowledge but our aims and our standards grow through an unending process of trial and error.

In a career spanning 60 years, Sir Karl Popper has made some of the most important contributions to the 20th century discussion of science and rationality. The Myth of the Framework is a collection of some of Popper's most important material on this subject.

Nearly a hundred years after its publication, Kurt Gödel's famous proof that every mathematical system must contain propositions that are true - yet never provable - continues to unsettle mathematics, philosophy, and computer science. Yet unlike Einstein, with whom he formed a warm and abiding friendship, Gödel has long escaped all but the most casual scrutiny of his life.

Bertrand Russell wrote that mathematics can exalt "as surely as poetry". This is especially true of one equation: ei(pi) + 1 = 0, the brainchild of Leonhard Euler, the Mozart of mathematics. More than two centuries after Euler's death, it is still regarded as a conceptual diamond of unsurpassed beauty. Called Euler's identity, or God's equation, it includes just five numbers but represents an astonishing revelation of hidden connections.

Asked to name a great physicist, most people would mention Newton or Einstein, Feynman or Hawking. But ask a physicist and there’s no doubt that James Clerk Maxwell will be near the top of the list. Maxwell, an unassuming Victorian Scotsman, explained how we perceive color. He uncovered the way gases behave. And, most significantly, he transformed the way physics was undertaken in his explanation of the interaction of electricity and magnetism, revealing the nature of light and laying the groundwork for everything from Einstein’s special relativity to modern electronics.

On July 23, 1999, the Chandra X-Ray Observatory, the most powerful X-ray telescope ever built, was launched aboard the space shuttle Columbia. Since then, Chandra has given us a view of the universe that is largely hidden from telescopes sensitive only to visible light. In Chandra's Cosmos, Wallace H. Tucker uses a series of short, connected stories to describe the telescope's exploration of the hot, high-energy face of the universe.

A brilliant research mathematician reveals math to be a creative art form on par with painting, poetry, and sculpture, and rejects the standard anxiety-producing teaching methods used in most schools today. Witty and accessible, Paul Lockhart's controversial approach will provoke spirited debate among educators and parents alike, altering the way we think about math forever.

Throughout history, scientists have come up with theories and ideas that just don't seem to make sense. These we call paradoxes. The paradoxes Al-Khalili offers are drawn chiefly from physics and astronomy and represent those that have stumped some of the finest minds. With elegant explanations that bring the listener inside the mind of those who've developed them, Al-Khalili helps us to see that, in fact, paradoxes can be solved if seen from the right angle.

Bayes' rule appears to be a straightforward, one-line theorem: by updating our initial beliefs with objective new information, we get a new and improved belief. To its adherents, it is an elegant statement about learning from experience. To its opponents, it is subjectivity run amok. Sharon Bertsch McGrayne here explores this controversial theorem and the human obsessions surrounding it.

Want to know how AT&T's Bell Labs developed semiconductor technology - and how its leading scientists almost came to blows in the process? Want to understand how radio and television work - and why RCA drove their inventors to financial ruin and early graves? Conquering the Electron offers these stories and more, presenting each revolutionary technological advance right alongside blow-by-blow personal battles that all too often took place.

There are deep connections between stars and atoms, between the cosmos and the microworld. Just six numbers, imprinted in the "Big Bang", determine the essential features of our entire physical world. Moreover, cosmic evolution is astonishingly sensitive to the values of these numbers. If any one of them were "untuned", there could be no stars and no life. This realization offers a radically new perspective on our universe, our place in it, and the nature of physical laws.

Is philosophy obsolete? Are the ancient questions still relevant in the age of cosmology and neuroscience, not to mention crowd-sourcing and cable news? The acclaimed philosopher and novelist Rebecca Newberger Goldstein provides a dazzlingly original plunge into the drama of philosophy, revealing its hidden role in today’s debates on religion, morality, politics, and science.

Although we have heard the music of J. S. Bach in countless performances and recordings, the composer himself still comes across only as an enigmatic figure in a single familiar portrait. As we mark the 250th anniversary of Bach's death, author Christoph Wolff presents a new picture that brings to life this towering figure of the Baroque era. This engaging new biography portrays Bach as the living, breathing, and sometimes imperfect human being that he was, while bringing to bear all the advances of the last half-century of Bach scholarship.

In Significant Figures, acclaimed mathematician Ian Stewart introduces the visionaries of mathematics throughout history. Delving into the lives of twenty-five great mathematicians, Stewart examines the roles they played in creating, inventing, and discovering the mathematics we use today. Through these short biographies, we get acquainted with the history of mathematics.

An illuminating guide to the scientific and technological achievements of the Middle Ages through the life of a crusading astronomer-monk.

Everyone has heard of DNA. But by itself, DNA is just an inert blueprint for life. It is the ribosome - an enormous molecular machine made up of a million atoms - that makes DNA come to life, turning our genetic code into proteins and therefore into us. Gene Machine is an insider account of the race for the structure of the ribosome, a fundamental discovery that both advances our knowledge of all life and could lead to the development of better antibiotics against life-threatening diseases.

Written for those with no physics background, Paul Levy's latest book, The Quantum Revelation: A Radical Synthesis of Science and Spirituality, is for those who have heard that quantum physics is a fascinating subject but don't quite understand how or why.