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.

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.

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.

Nobel Laureate Eugene Wigner once wondered about "the unreasonable effectiveness of mathematics" in the formulation of the laws of nature. Is God a Mathematician? investigates why mathematics is as powerful as it is. From ancient times to the present, scientists and philosophers have marveled at how such a seemingly abstract discipline could so perfectly explain the natural world. More than that - mathematics has often made predictions, for example, about subatomic particles or cosmic phenomena that were unknown at the time, but later were proven to be true.

In The Dream of Enlightenment, Anthony Gottlieb expertly navigates a second great explosion of thought, taking us to northern Europe in the wake of its wars of religion and the rise of Galilean science. In a relatively short period - from the early 1640s to the eve of the French Revolution - Descartes, Hobbes, Spinoza, Locke, Leibniz, and Hume all made their mark. The Dream of Enlightenment tells their story and that of the birth of modern philosophy.

Werner Heisenberg's "uncertainty principle" challenged centuries of scientific understanding, placed him in direct opposition to Albert Einstein, and put Niels Bohr in the middle of one of the most heated debates in scientific history. Heisenberg's theorem stated that there were physical limits to what we could know about sub-atomic particles; this "uncertainty" would have shocking implications.

Already a classic, this landmark study of early Western thought now appears in a new edition with expanded coverage of the Middle Ages. Author Anthony Gottlieb looks afresh at the writings of the great thinkers, questions much of conventional wisdom, and explains his findings with unbridled brilliance and clarity. From the pre-Socratic philosophers through the celebrated days of Socrates, Plato, and Aristotle, up to Renaissance visionaries like Erasmus and Bacon, philosophy emerges here as a phenomenon unconfined by any one discipline.

For thousands of years mathematicians solved progressively more difficult algebraic equations, until they encountered the quintic equation, which resisted solution for three centuries. Working independently, two prodigies ultimately proved that the quintic cannot be solved by a simple formula. The first popular account of the mathematics of symmetry and order, The Equation That Couldn't Be Solved is told not through abstract formulas but in a beautifully written and dramatic account of the lives and work of some of the greatest and most intriguing mathematicians in history.

Militant atheism is on the rise. In recent years, Richard Dawkins, Sam Harris, Daniel Dennett, and Christopher Hitchens have produced a steady stream of best-selling books denigrating religious belief. These authors are merely the leading edge of a larger movement that includes much of the scientific community. In response, mathematician David Berlinski, himself a secular Jew, delivers a biting defense of religious thought.

This engaging and accessible book invites the listener to explore the questions and arguments of philosophy through the work of 100 of the greatest thinkers within the Western intellectual tradition - covering philosophical, scientific, political, and religious thought over a period of 2500 years.

Hardly a club in the conventional sense, the organization referred to in the title of this superb literary hybrid (part history, part biography, part philosophy) consisted of four members and probably existed for less than nine months.

Geometry defines the world around us, helping us make sense of everything from architecture to military science to fashion. And for over 2,000 years, geometry has been equated with Euclid's Elements, arguably the most influential book in the history of mathematics. In The King of Infinite Space, renowned mathematics writer David Berlinski provides a concise homage to this elusive mathematician and his staggering achievements.

In There Is a God, one of the world's preeminent atheists discloses how his commitment to "follow the argument wherever it leads" led him to a belief in God as Creator. This is a compelling and refreshingly open-minded argument that will forever change the atheism debate.

Space is big. Really big. You just won't believe how vastly, hugely, mind-bogglingly big it is. I mean, you may think it's a long way down the street to the chemist, but that's just peanuts to space.' Douglas Adams, Hitch-hiker's Guide to the Galaxy.We human beings have trouble with infinity - yet infinity is a surprisingly human subject. Philosophers and mathematicians have gone mad contemplating its nature and complexity - yet it is a concept routinely used by schoolchildren. Exploring the infinite is a

In this fascinating history spanning continents and centuries, historian David Wootton offers a lively defense of science, revealing why the Scientific Revolution was truly the greatest event in our history. The Invention of Science goes back 500 years in time to chronicle this crucial transformation, exploring the factors that led to its birth and the people who made it happen. Wootton argues that the Scientific Revolution was actually five separate yet concurrent events that developed independently.

Author Jim Holt explores the greatest metaphysical mystery of all: why is there something rather than nothing? This runaway best seller, which has captured the imagination of critics and the public alike, traces our latest efforts to grasp the origins of the universe. Holt adopts the role of cosmological detective, traveling the globe to interview a host of celebrated scientists, philosophers, and writers.

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.

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.

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.

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.

Behind the familiar surfaces of the telephone, radio, and television lies a sophisticated and intriguing body of knowledge known as information theory. This is the theory that has permitted the rapid development of all sorts of communication, from color television to the clear transmission of photographs from the vicinity of Jupiter. Even more revolutionary progress is expected in the future.

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.

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.

Many people take math in high school and promptly forget much of it. But math plays a part in all of our lives all of the time, whether we know it or not. In The Joy of x, Steven Strogatz expands on his hit New York Times series to explain the big ideas of math gently and clearly, with wit, and insight.

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.

The aim of this book is to explain, carefully but not technically, the differences between advanced, research-level mathematics and the sort of mathematics we learn at school. The most fundamental differences are philosophical, and listeners of this book will emerge with a clearer understanding of paradoxical-sounding concepts such as infinity, curved space, and imaginary numbers. The first few chapters are about general aspects of mathematical thought.

Logic is often perceived as having little to do with the rest of philosophy, and even less to do with real life. In this lively and accessible introduction, Graham Priest shows how wrong this conception is. He explores the philosophical roots of the subject, explaining how modern formal logic deals with issues ranging from the existence of God and the reality of time to paradoxes of probability and decision theory. Along the way, the basics of formal logic are explained in simple, non-technical terms, showing that logic is a powerful and exciting part of modern philosophy.