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.

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.

On June 22, 1936, the philosopher Moritz Schlick was on his way to deliver a lecture at the University of Vienna when Johann Nelböck, a deranged former student of Schlick's, shot him dead on the university steps. Some Austrian newspapers defended the madman, while Nelböck himself argued in court that his onetime teacher had promoted a treacherous Jewish philosophy. David Edmonds traces the rise and fall of the Vienna Circle - an influential group of brilliant thinkers led by Schlick.

A paradigm-shifting work that revolutionizes our understanding of the origins and structure of science.

How does science work? Does it tell us what the world is "really" like? What makes it different from other ways of understanding the universe? In Theory and Reality, Peter Godfrey-Smith addresses these questions by taking the listener on a grand tour of 100 years of debate about science. The result is a completely accessible introduction to the main themes of the philosophy of science.

Vividly written, The Infidel and the Professor is a compelling account of a great friendship of two towering Enlightenment thinkers that had great consequences for modern thought. David Hume is widely regarded as the most important philosopher ever to write in English, but during his lifetime, he was attacked as "the Great Infidel" for his skeptical religious views and deemed unfit to teach the young. In contrast, Adam Smith was a revered professor of moral philosophy and is now often hailed as the founding father of capitalism.

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.

Most historians study the smallest slivers of time, emphasizing specific dates, individuals, and documents. But what would it look like to study the whole of history, from the big bang through the present day - and even into the remote future? How would looking at the full span of time change the way we perceive the universe, the earth, and our very existence? These were the questions David Christian set out to answer when he created the field of "Big History", the most exciting new approach to understanding where we have been, where we are, and where we are going.

A good book may have the power to change the way we see the world, but a great book actually becomes part of our daily consciousness, pervading our thinking to the point that we take it for granted, and we forget how provocative and challenging its ideas once were - and still are. The Structure of Scientific Revolutions is that kind of book.

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.

Earth is 4.5 billion years old. In just a fraction of that time, one species among countless others has conquered it. Us. We are the most advanced and most destructive animals ever to have lived. What makes us brilliant? What makes us deadly? What makes us sapiens? In this bold and provocative audiobook, Yuval Noah Harari explores who we are, how we got here, and where we're going.

Paul Dirac was among the great scientific geniuses of the modern age. One of the discoverers of quantum mechanics, the most revolutionary theory of the past century, his contributions had a unique insight, eloquence, clarity, and mathematical power. His prediction of antimatter was one of the greatest triumphs in the history of physics.

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.’

The year is 1919. The horror of the First World War is fresh for the protagonists of Time of the Magicians, each of whom finds himself at a crucial juncture. Benjamin is trying to flee his overbearing father and floundering in his academic career, living hand to mouth as a critic. Wittgenstein, by contrast, has dramatically decided to divest himself of the monumental fortune he stands to inherit, in search of spiritual clarity.

How will artificial intelligence affect crime, war, justice, jobs, society, and our very sense of being human? The rise of AI has the potential to transform our future more than any other technology - and there's nobody better qualified or situated to explore that future than Max Tegmark, an MIT professor who's helped mainstream research on how to keep AI beneficial.

Paul Dirac was among the great scientific geniuses of the modern age. One of the discoverers of quantum mechanics, the most revolutionary theory of the past century, his contributions had a unique insight, eloquence, clarity, and mathematical power. His prediction of antimatter was one of the greatest triumphs in the history of physics.

Robert Oppenheimer was among the most brilliant and divisive of men. As head of the Los Alamos Laboratory, he oversaw the successful effort to beat the Nazis in the race to develop the first atomic bomb – a breakthrough that was to have eternal ramifications for mankind and that made Oppenheimer the “Father of the Atomic Bomb.” But with his actions leading up to that great achievement, he also set himself on a dangerous collision course with Senator Joseph McCarthy and his witch-hunters. In Robert Oppenheimer: A Life Inside the Center, Ray Monk, author of peerless biographies of Ludwig Wittgenstein and Bertrand Russell, goes deeper than any previous biographer in the quest to solve the enigma of Oppenheimer’s motivations and his complex personality.

The history of European philosophy is usually constructed from the work of men. In Metaphysical Animals, a pioneering group biography, Clare Mac Cumhaill and Rachael Wiseman offer a compelling alternative. In the mid-twentieth century Elizabeth Anscombe, Mary Midgley, Philippa Foot, and Iris Murdoch were philosophy students at Oxford when most male undergraduates and many tutors were conscripted away to fight in the Second World War. Together, these young women, all friends, developed a philosophy that could respond to the war’s darkest revelations.

Since the fall of the Soviet Union, long-suppressed information has emerged on Heisenberg’s role in the Nazi atomic bomb project. In Beyond Uncertainty, Cassidy interprets this and other previously unknown material within the context of his vast research and tackles the vexing questions of a scientist’s personal responsibility and guilt when serving an abhorrent military regime.

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.

Benedict Cumberbatch, Greta Scacchi and Simon Russell Beale star in Michael Frayn's award-winning play about the controversial 1941 meeting between physicists Bohr and Heisenberg. Copenhagen, Autumn 1941. The two presiding geniuses of quantum physics, Niels Bohr and Werner Heisenberg meet for the first time since the breakout of war.

Jean-Paul Sartre is one of the undisputed giants of 20th-century philosophy. His intellectual writings popularizing existentialism, combined with his creative and artistic flair, have made him a legend of French thought. His tumultuous personal life - so inextricably bound up with his philosophical thinking - is a fascinating tale of love and lust, drug abuse, high-profile fallings-out and political and cultural rebellion.

Alan Mathison Turing. Mathematician, philosopher, codebreaker, a founder of computer science, and the father of Artificial Intelligence, Turing was one of the most original thinkers of the last century - and the man whose work helped create the computer-driven world we now inhabit. But he was also an enigmatic figure, deeply reticent yet also strikingly naive. Turing's openness about his homosexuality at a time when it was an imprisonable offense ultimately led to his untimely death at the age of only 41.

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.

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.

Ralph Waldo Emerson is one of the most important figures in the history of American thought, religion, and literature. The vitality of his writings and the unsettling power of his example continue to influence us more than a hundred years after his death. Now Robert D. Richardson Jr. brings to life an Emerson very different from the old stereotype of the passionless Sage of Concord.

In this collection of essays, Walter Isaacson reflects on the lessons to be learned from Benjamin Franklin, Albert Einstein, Bill Gates, Henry Kissinger, Ronald Reagan and Mikhail Gorbachev, Hillary Clinton and Bill Clinton, and various other interesting characters he has chronicled as a biographer and journalist. The people he writes about have an awesome intelligence, in most cases, but that is not the secret of their success.

There are many stories we can spin about previous ages, but which accounts get told? And by whom? Is there even such a thing as “objective” history? In this “witty, wise, and elegant” (The Spectator), book, Richard Cohen reveals how professional historians and other equally significant witnesses, such as the writers of the Bible, novelists, and political propagandists, influence what becomes the accepted record. Cohen argues, for example, that some historians are practitioners of “Bad History” and twist reality to glorify themselves or their country.

In honor of the 50th anniversary of C. S. Lewis' death, celebrated Oxford don Dr. Alister McGrath presents us with a compelling and definitive portrait of the life of C. S. Lewis, the author of the well-known Narnia series. For more than half a century, C. S. Lewis’ Narnia series has captured the imaginations of millions. In C. S. Lewis - A Life, Dr. Alister McGrath recounts the unlikely path of this Oxford don, who spent his days teaching English literature to the brightest students in the world and his spare time writing.

The flourishing of radical philosophy in Baron Thierry Holbach’s Paris salon from the 1750s to the 1770s stands as a seminal event in Western history. Holbach’s house was an international epicenter of revolutionary ideas and intellectual daring, bringing together such original minds as Denis Diderot, Laurence Sterne, David Hume, Adam Smith, Ferdinando Galiani, Horace Walpole, Benjamin Franklin, Guillaume Raynal, and Jean-Jacques Rousseau. In A Wicked Company, acclaimed historian Philipp Blom retraces the fortunes of this exceptional group of friends.

The year is 1919. The horror of the First World War is fresh for the protagonists of Time of the Magicians, each of whom finds himself at a crucial juncture. Benjamin is trying to flee his overbearing father and floundering in his academic career, living hand to mouth as a critic. Wittgenstein, by contrast, has dramatically decided to divest himself of the monumental fortune he stands to inherit, in search of spiritual clarity.

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.

Probing the life and work of Kurt Gödel, Incompleteness indelibly portrays the tortured genius whose vision rocked the stability of mathematical reasoning—and brought him to the edge of madness.

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.’

Ludwig Wittgenstein was born in Vienna in 1889 and died in Cambridge, England in 1951. He was one of the most influential philosophers of the 20th century.

On June 22, 1936, the philosopher Moritz Schlick was on his way to deliver a lecture at the University of Vienna when Johann Nelböck, a deranged former student of Schlick's, shot him dead on the university steps. Some Austrian newspapers defended the madman, while Nelböck himself argued in court that his onetime teacher had promoted a treacherous Jewish philosophy. David Edmonds traces the rise and fall of the Vienna Circle - an influential group of brilliant thinkers led by Schlick.

For mathematician Francis Su, a society without mathematical affection is like a city without concerts, parks, or museums. To miss out on mathematics is to live without experiencing some of humanity's most beautiful ideas. In this profound book, written for a wide audience but especially for those disenchanted by their past experiences, an award-winning mathematician and educator weaves parables, puzzles, and personal reflections to show how mathematics meets basic human desires - such as for play, beauty, freedom, justice, and love.

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.

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.

Number theory is the branch of mathematics that is primarily concerned with the counting numbers. Of particular importance are the prime numbers, the "building blocks" of our number system. The subject is an old one, dating back over two millennia to the ancient Greeks, and for many years has been studied for its intrinsic beauty and elegance, not least because several of its challenges are so easy to state that everyone can understand them, and yet no one has ever been able to resolve them. But number theory has also recently become of great practical importance.