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.

Two of the boldest and most creative scientists of all time were Michael Faraday (1791-1867) and James Clerk Maxwell (1831-1879). This is the story of how these two men - separated in age by 40 years - discovered the existence of the electromagnetic field and devised a radically new theory which overturned the strictly mechanical view of the world that had prevailed since Newton's time.

The Metaphysical Club was an informal group that met in Cambridge, Massachusetts, in 1872, to talk about ideas. Its members included Oliver Wendell Holmes, Jr., future associate justice of the United States Supreme Court; William James, the father of modern American psychology; and Charles Sanders Peirce, logician, scientist, and the founder of semiotics. The Club was probably in existence for about nine months. No records were kept. The one thing we know that came out of it was an idea - an idea about ideas. This book is the story of that idea.

Infinite Powers recounts how calculus tantalized and thrilled its inventors, starting with its first glimmers in ancient Greece and bringing us right up to the discovery of gravitational waves. Strogatz reveals how this form of math rose to the challenges of each age: how to determine the area of a circle with only sand and a stick; how to explain why Mars goes "backwards" sometimes; how to turn the tide in the fight against AIDS.

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.

Considered to be one of the most important philosophical works of all time, the History of Western Philosophy is a dazzlingly unique exploration of the ideologies of significant philosophers throughout the ages - from Plato and Aristotle through to Spinoza, Kant and the 20th century. Written by a man who changed the history of philosophy himself, this is an account that has never been rivaled since its first publication over 60 years ago.

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.

Every physicist agrees quantum mechanics is among humanity's finest scientific achievements. 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.

Why we think it’s a great listen: You thought he was a stodgy scientist with funny hair, but Isaacson and Hermann reveal an eloquent, intense, and selfless human being who not only shaped science with his theories, but politics and world events in the 20th century as well. Based on the newly released personal letters of Albert Einstein, Walter Isaacson explores how an imaginative, impertinent patent clerk became the mind reader of the creator of the cosmos.

Paris, 1933: Three contemporaries meet over apricot cocktails at the Bec-de-Gaz bar on the rue Montparnasse. They are the young Jean-Paul Sartre, Simone de Beauvoir, and longtime friend Raymond Aron, a fellow philosopher who raves to them about a new conceptual framework from Berlin called phenomenology. "You see," he says, "if you are a phenomenologist, you can talk about this cocktail and make philosophy out of it!"

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.

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.

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.

Paris, 1933: Three contemporaries meet over apricot cocktails at the Bec-de-Gaz bar on the rue Montparnasse. They are the young Jean-Paul Sartre, Simone de Beauvoir, and longtime friend Raymond Aron, a fellow philosopher who raves to them about a new conceptual framework from Berlin called phenomenology. "You see," he says, "if you are a phenomenologist, you can talk about this cocktail and make philosophy out of it!"

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.

On August 10, 1632, five men in flowing black robes convened in a somber Roman palazzo to pass judgment on a deceptively simple proposition: that a continuous line is composed of distinct and infinitely tiny parts. With the stroke of a pen the Jesuit fathers banned the doctrine of infinitesimals, announcing that it could never be taught or even mentioned. The concept was deemed dangerous and subversive, a threat to the belief that the world was an orderly place, governed by a strict and unchanging set of rules.

Few historians end up as historical actors in their own right, but Bernard Lewis has both witnessed and participated in some of the key events of the last century. When we think of the Middle East, we see it in terms that he defined and articulated.In this exceptional memoir he shares stories of his wartime service in London and Cairo, decrypting intercepts for MI6, with sometimes unexpected consequences. After the war, he was the first Western scholar ever invited into the Ottoman archives in Istanbul.

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.

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.

Every physicist agrees quantum mechanics is among humanity's finest scientific achievements. 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.

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.

As a journalist, historian, and novelist born into a family that included two past presidents of the United States, Henry Adams was constantly focused on the American experiment. An immediate bestseller awarded the Pulitzer Prize in 1919, The Education of Henry Adams recounts his own and the country's education from 1838, the year of his birth, to 1905, incorporating the Civil War, capitalist expansion, and the growth of the United States as a world power.

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.’

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.

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.

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.

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.

These stories from Quanta Magazine map the routes of mathematical exploration, showing listeners how cutting-edge research is done, while illuminating the productive tension between conjecture and proof, theory and intuition. Listeners of The Prime Number Conspiracy are headed on "breathtaking intellectual journeys to the bleeding edge of discovery strapped to the narrative rocket of humanity's never-ending pursuit of knowledge," says Quanta editor-in-chief Thomas Lin.

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.

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.