Through Euclid's Window Leonard Mlodinow brilliantly and delightfully leads us on a journey through five revolutions in geometry, from the Greek concept of parallel lines to the latest notions of hyperspace. Here is an altogether new, refreshing, alternative history of math revealing how simple questions anyone might ask about space -- in the living room or in some other galaxy -- have been the hidden engine of the highest achievements in science and technology.

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.

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.

One night in 1661, Nicholas Fouquet, a superintendent under Louis XIV, was arrested. His crime was peculiar: He had dared to construct a grand geometrical garden. In doing so, he violated an irrefutable hierarchy: that geometry, in its perfection, was a testament to divine right. The elegant, symmetrical designs were more than just ornament; they were proofs of incontestable certainty, and thus the authority to rule. But how did the French royalty fall in love with this peculiar landscape design? Wherefore Versailles?

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.

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.

On November 21, 1914, after sailing more than ten thousand miles from Norway to the Antarctic Ocean, the Endurance finally succumbed to the surrounding ice. Ernest Shackleton and his crew had navigated the 144-foot, three-masted wooden vessel to Antarctica to become the first to cross the barren continent, but early season pack ice trapped them in place offshore. They watched in silence as the ship’s stern rose twenty feet in the air and disappeared into the frigid sea, then spent six harrowing months marooned on the ice in its wake.

The bestselling author of Leonardo da Vinci and Steve Jobs returns with a “compelling” (The Washington Post) account of how Nobel Prize winner Jennifer Doudna and her colleagues launched a revolution that will allow us to cure diseases, fend off viruses, and have healthier babies.

Durant lucidly describes the philosophical systems of such world-famous “monarchs of the mind” as Plato, Aristotle, Francis Bacon, Spinoza, Kant, Voltaire, and Nietzsche. Along with their ideas, he offers their flesh-and-blood biographies, placing their thoughts within their own time and place and elucidating their influence on our modern intellectual heritage. This book is packed with wisdom and wit.

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.

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.

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 Cave and the Light reveals how two Greek philosophers became the twin fountainheads of Western culture, and how their rivalry gave Western civilization its unique dynamism down to the present.

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.

The Mongol army led by Genghis Khan subjugated more lands and people in 25 years than the Romans did in 400. In nearly every country the Mongols conquered, they brought an unprecedented rise in cultural communication, expanded trade, and a blossoming of civilization.

Best-selling author Richard E. Rubenstein brings the past to life in this engrossing story of social, religious, and scientific revolution during one of the darkest periods in European history. When a group of Dark Ages scholars rediscovered the works of Aristotle, the great thinker's ideas ignited a firestorm of enlightened thought. This is the endlessly fascinating account of the pivotal period in history when the modern era took root.

Here is the remarkable story of how medieval Arab scholars made dazzling advances in science and philosophy, and of the itinerant Europeans who brought this knowledge back to the West. For centuries following the fall of Rome, Western Europe was a benighted backwater, a world of subsistence farming, minimal literacy, and violent conflict. Meanwhile, Arab culture was thriving, dazzling those Europeans fortunate enough to catch even a glimpse.

Western civilization has given us modern science, the wealth of free-market economics, the security of law, a sense of human rights and freedom, charity as a virtue, splendid art and music, philosophy grounded in reason, and innumerable other gifts we take for granted.

If you were taught that the Middle Ages were a time of intellectual stagnation, superstition, and ignorance, you were taught a myth that has been utterly refuted by modern scholarship. As a physicist and historian of science James Hannam shows in his brilliant new book, The Genesis of Science: How the Christian Middle Ages Launched the Scientific Revolution, without the scholarship of the "barbaric" Middle Ages, modern science simply would not exist. The Middle Ages were a time of one intellectual triumph after another.

Lost Enlightenment recounts how, between the years 800 and 1200, Central Asia led the world in trade and economic development, the size and sophistication of its cities, the refinement of its arts, and, above all, in the advancement of knowledge in many fields. Central Asians achieved signal breakthroughs in astronomy, mathematics, geology, medicine, chemistry, music, social science, philosophy, and theology, among other subjects.

The Cave and the Light reveals how two Greek philosophers became the twin fountainheads of Western culture, and how their rivalry gave Western civilization its unique dynamism down to the present.

The world hates the Church that Jesus founded, just as He said it would (John 15:18). It reviles her doctrines, mocks her moral teachings and invents lies about her history. In every age, but especially in our modern day, historians and political powers have distorted the facts about her past (or just made up novel falsehoods from scratch) to make the Church, and the civilization it fostered, seem corrupt, backward, or simply evil.

The Arabic legacy of science and philosophy has long been hidden from the West. British-Iraqi physicist Jim Al-Khalili unveils that legacy to fascinating effect by returning to its roots in the hubs of Arab innovation that would advance science and jump-start the European Renaissance.

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.

First published in 1976, Paul Johnson's exceptional study of Christianity has been loved and widely hailed for its intensive research, writing, and magnitude. Weaving a great range of material, the scholar and author Johnson creates an ambitious panoramic overview of the evolution of the Western world since the founding of a little-known "Jesus sect".

Ibn Khaldun (1332-1406) is generally regarded as the greatest intellectual ever to have appeared in the Arab world - a genius who ranks as one of the world's great minds. Yet the author of the Muqaddima, the most important study of history ever produced in the Islamic world, is not as well known as he should be, and his ideas are widely misunderstood. In this groundbreaking intellectual biography, Robert Irwin provides an engaging and authoritative account of Ibn Khaldun's extraordinary life, times, writings, and ideas.

The Civilization of the Middle Ages incorporates current research, recent trends in interpretation, and novel perspectives, especially on the foundations of the Middle Ages and the Later Middle Ages of the fourteenth and fifteenth centuries. A sharper focus on social history, Jewish history, women’s roles in society, and popular religion and heresy distinguish the book.

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.

By early 1943, it had become increasingly clear the Allies would win the Second World War. Christian intellectuals on both sides of the Atlantic thought the soon-to-be-victorious nations were not culturally or morally prepared for their success. These Christian intellectuals - Jacques Maritain, T. S. Eliot, C. S. Lewis, W. H. Auden, and Simone Weil, among others - sought both to articulate a sober and reflective critique of their own culture and to outline a plan for the moral and spiritual regeneration of their countries in the post-war world.

Astrophysicist and best-selling author Mario Livio draws on his own scientific expertise to provide captivating insights into how Galileo reached his bold new conclusions about the cosmos and the laws of nature. A freethinker who followed the evidence wherever it led him, Galileo was one of the most significant figures behind the scientific revolution. He believed that every educated person should know science as well as literature, and insisted on reaching the widest audience possible, publishing his books in Italian rather than Latin.

One night in 1661, Nicholas Fouquet, a superintendent under Louis XIV, was arrested. His crime was peculiar: He had dared to construct a grand geometrical garden. In doing so, he violated an irrefutable hierarchy: that geometry, in its perfection, was a testament to divine right. The elegant, symmetrical designs were more than just ornament; they were proofs of incontestable certainty, and thus the authority to rule. But how did the French royalty fall in love with this peculiar landscape design? Wherefore Versailles?

In 2020, an invisible germ - a virus - wholly upended our lives. We're most familiar with the viruses that give us colds or Covid-19. But viruses also cause a vast range of other diseases, including one disorder that makes people sprout branch-like growths as if they were trees. Viruses have been a part of our lives for so long that we are actually part virus: the human genome contains more DNA from viruses than our own genes. Meanwhile, scientists are discovering viruses everywhere they look: in the soil, in the ocean, even in deep caves miles underground.

Something is wrong. We all know it. American life expectancy is declining for a third straight year. Birth rates are dropping. Nearly half of us think the other political party isn’t just wrong; they’re evil. We’re the richest country in history, but we’ve never been more pessimistic. What’s causing the despair? In Them, bestselling author and U.S. senator Ben Sasse argues that, contrary to conventional wisdom, our crisis isn’t really about politics. It’s that we’re so lonely we can’t see straight—and it bubbles out as anger. Local communities are collapsing.

This book is a sweeping transatlantic history of Puritanism from its emergence out of the religious tumult of Elizabethan England to its founding role in the story of America. Shedding critical new light on the diverse forms of Puritan belief and practice in England, Scotland, and New England, David Hall provides a multifaceted account of a cultural movement that judged the Protestant reforms of Elizabeth's reign to be unfinished.

Almost all of us have sat in a math class, wondering when we'd ever need to know how to find the roots of a polynomial or graph imaginary numbers. And in one sense, we were right: If we needed to, we'd use a computer. But as Ian Stewart argues in What's the Use?, math isn't just about boring computations. Rather, it offers us new and profound insights into our world, allowing us to accomplish feats as significant as space exploration and organ donation.

America was made by the railroads. The opening of the Baltimore & Ohio line—the first American railroad—in the 1830s sparked a national revolution in the way that people lived thanks to the speed and convenience of train travel. Built through heroic effort, the American railroad network was bigger in every sense than Europe's, and facilitated everything from long-distance travel to commuting and transporting goods to waging war. It united far-flung parts of the country, boosted economic development, and was the catalyst for America's rise to world-power status.

For centuries, people have been returning to the same tired nature-versus-nurture debate, trying to determine what we learn and what we inherit. In Dancing Cockatoos and the Dead Man Test, biologist Marlene Zuk goes beyond the binary and instead focuses on interaction, or the way that genes and environment work together. Driving her investigation is a simple but essential question: How does behavior evolve?

Throughout history, thinkers from mathematicians to theologians have pondered the mysterious relationship between numbers and the nature of reality. In this fascinating book, Mario Livio tells the tale of a number at the heart of that mystery: phi, or 1.6180339887.... This curious mathematical relationship, widely known as "The Golden Ratio", was discovered by Euclid more than 2,000 years ago. Since then it has shown a propensity to appear in the most astonishing variety of places.

Over thousands of years, the Mississippi watershed was home to millions of Indigenous people who regarded "the great river" with awe and respect, adorning its banks with astonishing spiritual earthworks. But European settlers and American pioneers had a different vision: the river was a foe to conquer. In this landmark work of natural history, Boyce Upholt tells the epic story of human attempts to own and contain the Mississippi River, from Thomas Jefferson's expansionist land hunger through today's era of environmental concern

In Indigenous Continent, acclaimed historian Pekka Hämäläinen presents a sweeping counternarrative that shatters the most basic assumptions about American history. Shifting our perspective away from Jamestown, Plymouth Rock, the Revolution, and other well-trodden episodes on the conventional timeline, he depicts a sovereign world of Native nations whose members, far from helpless victims of colonial violence, dominated the continent for centuries after the first European arrivals.

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.