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.

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?

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.

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.

When he was six years old, Roger Penrose discovered a sundial in a clearing near his house. Through that machine made of light, shadow, and time, Roger glimpsed a “world behind the world” of transcendently beautiful geometry. It spurred him on a journey to become one of the world’s most influential mathematicians, philosophers, and physicists. Penrose would prove the limitations of general relativity, set a new agenda for theoretical physics, and astound colleagues and admirers with the elegance and beauty of his discoveries.

The Clockwork Universe is the story of a band of men who lived in a world of dirt and disease but pictured a universe that ran like a perfect machine. A meld of history and science, this book is a group portrait of some of the greatest minds who ever lived as they wrestled with natures most sweeping mysteries. The answers they uncovered still hold the key to how we understand the world.