The history of warfare cannot be fully understood without considering the technology of killing. In Firepower, acclaimed historian Paul Lockhart tells the story of military technology from the Renaissance to the dawn of the atomic era -- five-hundred-year-long "age of firepower" during which the evolution of weaponry transformed the conduct of warfare in the West. Weapons technology had always influenced warfare. But the introduction of gunpowder weapons at the close of the Middle Ages made military technology the largest single factor shaping warfare's tactics, strategy, and logistics. Over the five centuries leading up to World War II, the art of war revolved around the ever-more-effective delivery of firepower, and the driving force of weapons development was the compulsion to make that possible. But for centuries, even as it became more effective, military weaponry remained simple and affordable enough that nearly any state could afford to equip a respectable army; weapons could be used and used again until they physically wore out. That all changed, very suddenly, around 1870. Widespread industrialization and rapid advances in metallurgy and chemistry meant that by the start of World War I, only a handful of great powers could afford to manufacture their own weapons. Revolutions in military technology, in short, triggered a revolution in the structure of power in the West, significantly reducing the number of nations that could act assertively in international politics -- and reducing the others to a condition of permanent subordination. Going beyond the battlefield to consider the profound political and social contexts of armed conflict, Firepower ultimately reveals how the evolution of weapons technology, and the uses to which it has been put, have together transformed human history.

"Inspiring and informative...deserves to be widely read." -Wall Street Journal "This fun book offers a philosophical take on number systems and revels in the beauty of math." -Science News Because we have ten fingers, grouping by ten seems natural, but twelve would be better for divisibility, and eight is well suited to repeated halving. Grouping by two, as in binary code, has turned out to have its own remarkable advantages. Paul Lockhart presents arithmetic not as rote manipulation of numbers-a practical if mundane branch of knowledge best suited for filling out tax forms-but as a fascinating, sometimes surprising intellectual craft that arises from our desire to add, divide, and multiply important things. Passionate and entertaining, Arithmetic invites us to experience the beauty of mathematics through the eyes of a beguiling teacher. "A nuanced understanding of working with numbers, gently connecting procedures that we once learned by rote with intuitions long since muddled by education... Lockhart presents arithmetic as a pleasurable pastime, and describes it as a craft like knitting." -Jonathon Keats, New Scientist "What are numbers, how did they arise, why did our ancestors invent them, and how did they represent them? They are, after all, one of humankind's most brilliant inventions, arguably having greater impact on our lives than the wheel. Lockhart recounts their fascinating story... A wonderful book." -Keith Devlin, author of Finding Fibonacci

The image of the Baron de Steuben training Washington's ragged, demoralized troops in the snow at Valley Forge is part of the iconography of our Revolutionary heritage, but most history fans know little more about this fascinating figure.

In the first book on Steuben since 1937, Paul Lockhart, an expert in European military history, finally explains the significance of Steuben's military experience in Europe. Steeped in the traditions of the Prussian army of Frederick the Great--the most ruthlessly effective in Europe--he taught the soldiers of the Continental Army how to fight like Europeans. His guiding hand shaped the army that triumphed over the British at Monmouth, Stony Point, and Yorktown. And his influence did not end with the Revolution. Steuben was instrumental in creating West Point, and in writing the "Blue Book"--the first official regulations of the American army. His principles have guided the American armed forces to this day.

Steuben's life is also a classic immigrant story. A failure in midlife, he uprooted himself from his native Europe to seek one last chance at glory and fame in the New World. In America he managed to reinvent himself--making his background quite a bit more glamorous than was the reality--but redeeming himself by his exceptional service and becoming, in a sense, the man he claimed to be.

For seven years, Paul Lockhart's A Mathematician's Lament enjoyed a samizdat-style popularity in the mathematics underground, before demand prompted its 2009 publication to even wider applause and debate. An impassioned critique of K-12 mathematics education, it outlined how we shortchange students by introducing them to math the wrong way. Here Lockhart offers the positive side of the math education story by showing us how math should be done. Measurement offers a permanent solution to math phobia by introducing us to mathematics as an artful way of thinking and living. In conversational prose that conveys his passion for the subject, Lockhart makes mathematics accessible without oversimplifying. He makes no more attempt to hide the challenge of mathematics than he does to shield us from its beautiful intensity. Favoring plain English and pictures over jargon and formulas, he succeeds in making complex ideas about the mathematics of shape and motion intuitive and graspable. His elegant discussion of mathematical reasoning and themes in classical geometry offers proof of his conviction that mathematics illuminates art as much as science. Lockhart leads us into a universe where beautiful designs and patterns float through our minds and do surprising, miraculous things. As we turn our thoughts to symmetry, circles, cylinders, and cones, we begin to see that almost anyone can "do the math" in a way that brings emotional and aesthetic rewards. Measurement is an invitation to summon curiosity, courage, and creativity in order to experience firsthand the playful excitement of mathematical work.

Because evolution endowed humans with a complement of ten fingers, a grouping size of ten seems natural to us, perhaps even ideal. But from the perspective of mathematics, groupings of ten are arbitrary, and can have serious shortcomings. Twelve would be better for divisibility, and eight is smaller and well suited to repeated halving. Grouping by two, as in binary code, has turned out to have its own remarkable advantages. Paul Lockhart reveals arithmetic not as the rote manipulation of numbers-a practical if mundane branch of knowledge best suited for balancing a checkbook or filling out tax forms-but as a set of ideas that exhibit the fascinating and sometimes surprising behaviors usually reserved for higher branches of mathematics. The essence of arithmetic is the skillful arrangement of numerical information for ease of communication and comparison, an elegant intellectual craft that arises from our desire to count, add to, take away from, divide up, and multiply quantities of important things. Over centuries, humans devised a variety of strategies for representing and using numerical information, from beads and tally marks to adding machines and computers. Lockhart explores the philosophical and aesthetic nature of counting and of different number systems, both Western and non-Western, weighing the pluses and minuses of each. A passionate, entertaining survey of foundational ideas and methods, Arithmetic invites readers to experience the profound and simple beauty of its subject through the eyes of a modern research mathematician.

"One of the best critiques of current mathematics education I have ever seen."--Keith Devlin, math columnist on NPR's "Morning Edition"

A brilliant research mathematician who has devoted his career to teaching kids reveals math to be creative and beautiful and rejects standard anxiety-producing teaching methods. Witty and accessible, Paul Lockhart's controversial approach will provoke spirited debate among educators and parents alike and it will alter the way we think about math forever.

Paul Lockhart, has taught mathematics at Brown University and UC Santa Cruz. Since 2000, he has dedicated himself to K-12 level students at St. Ann's School in Brooklyn, New York.

This is a survey of the point in history when Sweden rose to preeminence in Europe. Drawing on the latest literature in Swedish and other languages, Paul Lockhart examines the institutions of the Swedish 'empire' at the height of its influence, while focusing on the key historical questions: why did this impoverished state become a great power, how was it able to maintain this status, and what brought about its eventual decline?