Now regarded as the bane of many college students' existence, calculus was one of the most important mathematical innovations of the seventeenth century. But a dispute over its discovery sewed the seeds of discontent between two of the greatest scientific giants of all time -- Sir Isaac Newton and Gottfried Wilhelm Leibniz. Today Newton and Leibniz are generally considered the twin independent inventors of calculus, and they are both credited with giving mathematics its greatest push forward since the time of the Greeks. Had they known each other under different circumstances, they might have been friends. But in their own lifetimes, the joint glory of calculus was not enough for either and each declared war against the other, openly and in secret. This long and bitter dispute has been swept under the carpet by historians -- perhaps because it reveals Newton and Leibniz in their worst light -- but The Calculus Wars tells the full story in narrative form for the first time. This vibrant and gripping scientific potboiler ultimately exposes how these twin mathematical giants were brilliant, proud, at times mad and, in the end, completely human.

Winner of the Jefferson Davis Award Winner of the Johns Family Book Award Winner of the Army Historical Foundation Distinguished Writing Award “A work of deep intellectual seriousness, sweeping and yet also delicately measured, this book promises to resolve longstanding debates about the nature of the Civil War.” —Gregory P. Downs, author of After Appomattox Shiloh, Chancellorsville, Gettysburg—tens of thousands of soldiers died on these iconic Civil War battlefields, and throughout the South civilians suffered terrible cruelty. At least three-quarters of a million lives were lost during the American Civil War. Given its seemingly indiscriminate mass destruction, this conflict is often thought of as the first “total war.” But Aaron Sheehan-Dean argues for another interpretation. The Calculus of Violence demonstrates that this notoriously bloody war could have been much worse. Military forces on both sides sought to contain casualties inflicted on soldiers and civilians. In Congress, in church pews, and in letters home, Americans debated the conditions under which lethal violence was legitimate, and their arguments differentiated carefully among victims—women and men, black and white, enslaved and free. Sometimes, as Sheehan-Dean shows, these well-meaning restraints led to more carnage by implicitly justifying the killing of people who were not protected by the laws of war. As the Civil War raged on, the Union’s confrontations with guerrillas and the Confederacy’s confrontations with black soldiers forced a new reckoning with traditional categories of lawful combatants and raised legal disputes that still hang over military operations around the world today. In examining the agonizing debates about the meaning of a just war in the Civil War era, Sheehan-Dean discards conventional abstractions—total, soft, limited—as too tidy to contain what actually happened on the ground.

Mathematics has for centuries been stimulated, financed and credited by military purposes. Some mathematical thoughts and mathematical technology have also been vital in war. During World War II mathematical work by the Anti-Hitler coalition was part of an aspiration to serve humanity and not help destroy it. At present, it is not an easy task to view the bellicose potentials of mathematics in a proper perspective. The book presents historical evidence and recent changes in the interaction between mathematics and the military. It discusses the new mathematically enhanced development of military technology which seems to have changed the very character of modern warfare.

This book proposes a novel theoretical framework of "interactive arming" in order to explain armament dynamics in contemporary Asia. Frequently, the modernisation of contemporary naval forces in Asia is described as an "arms race," with the underlying assumption being that weapons acquisitions and increases in defence expenditure are competitive and bilateral and due to conflicting purposes or mutual fears. This book argues that the concept of an arms race is an unsuitable one for explaining contemporary military modernisation in 21st-century Asia. Instead, it proposes a novel and innovative concept of "interactive arming" and argues that what drives conflict is political rivalry, not weapons acquisitions. Instead of perceiving arming as abnormal behaviour, the book views arming as a natural strategic behaviour of states and military modernisation as a basic requirement for a state’s ability to survive. This book will be of much interest to students of Asian security, strategic studies and international relations in general.