“Packed with vivid detail and founded on solid scholarship, is both a rich history and a gripping page turner.” ―Jordan Ellenberg, The Wall Street Journal “You probably don't think of the development of calculus as ripe material for a political thriller, but Amir Alexander has given us just that in Infinitesimal.” A bracing reminder of the human drama behind mathematical formulas. But as readers explore the personalities and life trajectories of the combatants, they will recognize complexities that do not fit into Alexander’s overall script: Bonaventura Cavalieri (one of the discoverers of indivisibles) was a cautious monk, while RenéDescartes (the father of modern philosophy) rejected the new mathematics. Alexander credits the champions of indivisibles with helping to usher in an era of progressive tolerance and democracy, and he indicts their foes as hidebound authoritarians. Beyond what it teaches about mathematics, the intellectual combat illuminates the tempestuous birth of modernity. Alexander compellingly chronicles the clashes as Galileo squares off with Pope Urban VIII in Italy, and royalist Thomas Hobbes crosses swords with puritan John Wallis in England. But it also subverted Aristotelian philosophical principles, so alarming defenders of the status quo. Premised on the definition of a line as a composite of countless infinitesimally small elements, the method of indivisibles opened the door to calculus. Yet in recounting how that method originated, provoked vigorous resistance, and finally prevailed, Alexander tells a story with implications far beyond mathematics. *Starred Review* Convinced that it opened the Royal Road through the mathematical thicket, seventeenth-century mathematician Evangelista Torricelli trumpeted the method of indivisibles. The legitimacy of popes and kings, as well as our beliefs in human liberty and progressive science, were at stake-the soul of the modern world hinged on the infinitesimal. In Italy, the defeat of the infinitely small signaled an end to that land's reign as the cultural heart of Europe, and in England, the triumph of infinitesimals helped launch the island nation on a course that would make it the world's first modern state.įrom the imperial cities of Germany to the green hills of Surrey, from the papal palace in Rome to the halls of the Royal Society of London, Alexander demonstrates how a disagreement over a mathematical concept became a contest over the heavens and the earth. The story takes us from the bloody battlefields of Europe's religious wars and the English Civil War and into the lives of the greatest mathematicians and philosophers of the day, including Galileo and Isaac Newton, Cardinal Bellarmine and Thomas Hobbes, and Christopher Clavius and John Wallis. As Alexander reveals, it wasn't long before the two camps set off on a war that pitted Europe's forces of hierarchy and order against those of pluralism and change. Philosophers, scientists, and mathematicians across Europe embraced infinitesimals as the key to scientific progress, freedom of thought, and a more tolerant society. Indeed, not everyone agreed with the Jesuits. In Infinitesimal, the award-winning historian Amir Alexander exposes the deep-seated reasons behind the rulings of the Jesuits and shows how the doctrine persisted, becoming the foundation of calculus and much of modern mathematics and technology. If infinitesimals were ever accepted, the Jesuits feared, the entire world would be plunged into chaos. 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. With the stroke of a pen the Jesuit fathers banned the doctrine of infinitesimals, announcing that it could never be taught or even mentioned. 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. Pulsing with drama and excitement, Infinitesimal celebrates the spirit of discovery, innovation, and intellectual achievement-and it will forever change the way you look at a simple line.
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