'Fascinating. Amir Alexander vividly recreates a wonderfully strange chapter of scientific history... You will never look at calculus the same way again.' -- Jordan Ellenberg, Professor of Mathematics, University of Wisconsin-Madison 'Clever and enthralling.' -- Simon Schaffer, Professor of the History of Science, University of Cambridge 'We thought we knew the whole story: Copernicus, Galileo, the sun in the centre, the Church rushing to condemn. Now this remarkable book puts the deeply subversive doctrine of atomism and its accompanying mathematics at the heart of modern science.' -- Margaret C. Jacob, Distinguished Professor of History, University of California, Los Angeles 'A seamless synthesis of cultural history and storytelling... The history of mathematics has rarely been so readable.' -- Michael Harris, Professor of Mathematics, Columbia University and Universite Paris Diderot 'You may find it hard to believe that illustrious mathematicians, philosophers, and religious thinkers would engage in a bitter dispute over infinitely small quantities. Yet this is precisely what happened in the seventeenth century. In Infinitesimal, Amir Alexander puts this fascinating battle in historical and intellectual context.' -- Mario Livio, Astrophysicist, Space Telescope Science Institute, and author of Brilliant Blunders: Fr 'Gripping... Amir Alexander writes with elegance and verve... A page-turner full of fascinating stories about the struggles of remarkable individuals and ideas, Infinitesimal will help you understand the world at a deeper level.' -- Edward Frenkel, Professor, University of California at Berkeley, and author of Love and Math 'A real-world Da Vinci Code' Publishers Weekly "[Told with] high drama and thrilling tension." Kirkus Reviews (starred review) 'A gripping tale of mathematical, philosophical, and theological controversies in the run-up to calculus.' Ian Stewart, author of Professor Stewart's Cabinet of Mathematical Curiosities "Bertrand Russell once wrote that mathematics had a 'beauty cold and austere'... Amir Alexander shows that mathematics can also become entangled in ugliness hot and messy... [a] fascinating narrative." New York Times 'A gripping and thorough history of the ultimate triumph of the mathematical tool... Infinitesimal will inspire you to dig deeper into the implications of the philosophy of mathematics and knowledge' New Scientist 'A complex story told with skill and verve... Alexander does an excellent job of presenting both sides of the debate.' THES Book of the Week 'Amir Alexander's enthralling book presents a controversial mathematical breakthrough, vividly describing the players and showing exactly what was at stake.' Tony Mann, Director of the Maths Centre, University of Greenwich and Former President of the British 'A well-spun yarn, a cracking read... engaging...unique' History Today 'fluent and richly informative' Literary Review
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.
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. With the stroke of a pen the Jesuit fathers banned the doctrine of infinitesimals, announcing that it could never be taught or even mentioned. 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. If infinitesimals were ever accepted, the Jesuits feared, the entire world would be plunged into chaos.
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. Indeed, not everyone agreed with the Jesuits. Philosophers, scientists, and mathematicians across Europe embraced infinitesimals as the key to scientific progress, freedom of thought, and a more tolerant society. 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.
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. 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.
From 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 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.