Review by Choice Review
The theory of infinitesimals--that the continuum is composed of infinitely many, infinitely small "indivisibles"--is the driving force behind the development of calculus and thus much of modern mathematics. Historian Alexander (UCLA; Geometrical Landscapes, CH, Feb'03, 40-3371) offers a rich, lively portrayal of the intellectual and political history of infinitesimals. In part 1 of the book, he considers the prehistory of infinitesimals in late Renaissance Italy: the work of Christopher Clavius and the Catholic Church's elevation of mathematics, particularly Euclidean geometry, as a demonstration of unchanging order and certitude. He discusses the pioneering efforts of Bonaventura Cavalieri, Evangelista Torricelli, and Galileo Galilei regarding indivisibles and the subsequent repudiation of infinitesimals by the Jesuits. In part 2, Alexander turns to England and the fierce intellectual conflicts between, especially, Thomas Hobbes and John Wallis and the ultimate acceptance of the infinitesimal method. Alexander highlights how the use of infinitesimals signaled a profound change in mathematics from that of a system of rigorous, formal reasoning not always of easy practical use to one allowing some informality, which enabled much greater application. The text requires an appreciation of some subtle and clever arguments rather than much mathematical knowledge. --Susan Jane Colley, Oberlin College
Copyright American Library Association, used with permission.
Review by New York Times Review
THE MASTER OF CONFESSIONS: The Making of a Khmer Rouge Torturer, by Thierry Cruvellier. Translated by Alex Gilly. (Ecco/Harper-Collins, $16.99.) Cruvellier, who has reported on some of the world's most notorious war crimes, recounts the trial of Duch, the director of the Khmer Rouge's S-21 prison, where thousands of people were killed. His exhaustive account includes a sly commentary on the whims and limits of the international justice system. AN UNNECESSARY WOMAN, by Rabih Alameddine. (Grove, $16.) Divorced and childless, 72-year-old Aaliya lives in her Beirut apartment alone, deemed "unnecessary" by the rest of her family. Her life may appear solitary, but she is kept company by stacks of favorite books, one of which she chooses to translate into Arabic every year. Though her life is physically grounded in her home, Aaliya's memories roam through chapters of Beirut's history and span decades of literature. ON LEAVE, by Daniel Anselme. Translated by David Bellos. (Faber & Faber, $14.) First published in 1957 during the Algerian War, "On Leave" follows three French soldiers who return from North Africa to a society coolly uninterested in their wartime experiences. Bellos's translation gives new life to the book, which was never reprinted and largely disappeared from the French literary landscape. MY SALINGER YEAR, by Joanna Rakoff. (Vintage, $15.95.) After leaving graduate school, Rakoff found a job as an assistant in a stubbornly anachronistic literary agency whose most celebrated client was J. D. Salinger. Tasked with responding to Salinger's fans with an outdated form letter (Salinger himself had stopped responding decades earlier), Rakoff chose to write back herself. SPOILED BRATS: Stories, by Simon Rich. (Back Bay/Little, Brown, $15.) Often based on surreal premises (the opening story is narrated by a traumatized classroom hamster), the tales in Rich's latest collection add up to a hilarious portrait of the millennial generation. Rich, a frequent contributor to The New Yorker and a millennial himself, makes occasional cameo appearances here, too. INFINITESIMAL: How a Dangerous Mathematical Theory Shaped the Modern World, by Amir Alexander. (Scientific American/Farrar, Straus & Giroux, $16.) Alexander, who studies mathematical theory in a cultural context, offers an overview of infinitesimals, a reflection of the idea that a continuous line is composed of an infinite number of small, distinct parts. The math is settled now, but in the 16th and 17th centuries, the concept pitted Jesuits against Protestants and was the subject of a decades-long debate between Thomas Hobbes and his mathematical adversaries. Alexander's book shows how something infinitely small by definition can have profound effects on history. FRIENDSWOOD, by René Steinke. (Riverhead, $16.) A small Texas community, modeled on Steinke's hometown, suffers collective amnesia about its toxic waste, in a novel that abounds with questions of moral responsibility.
Copyright (c) The New York Times Company [June 21, 2015]
Review by Booklist Review
*Starred Review* Convinced that it opened the Royal Road through the mathematical thicket, seventeenth-century mathematician Evangelista Torricelli trumpeted the method of indivisibles. Yet in recounting how that method originated, provoked vigorous resistance, and finally prevailed, Alexander tells a story with implications far beyond mathematics. Premised on the definition of a line as a composite of countless infinitesimally small elements, the method of indivisibles opened the door to calculus. But it also subverted Aristotelian philosophical principles, so alarming defenders of the status quo. 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. Beyond what it teaches about mathematics, the intellectual combat illuminates the tempestuous birth of modernity. 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. 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 ReneDescartes (the father of modern philosophy) rejected the new mathematics. A bracing reminder of the human drama behind mathematical formulas.--Christensen, Bryce Copyright 2014 Booklist
From Booklist, Copyright (c) American Library Association. Used with permission.
Review by Publisher's Weekly Review
UCLA historian and mathematician Alexander (Geometrical Landscapes) gives readers insight into a real-world Da Vinci Code-like intrigue with this look at the history of a simple, yet pivotal, mathematical concept. According to classic geometry, a line is made of a string of points, or "indivisibles," which cannot be broken down into anything smaller. But if that's so, how many indivisibles are in a line, and how big are they? And what happens when you divide the line into smaller segments? It seemed that indivisibles weren't really indivisible at all, a "deeply troubling" idea to the medieval Church and its adherents, who demanded a rigidly unchanging cosmos with no surprises. Churchmen and respected thinkers like Descartes railed against infinitesimals, while Galileo, Newton, and others insisted the concept defined the real world. The argument became an intellectual and philosophical battleground, in a Church already threatened by doctrinal schisms and social upheaval. Focusing on the Jesuits, beginning with the German Jesuit mathematician Christopher Clavius, Alexander explores this war of ideas in the context of a world seething with political and social unrest. This in-depth history offers a unique view into the mathematical idea that became the foundation of our open, modern world. Agent: the Garamond Agency. (Apr.) (c) Copyright PWxyz, LLC. All rights reserved.
(c) Copyright PWxyz, LLC. All rights reserved
Review by Kirkus Book Review
In the mid-17th century, debate raged over a mathematical concept of the infinitely smalland nothing less than modernity as we know it was at stake. At its core, the public argument over the infinitesimalthe idea that a line is composed of an endless number of immeasurably small component partsis rooted in the ideological scope of post-Reformation Europe. The church, struggling to maintain autonomy over an increasingly disparate populace, fought to bar the infinitesimal from mathematical doctrine due to its implication that nature itself is not orderly, logical and completely subject to deductive reasoning. At the same time, leading intellectuals like Thomas Hobbes and John Wallis insisted that embracing the idea of the infinite in mathematics would open up a remarkable new opportunity to experimentally explore the world around us. Alexander (History/UCLA; Duel at Dawn: Heroes, Martyrs, and the Rise of Modern Mathematics, 2010, etc.) tells this story of intellectual strife with the high drama and thrilling tension it deserves, weaving a history of mathematics through the social and religious upheavals that marked much of the era. For the people of Europe, more than just academic success was on the line: The struggle for civil liberties and rebellion against the rigid doctrines of the establishment were entrenched in the conceptual war over the infinitesimal. The fact that progressive mathematics prevailed was unquestionably momentous, as the addition of the concept of the infinitesimal eventually led to calculus, physics and many of the technological advances that are the bedrock of modern science and society. The author navigates even the most abstract mathematical concepts as deftly as he does the layered social history, and the result is a book about math that is actually fun to read. A fast-paced history of the singular idea that shaped a multitude of modern achievements.]] Copyright Kirkus Reviews, used with permission.
Copyright (c) Kirkus Reviews, used with permission.
