To the fourth-century philosopher and theologian Saint Augustine, infinity was \u201ctoo incomprehensible for the human mind.\u201d Yet, in his New York Times bestselling book, \u201cInfinite Powers,\u201d applied mathematician Steven Strogatz contends that humanity has not only dared to confront this unfathomable concept, but has learned to use it through the mathematical discipline of calculus. In Strogatz\u2019s hands, the infinite transforms from a philosophical impasse to the very foundation for understanding reality.\u00a0<\/p>\n\n\n\n
Calculus is the mathematics of change, the defining constant of existence. As Henry David Thoreau once wrote, \u201cAll change is a miracle to contemplate, but it is a miracle which is taking place every instant.\u201d By partitioning space and time into infinitesimal pieces, calculus addresses the two fundamental mysteries of the physical world: curvature and motion. It enables scientists and engineers to model everything from planetary motion to the way light bends to the behavior of epidemics with staggering precision. <\/p>\n\n\n\n
Yet, calculus rests on a paradox. Strogatz argues that infinity is calculus\u2019s \u201coriginal sin\u201d \u2014 the source of its astonishing power and its logical peril. Dissecting reality into endlessly small parts raises ontological quandaries. How can adding an infinite number of infinitesimally small quantities yield a finite result? In other words, summing \u201cinfinitely many nothings\u201d shouldn\u2019t amount to something, and strangely, it does. Time and time again, calculus works\u2014predictably, repeatedly and somehow precisely. \u201cThe one represents the many and stands for it,\u201d Strogatz writes, \u201crepresenting it perfectly and faithfully.\u201d\u00a0<\/p>\n\n\n\n
Quoting Picasso\u2019s remark that \u201cart is a lie that makes us realize truth,\u201d Strogatz suggests that the infinite in calculus functions similarly: an \u201celegant fiction,\u201d an abstraction that, while not literally accurate, reveals hidden truths about the natural world. Though infinity itself eludes complete comprehension, it nonetheless remains instrumental in explaining other fundamental mysteries of the universe. According to Strogatz,\u00a0 infinity is \u201cthe numerical counterpart of something deep in our psyches, in our nightmares of bottomless pits, and our hopes for eternal life.\u201d\u00a0<\/p>\n\n\n\n
The book takes readers on a historical tour. It begins with the work of Archimedes, the ancient Greek mathematician whose treatise, \u201cThe Method,\u201d was believed lost until its rediscovery in 1906. The writings, recovered from a palimpsest in a Byzantine prayer book, contain Archimedes\u2019 use of infinitesimals to calculate areas and volumes; the Sicilian had anticipated integral calculus by over a thousand years. Archimedes hoped his work \u201cwould survive the seas of time and be appreciated by a more modern world,\u201d Strogatz writes. In the late sixteenth century, Galileo Galilei of Pisa resumed his line of inquiry by demonstrating that existing mathematical tools inadequately described continuous change, through his experiments on motion and falling bodies. The French mathematician and philosopher Ren\u00e9 Descartes further advanced the field in the early 17th century by introducing a coordinate system that formally linked geometry and algebra.\u00a0<\/p>\n\n\n\n
In the late seventeenth century, at the dawn of the Age of Enlightenment, these earlier developments culminated in the formulation of calculus by Isaac Newton in England and Gottfried Wilhelm Leibniz in Germany. They discovered that by breaking complex phenomena into infinitesimal parts and reassembling them\u2014processes known as differentiation and integration\u2014they could accurately model the natural world. Even more remarkably, they realized these two central operations are inverse processes, a relationship later defined as the Fundamental Theorem of Calculus.<\/p>\n\n\n\n
Physicist Richard Feynman, once a young scientist working on the Manhattan Project, once called calculus the \u201clanguage God talks.\u201d Robert Montera, who teaches 9th grade history at Fieldston, says \u201cit helps to map the contours of our realities.\u201d While Newtonian physics breaks down at the subatomic scale, Newtonian calculus remains applicable. Strogatz asserts that the enduring relevance of calculus across centuries makes it humanity\u2019s most powerful tool for understanding the universe.\u00a0<\/p>\n\n\n\n
Erudite without being esoteric, Infinite Powers <\/em>is no daunting academic text meant only for mathematicians. Strogatz delivers a deftly written exploration of calculus and its role in shaping the modern world. For those interested in math, science, philosophy or the history of ideas, this book is an essential read. <\/p>\n\n\n\n Ultimately, Infinite Powers <\/em>is a beautiful tribute to human ingenuity. It is a grand narrative about the power of the infinite, and, despite the warning from a particular bishop from Hippo, the incredible minds who dared to tame it.\u00a0<\/p>\n","protected":false},"excerpt":{"rendered":" To the fourth-century philosopher and theologian Saint Augustine, infinity was \u201ctoo incomprehensible for the human mind.\u201d Yet, in his New York Times bestselling book, \u201cInfinite Powers,\u201d applied mathematician Steven Strogatz contends that humanity has not only dared to confront this unfathomable concept, but has learned to use it through the mathematical discipline of calculus. In Strogatz\u2019s hands, the infinite transforms from a philosophical impasse to the very foundation for understanding reality.\u00a0 Calculus is the mathematics<\/p>\n","protected":false},"author":358,"featured_media":11899,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[647,318,638],"tags":[],"coauthors":[630],"class_list":["post-11898","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-book-recommendation","category-news","category-review"],"jetpack_featured_media_url":"https:\/\/fieldstonnews.com\/home\/wp-content\/uploads\/2025\/06\/Screenshot-2025-06-28-at-9.03.46-AM-e1751126687480.png","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/fieldstonnews.com\/home\/wp-json\/wp\/v2\/posts\/11898","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/fieldstonnews.com\/home\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/fieldstonnews.com\/home\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/fieldstonnews.com\/home\/wp-json\/wp\/v2\/users\/358"}],"replies":[{"embeddable":true,"href":"https:\/\/fieldstonnews.com\/home\/wp-json\/wp\/v2\/comments?post=11898"}],"version-history":[{"count":1,"href":"https:\/\/fieldstonnews.com\/home\/wp-json\/wp\/v2\/posts\/11898\/revisions"}],"predecessor-version":[{"id":11900,"href":"https:\/\/fieldstonnews.com\/home\/wp-json\/wp\/v2\/posts\/11898\/revisions\/11900"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/fieldstonnews.com\/home\/wp-json\/wp\/v2\/media\/11899"}],"wp:attachment":[{"href":"https:\/\/fieldstonnews.com\/home\/wp-json\/wp\/v2\/media?parent=11898"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/fieldstonnews.com\/home\/wp-json\/wp\/v2\/categories?post=11898"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/fieldstonnews.com\/home\/wp-json\/wp\/v2\/tags?post=11898"},{"taxonomy":"author","embeddable":true,"href":"https:\/\/fieldstonnews.com\/home\/wp-json\/wp\/v2\/coauthors?post=11898"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}