Infinite Powers

January 15, 2019
A complex attempt to render calculus accessible.Strogatz (Applied Mathematics/Cornell Univ.; The Joy of X: A Guided Tour of Math, from One to Infinity, 2013, etc.) emphasizes that "calculus is an imaginary realm of symbols and logic" that "lets us peer into the future and predict the unknown. That's what makes it such a powerful tool for science and technology." It works by breaking problems down into tiny parts--infinitely tiny--and then putting them back together. Breaking down is the work of differential calculus; putting together requires integral calculus. Early civilizations, including the Babylonians, Greeks, and Chinese, had no trouble measuring anything straight, including complex structures such as the icosahedron, but curves and movement caused problems. Thus, finding the area of a circle by converting it into a 10-sided polygon and measuring the polygon's area yields a fair approximation. A 100-sided polygon gave a more accurate result. Perfection required a polygon with an infinite number of infinitely small sides, but dealing with infinity was particularly tricky. Invented in its modern version by Newton and Leibniz in the late 17th century, calculus solved the problem. Readers who pay close attention to Strogatz's analogies, generously supplied with graphs and illustrations, may or may not see the light, but all will enjoy the long final section, which eschews education in favor of a history of modern science, which turns out to be a direct consequence of this mathematics. The best introduction to calculus remains a textbook--Calculus Made Easy by Silvanus P. Thompson--published in 1910 and, amazingly, still in print. Readers who dip into Thompson will understand Strogatz's enthusiasm. His own explanations will enlighten those with some memory of high school calculus, but innumerate readers are likely to remain mystified.An energetic effort that successfully communicates the author's love of mathematics, if not the secrets of calculus itself.

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April 1, 2019

For anyone who has struggled through a required calculus course, this latest book by Strogatz (Jacob Gould Schurman Professor of Applied Mathematics, Cornell Univ.; The Joy of X) is especially welcome. Strogatz does a great job of explaining a difficult subject, both to those in need of a refresher and those who have never taken calculus. After describing calculus's history and the people who created it, the author uses real examples, ranging from athletics to medicine, to show some of its many old, new and, potentially future applications. Most importantly, he lays out the case that calculus is fundamental to the way we live today. Simply put, without calculus, there would be no modern physics, and without physics we wouldn't have the technology that shapes our modern world. VERDICT A solid choice for readers who want to know what calculus is all about, and for teachers who wish to improve their presentation.--Harold D. Shane, Mathematics Emeritus, Baruch Coll. Lib., CUNY

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