Science in the Spotlight: Infinite Powers

Yu Jun Shen | yujun.shen@yale.edu March 15, 2020

Science in the Spotlight: Infinite Powers

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Have you ever wondered how DreamWorks animators created Shrek? Or how we may measure the speed of light using cheese in a microwave? Calculus holds the key. Whether you are a prospective STEM major or just hoping to pass your mandatory math class, Steven Strogatz will intrigue you with his book Infinite Powers: How Calculus Reveals the Secrets of the Universe. Infinite Powers has no complex formulae or rigorous proofs; rather it sketches out the logic behind some of mathematics’ greatest breakthroughs by revealing the stories and characters that led to their discovery.

Strogatz’s central theme is the pervasiveness of calculus. From classical examples in physics, to modern applications in computer animation and biological systems, we rely on calculus every day. It is for this reason that Strogatz loves calculus and “wanted to share that love with a wider audience,” he says. “Many students never really see the point of it.”

Infinite Powers progresses chronologically, starting with the earliest forays into the “infinite.” Sandwiching a circle between two increasingly many-sided polygons, Archimedes approached pi. Modern physics emerged when Kepler and Galileo scrutinized the problem of motion using mathematics. In subsequent pages, more mathematicians appear—Descartes (the namesake of Cartesian coordinates), Fermat (who explained how light travels to minimize time), and Newton (who established classical mechanics). Strogatz carefully introduces, and then explains, the concepts of derivatives and integrals. The history of the fundamental theorem of calculus—the telescopic sum of many steps equals the difference between two boundary points—is rarely known, even for readers who have tackled calculus in school.

A key strength of Infinite Powers is how it showcases the mathematicians’ varied personalities. Strogatz describes Kepler and Galileo—who established the foundations of modern astronomy and physics—as the mystic and rational heirs, respectively, to Pythagoras and Archimedes. We glimpse Descartes’s disdain in 1638 of Fermat’s work on calculating gradients: “I do not even want to name him, so that he will feel less shame at the errors that I have found,” Descartes wrote. Similar rivalry appeared between Newton and Leibniz, as British and continental European mathematicians bickered over who developed calculus first.

Amidst this historically male-dominated field, Sophie Germain stands out as a tenacious female mathematician who “wrapped herself in quilts and worked by the light of stolen candles” to study mathematics, eventually solving a difficult standing wave problem. These delightful stories bring to life the stale portraits typically found in college textbooks. “[Calculus is] one of humanity’s greatest collective achievements … and the story of how it was discovered and developed is one of the greatest intellectual adventures of all time,” Strogatz explained.

As promised, Infinite Powers explains calculus for everyday readers. It is also a valuable addition for science and engineering majors given the sheer breadth of applications covered. With any luck, you will find calculus less intimidating and obscure than before and be inspired to dive deeper into the magic that powers our modern world.

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