Summarizing 2,500 years of mathematics milestones and the mathematicians who made them.
Even a popularizer as skilled and prolific as Stewart (Mathematics/Univ. of Warwick; Calculating the Cosmos: How Mathematics Unveils the Universe, 2016, etc.) cannot expect general readers to fully digest his highly distilled explanations of what these significant figures did to resolve ever more complex conundrums as math advanced. The author clearly reviews Euclid and highlights the contributions of Arabic and Indian innovators in algebra and trigonometry, but things get more complicated as he turns to differential equations, three-dimensional manifolds, or multiholed tori. Thankfully, Stewart’s brief but colorful sketches of the life and times of the innovators keep the pages turning. Besides well-known figures such as Archimedes, Pierre de Fermat, Isaac Newton, Alan Turing, and Kurt Gödel, the author also discusses Évariste Galois, the algebraist killed in a duel at age 20; Georg Cantor, who was driven to depression and breakdown by critics of his ideas of higher orders of numerical infinity; and Srinivasa Ramanujan, the self-taught Indian number theorist of phenomenal intuition. Among other biographical nuggets, we learn that Turing may not have died from self-inflicted cyanide poisoning but from inhaling fumes from other causes and that Gödel so feared being poisoned that he died of slow starvation. Stewart includes three women in his pantheon (Ada Lovelace, Sofia Kovalevskaia, and Emmy Noether) and blames centuries of cultural bias and not genes for their scant representation. In the final chapter, the author ponders what his subjects have in common. Most seem to have manifested aptitude at an early age, but otherwise, there are few shared aspects of class, character, education, or family background. One thing is certain, however: they all had a profound love for math.
A text for teachers, precocious students, and intellectually curious readers unafraid to tread unfamiliar territory and learn what mad pursuits inspire mathematicians.