Algebra the Beautiful

May 30, 2022
Math professor Williams (How Math Works) successfully makes his case that algebra is “big, varied, dramatic, and relevant” in this shrewd attempt to win over math-averse readers. Using what he terms humanistic, aesthetic, and conceptual approaches, he relates the field to “other great areas of human activity, expression, and ambition.” Algebraic equations, for example, involve “linking together conceptually similar entities,” akin to using analogies and metaphors, while variations in music, like in algebra, can be transcribed on paper in the form of musical notations, which leads to a discussion of mathematical symbols and, in turn, to the relationship between stable and variable values. Those variables, Williams suggests, occur in automobiles, spoken languages, and nations. For those willing to get into the weeds, an appendix offers word problems that put the theory into practice, such as “an unknown number added to ten more than fifteen times itself gives one hundred six. Find the number.” Williams can get revel a bit too much in the nitty-gritty, but his passion is worth sticking around for. Readers willing to stay the course will find plenty of insight.