Terence Tao *96’s book, Solving Mathematical Problems: A Personal Perspective, is an engagingly slender volume, full of insights on how to approach problems in number theory, algebra, Euclidean geometry, and analytic geometry.
He was commissioned to write it by Deakin University, in Victoria, Australia, near his hometown of Adelaide, in the hope that it could be used to train secondary-school math teachers. Tao began by setting out some sensible strategies for problem-solving, including these: Understand the problem, understand the data, understand the objective, select good notation, and write down everything you know. He also hoped for something less rote. “A solution,” Tao proposed, “should be relatively short, understandable, and hopefully have a touch of elegance. It should be fun to discover.”