Many of the most significant areas of mathematics have emerged from questions about extremes: the shortest path between two points on a curved surface, the fewest colors needed for a map, the fastest fall, the weirdest symmetry, or the shortest proof. These puzzles have long pushed scholars toward extremes. Solving the question of the shortest route enclosing a given area, for example, can be traced to ancient Carthage. Plateau’s problem of soap bubble geometry led to the notion of a minimal surface now used in cosmology and biology. Meanwhile, the 2023 discovery of a single tile shape that covers the infinite plane without patterned repetition has no application yet.
To illuminate how mathematicians drive knowledge forward by reaching for the edges, author and mathematician Ian Stewart explores stories of superlative problems—their history, the struggles to solve them, and the uses of some of the results.
His new book, Reaching for the Extreme: How the Quest for the Biggest, Fewest and Weirdest Makes Math (Princeton University Press), is available for purchase.
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