The Accidental Discovery of the Integral of the Secant

The integral of sec(x) is a seemingly simple formula, yet its history is anything but straightforward. First posed in 1569 by Mercator for his famous map projections, its solution eluded mathematicians for 86 years. It was then accidentally discovered by a teacher, with a formal proof finally appearing 23 years later. This article tells the story, weaving together trigonometry, calculus, and map projections, revealing the serendipity and complexity inherent in mathematical discovery.