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The brachistochrone problem shows that the shortest path is not always the fastest. When an object slides down a slope, it covers a short distance but accelerates slowly. In contrast, the brachistochrone curve starts steep, giving the object high speed, then flattens to maintain that speed, resulting in a longer path but shorter travel time. The problem was posed in 1696 by Johann Bernoulli and attracted the attention of geniuses such as Leibniz, L'Hôpital, and even Newton. The brachistochrone is the path traced by a point on the rim of a rolling wheel: a cycloid. Its solution emerged from early calculus of variations, a branch of mathematics that finds optimal paths.