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Abstract / Synopsis

Many problems, from optics to economics, can be solved mathematically by finding the highest, the quickest, the shortest—the best of something. This has been true from antiquity to the present. Why did we start looking for such explanations, and how and why did we conclude that we could productively do so? In this article we explore these question and tell a story about the history of optimization. Scientific examples we use to illustrate our story include problems from ancient optics, and more modern questions in optics and classical mechanics, drawing on ideas from Newton’s and Leibniz’s calculus and from the Euler-Lagrange calculus of variations. A surprising role is also played by philosophical and theological ideas, including those of Leibniz, Maupertuis, Maclaurin, and Adam Smith.

DOI

10.5642/jhummath.202101.05

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