Fermat's Principle - History

History

Hero of Alexandria (Heron) (c. 60) described a principle of reflection, which stated that a ray of light that goes from point A to point B, suffering any number of reflections on flat mirrors, in the same medium, has a smaller path length than any nearby path.

Ibn al-Haytham (Alhacen), in his Book of Optics (1021), expanded the principle to both reflection and refraction, and expressed an early version of the principle of least time. His experiments were based on earlier works on refraction carried out by the Greek scientist Ptolemy

The generalized principle of least time in its modern form was stated by Fermat in a letter dated January 1, 1662, to Cureau de la Chambre. It was met with objections made in May 1662 by Claude Clerselier, an expert in optics and leading spokesman for the Cartesians at that time. Amongst his objections, Clerselier states:

... Fermat's principle can not be the cause, for otherwise we would be attributing knowledge to nature: and here, by nature, we understand only that order and lawfulness in the world, such as it is, which acts without foreknowledge, without choice, but by a necessary determination.

The original French, from Mahoney, is as follows:

Le principe que vous prenez pour fondement de votre démonstration, à savoir que la nature agit toujours par les voies les plus courtes et les plus simples, n’est qu’un principe moral et non point physique, qui n’est point et qui ne peut être la cause d’aucun effet de la nature.

Indeed Fermat's principle does not hold standing alone, we now know it can be derived from earlier principles such as Huygens' principle.
Historically, Fermat's principle has served as a guiding principle in the formulation of physical laws with the use of variational calculus (see Principle of least action).