The Brachistochrone — Newton 'Recognised by the Claw'

In June 1696, Johann Bernoulli issued a challenge to all mathematicians: find the curve along which a bead slides from one point to another in the shortest possible time under gravity — the brachistochrone. The answer is not a straight line, nor a circle, but a cycloid. By early February 1697, solutions had arrived from Leibniz, l'Hôpital, Tschirnhaus, and Jakob Bernoulli — and from an anonymous submission. Johann recognised it instantly as Newton's: 'I recognise the lion by his claw.' Newton had received the problem late one evening and solved it before breakfast. The brachistochrone problem founded the calculus of variations — optimisation over entire functions rather than single values.