Background
Clairaut was born on May 13, 1713, in Paris, France, the son of Jean-Baptiste and Catherine Petit Clairaut. The couple had 20 children, however only a few of them survived childbirth. His father taught mathematics.
Astronomer geophysicist mathematician scientist
Clairaut was born on May 13, 1713, in Paris, France, the son of Jean-Baptiste and Catherine Petit Clairaut. The couple had 20 children, however only a few of them survived childbirth. His father taught mathematics.
Alexis was a prodigy - he would probably have learned the alphabet from the figures in Euclid’s Elements. When he was nine years old his father had him study Guisnée’s Application de l’algèbre à la géométrie.
Around 1726 the young Clairaut, together with Jean Paul de Gua de Malves, who was barely fourteen years old; Jean Paul Grandjean de Fouchy, nineteen; Charles Marie de la Condamine, twenty-five; Jean-Antoine Nollet, twenty-six; and others founded the Société des Arts. Even though this learned society survived for only a few years, it was nonetheless a training ground for future members of the Académie des Sciences.
Around this time also Clairaut began his research on gauche curves. This work culminated in 1729 in a treatise (published in 1731) that led to his election to the Academy. The Academy proposed his election to the Crown on 4 September 1729, but it was not confirmed by the king until 11 July 1731, at which time he was still only eighteen.
In the Academy, Clairaut became interested in geodesy through Cassini’s work on the measurement of the meridian. He allied himself with Maupertuis and the small but youthful and pugnacious group supporting Newton. It is difficult, however, to specify the moment at which he turned toward this new area of physics, for which his mathematical studies had so well prepared him.
He became a close friend of Maupertuis and was much in the company of the marquise du Châtelet and Voltaire. During the fall of 1734 Maupertuis and Clairaut spent a few months with Johann Bernoulli in Basel, and in 1735 they retired to Mont Valérien, near Paris, to concentrate on their studies in a calm atmosphere.
On 20 April 1736 Clairaut left Paris for Lapland, where he was to measure a meridian arc of one degree inside the arctic circle. Maupertuis was director of the expedition, which included Le Monnier, Camus, the Abbé Outhier, and Celsius. This enthusiastic group accomplished its mission quickly and precisely, in an atmosphere of youthful gaiety for which some reproached them. On 20 August 1737 Clairaut was back in Paris.
Clairaut’s “Sur quelques questions de maximis et minimis” (1733) was noteworthy in the history of the calculus of variations. It was written, as were all his similar works, in the style of the Bernoulli brothers, by likening the infinitesimal arc of the curve of three elementary rectilinear segments. In the same vein was the memoir “Détermination géométrique… à la méridienne…” (1733), in which Clairaut made an elegant study of the geodesics of quadrics of rotation. It includes the property already pointed out by Johann Bernoulli: the osculating plane of the geodesic is normal to the surface.
What we call “Clairaut’s differential equations” first appeared in the Mémoires de l’Académie des sciences for 1734. They are solved by differentiation and, in addition to the general integral, also allow for a singular solution.
In his research on integral calculus (1739-1740) Clairaut showed that for partial derivatives of the mixed second order, the order of differentiation is unimportant; and he established the existence of an integrating factor for linear differential equations of the first order.
His most significant paper on mechanics, however, is probably “Sur quelques principes… de dynamique” (1742), on the relative movement and the dynamics of a body in motion. Even though he did not clarify Coriolis’s concept of acceleration, he did at least indicate a method of attacking the problem.
His work turned increasingly toward celestial mechanics, and he published several studies annually in Mémoires de l’Académie des sciences. From 1734 until his death, he also contributed to the Journal des sçavans. Clairaut guided the marquise du Châtelet in her studies, especially in her translation of Newton’s Principia and in preparing the accompanying explanations. Even though the work was so sufficiently advanced in 1745 that a grant could be applied for and awarded, it did not appear until 1756, seven years after the marquise’s death.
Vivacious by nature, attractive, of average height but well built, Clairaut was successful in society and, it appears, with women.
Clairaut was unmarried, and known for leading an active social life.