He was a prominent Newtonian whose work helped to establish the validity of the principles and results that Sir Isaac Newton had outlined in the Principia of 1687.
He also tackled the gravitational three-body problem, being the first to obtain a satisfactory result for the apsidal precession of the Moon's orbit.
[3] When only sixteen he finished a treatise on Tortuous Curves, Recherches sur les courbes a double courbure, which, on its publication in 1731, procured his admission into the Royal Academy of Sciences, although he was below the legal age as he was only eighteen.
[2] His growing popularity in society hindered his scientific work: "He was focused," says Bossut, "with dining and with evenings, coupled with a lively taste for women, and seeking to make his pleasures into his day to day work, he lost rest, health, and finally life at the age of fifty-two."
In 1736, together with Pierre Louis Maupertuis, he took part in the expedition to Lapland, which was undertaken for the purpose of estimating a degree of the meridian arc.
His article in Philosophical Transactions created much controversy, as he addressed the problems of Newton's theory, but provided few solutions to how to fix the calculations.
[2] In 1849 George Stokes showed that Clairaut's result was true whatever the interior constitution or density of the Earth, provided the surface was a spheroid of equilibrium of small ellipticity.
He believed that instead of having students repeatedly work problems that they did not fully understand, it was imperative for them to make discoveries themselves in a form of active, experiential learning.
Along with Clairaut, there were two other mathematicians who were racing to provide the first explanation for the three body problem; Leonhard Euler and Jean le Rond d'Alembert.
Euler in particular believed that the inverse square law needed revision to accurately calculate the apsides of the Moon.
In 1750 he gained the prize of the St Petersburg Academy for his essay Théorie de la lune; the team made up of Clairaut, Jérome Lalande and Nicole Reine Lepaute successfully computed the date of the 1759 return of Halley's comet.
It allowed sailors to determine the longitudinal direction of their ships, which was crucial not only in sailing to a location, but finding their way home as well.
[9] This held economic implications as well, because sailors were able to more easily find destinations of trade based on the longitudinal measures.
He also used applied mathematics to study Venus, taking accurate measurements of the planet's size and distance from the Earth.