The only complete French translation of Isaac Newton's Principia, his book on motion and gravity, is the one Émilie du Châtelet finished in 1749, the year she died. Almost two-thirds of its second volume is her own commentary. Yet in her book of philosophy she argued that Newton was right about how bodies move but had left physics without foundations, and she took the foundations from Leibniz, Newton's rival over the invention of the calculus.
She came to science through private teachers, because the Paris Académie des sciences, the body that judged and published French science, admitted no women. From 1733 she studied mathematics with Pierre Louis Moreau de Maupertuis, a member of the Académie, and later with Alexis Clairaut, who would work through the Principia with her and see her translation into print. In 1734 Voltaire, the writer who had become her lover, settled at Cirey, her husband's estate, and the two fitted the house with a laboratory. When the Académie set fire as the subject of a prize, she wrote an entry without telling Voltaire. Leonhard Euler won, but in 1739 the Académie printed her essay, the first work by a woman it had published.
Institutions de physique (1740) is where she broke with the Newtonians around her. Physics, she argued, cannot rest on experiment alone. It needs first principles, among them Leibniz's principle of sufficient reason: nothing is so rather than otherwise without a reason why. She also defended hypotheses. Newton had declared that he framed none, and his followers used the line to ban them; she answered that the greatest scientists, Newton included, had advanced by framing them. Samuel Koenig, who tutored her from 1739, later claimed the book's Leibnizian ideas as his; her draft, written before he arrived, already contained them.
The sharpest dispute was over force. Followers of Descartes measured a moving body's force by its mass times its speed; Leibniz by the mass times the square of the speed, a quantity he called vis viva, living force. She sided with Leibniz and publicised the experiments of Willem 's Gravesande, a Dutch physicist, who dropped balls into soft clay and found the dents grew with the square of the speed. In 1741 Jean-Jacques Dortous de Mairan, the Académie's perpetual secretary, answered her book with a printed letter accusing her of misreading him. Her printed reply took his charges one at a time, and Mairan withdrew. The quantity she defended survives in physics as kinetic energy.
Her exclusion was a subject she wrote about. In the preface to her translation of Bernard Mandeville's Fable of the Bees, a satire on vice and prosperity, she asked why in so many centuries no good tragedy, poem or book of physics had come from a woman, and argued for educating women. Her private essay on happiness ranks the love of study above every other passion, and says it matters more to women, who are shut out of every other road to glory.
In his first published work, printed in 1749, Kant took up the debate over living forces and her reply to Mairan; years later he wrote that a woman who disputes about mechanics might as well wear a beard. After her death, six days after the birth of her fourth child, she was remembered chiefly as Voltaire's companion. Two scholarly studies split over whether her thought was her own: Ira Wade's, in 1947, argued that it was, while William Barber's, in 1967, judged it derived from the men around her, Voltaire above all. Recent scholarship has largely taken Wade's side, and reads the Institutions as a work of philosophy in its own right.