Among her teachers in mathematics were Clairaut, Koenig, Maupertuis, Père Jaquier and Jean Bernouilli, the immediate predecessors of such distinguished mathematicians as Monge, Lagrange, d'Alembert and Laplace. At her Chateau of Cirey, where she and Voltaire spent many years together, she was visited by learned men from various parts of Europe. Among these was the Italian scholar, Francisco Algarotti, who was the author of a work entitled Newtonism for Women. And as Mme. du Châtelet was an ardent admirer of Newton, the author of the Principia soon became a strong bond of union between her and the brilliant Italian. She called the savants who frequented her château at Cirey the Émiliens and purposed writing memoirs to be entitled Emiliana—a design, however, which she was never able to execute.
The first work of importance from the pen of the Marquise was entitled Institutions de Physique. In it she gave an exposition of the philosophy of Leibnitz and dissertations on space, time and force. In the discussion of the last topic she seems to have anticipated some of the later conclusions of science respecting the nature of energy.
Her most noted achievement, however, was her translation of Newton's Principia, the first translation into French of this epoch-making work. To translate this masterpiece from its original Latin, it was necessary that the Marquise, in order to make it intelligible to others, should have a thorough understanding of it herself. To the translation she added a commentary, which shows that Mme. du Châtelet had a mathematical mind of undoubted power. She labored assiduously on this great undertaking for many years and completed it only shortly before her death; but it was not published until ten years after her demise.
In his Élogie Historique on the Marquise's translation of the Principia, Voltaire, in his usual flamboyant style, declares "Two wonders have been performed: one that Newton was able to write this work, the other that a woman could translate and explain it." In an effort to express in a single sentence all his admiration for his talented friend he does not hesitate to state: "Never was woman so learned as she, and never did anyone less deserve that people should say of her, 'She is a learned woman.'" Again he refers to her with characteristic Frenchiness as "a woman who has translated and explained Newton, in one word a very great man—en un mot un très grand homme."[122]
But, although the extent of her attainments and her ability as a mathematician were unquestionable, she fell far short of her great contemporary, Gaetana Agnesi, both in the depth and breadth of her scholarship and in her power of infinitesimal analysis. As to her moral character, she was infinitely inferior to the saintly savante of Milan. She was by inclination and profession an Epicurean and an avowed sensualist. In her little treatise, Réflexions sur le Bonheur—Reflections on Happiness—she unblushingly asserts "that we have nothing to do in this world except procure for ourselves agreeable sensations." Considering her profligate life, bordering at times on utter abandon, we are not surprised that one of her countrymen has characterized her as "Femme sans foi, sans mœurs, sans pudeur,"—a woman without faith, without morals, without shame.[123]
Anna Barbara Reinhardt of Winterthur in Switzerland was another woman of exceptional mathematical talent. She is remarkable for having extended and improved the solution of a difficult problem that specially engaged the attention of Maupertuis. According to so competent an authority as Jean Bernouilli, she was the superior, as a mathematician, of the Marquise de Châtelet.
Of a more original and profound mathematical mind was Sophie Germain, a countrywoman of the Marquise du Châtelet. Hers was the glory of being one of the founders of mathematical physics. A pupil of Lagrange and a co-worker with Biot, Legendre, Poisson and Lagrange, she has justly been called by De Prony "the Hypatia of the nineteenth century."
Her success, however, was not achieved without overcoming many and great difficulties. In the first place, she had to overcome the opposition of her family, who were decidedly averse to her studying mathematics. "Of what use," they asked, "was geometry to a girl?" But in trying to extinguish her ardor for mathematics they but augmented it. Alone and unaided she read every work on mathematics she could find. The study of this science had such a fascination for her that it became a passion. It occupied her mind day and night. Finally her parents, becoming alarmed about her health and resolved to force her to take the necessary repose, left her bedroom without fire or light, and even removed from it her clothing after she had gone to bed. She feigned to be resigned; but when all were asleep, she arose and, wrapping herself in quilts and blankets, she devoted herself to her favorite studies, even when the cold was so intense that the ink was frozen in her ink-horn. Not infrequently she was found in the morning chilled through, having been so engrossed in her studies that she was not aware of her condition. Before such a determined will, so extraordinary for one of her age, the family of the young Sophie had the wisdom to permit her to dispose of her time and genius according to her own pleasure. And they did well. Like the great geometer of Syracuse, Archimedes, who had ever been her inspiration in the study of mathematics, she would have died rather than abandon a problem which, for the time being, engaged her attention.