Émilie du Châtelet

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Émilie du Châtelet
Emilie Chatelet portrait by Latour.jpg
Born (1706-12-17)17 December 1706
Paris, France
Died 10 September 1749(1749-09-10) (aged 42)
Lunéville, France
Nationality French
Fields mathematics
Known for Advocacy of kinetic energy
Influences Isaac Newton, Gottfried Leibniz, Willem 's Gravesande

Gabrielle Émilie Le Tonnelier de Breteuil, marquise du Châtelet (French: [dy ʃɑtlɛ]; 17 December 1706  – 10 September 1749) was a French mathematician, physicist, and author during the Age of Enlightenment. Her most celebrated achievement is considered to be her translation and commentary on Isaac Newton's work Principia Mathematica. The translation, published posthumously in 1759, is still considered the standard French translation. Her commentary includes a profound contribution to Newtonian mechanics—the postulate of an additional conservation law for total energy, of which kinetic energy of motion is one element.

Voltaire, one of her lovers, declared in a letter to his friend King Frederick II of Prussia that du Châtelet was "a great man whose only fault was being a woman".[1][2] She was also romantically linked with two other influential philosophers of the period, Pierre-Louis Moreau de Maupertuis (1698–1759) and Julien Offray de La Mettrie (1709–1751).[3]


Significant places in the life of Émilie du Châtelet

Early life[edit]

Émilie du Châtelet was born on 17 December 1706 in Paris, the only girl amongst six children. Three brothers lived to adulthood: René-Alexandre (b. 1698), Charles-Auguste (b. 1701), and Elisabeth-Théodore (b. 1710). Her eldest brother, René-Alexandre, died in 1720, and the next brother, Charles-Auguste, died in 1731. However, her younger brother, Elisabeth-Théodore, lived to a successful old age, becoming an abbé and eventually a bishop. Two other brothers died very young.[4] Du Châtelet also had an illegitimate half-sister, Michelle, who was born of her father and Anne Bellinzani, an intelligent woman who was interested in astronomy and married to an important Parisian official.[5]

Her father was Louis Nicolas le Tonnelier de Breteuil, a member of the lesser nobility. At the time of du Châtelet's birth, her father held the position of the Principal Secretary and Introducer of Ambassadors to King Louis XIV. He held a weekly salon on Thursdays, to which well-respected writers and scientists were invited.

Early education[edit]

Du Châtelet's education has been the subject of much speculation, but nothing is known with certainty.[6]

Among their acquaintances was Fontenelle, the perpetual secretary of the French Académie des Sciences. Émilie's father Louis-Nicolas, recognizing her early brilliance, arranged for Fontenelle to visit and talk about astronomy with her when she was 10 years old.[1] Émilie's mother, Gabrielle-Anne de Froulay, was brought up in a convent, at the time the predominant educational institution available to French girls and women.[1] While some sources believe her mother did not approve of her intelligent daughter, or of her husband's encouragement of Émilie's intellectual curiosity,[1] there are also other indications that her mother not only approved of du Châtelet's early education, but actually encouraged her to vigorously question stated fact.[7]

In either case, such encouragement would have been seen as unusual for parents of their time and status. When she was small, her father arranged training for her in physical activities such as fencing and riding, and as she grew older, he brought tutors to the house for her.[1] As a result, by the age of twelve she was fluent in Latin, Italian, Greek and German; she was later to publish translations into French of Greek and Latin plays and philosophy. She received education in mathematics, literature, and science. Her mother Gabrielle-Anne was horrified at her progress and fought Louis-Nicolas at every step, once attempting to have Émilie sent to a convent.[7]

Émilie also liked to dance, was a passable performer on the harpsichord, sang opera, and was an amateur actress. As a teenager, short of money for books, she used her mathematical skills to devise highly successful strategies for gambling.[1]


On 12 June 1725, she married the Marquis Florent-Claude du Chastellet-Lomont.[8][note 1] Her marriage conferred the title of Marquise du Chastellet.[note 2] Like many marriages among the nobility, theirs was arranged. As a wedding gift, the husband was made governor of Semur-en-Auxois in Burgundy by his father; the recently married couple moved there at the end of September 1725. Du Châtelet was eighteen at the time, her husband thirty-four.


The Marquis Florent-Claude du Chastellet and Émilie du Châtelet had three children: Françoise Gabriel Pauline (born 30 June 1726), Louis Marie Florent (born 20 November 1727), and Victor-Esprit (born 11 April 1733).[9] Victor-Esprit died as a toddler in late summer 1734, likely the last Sunday in August.[10] In 1749 Émilie du Châtelet gave birth to Stanislas-Adélaïde du Châtelet (daughter of Jean François de Saint-Lambert). She was born on 4 September 1749. The infant died in Lunéville on 6 May 1751.[11]

Resumption of studies[edit]

In 1733, at the age of 26, du Châtelet resumed her mathematical studies. Initially, she was tutored in algebra and calculus by Moreau de Maupertuis, a member of the Academy of Sciences. Although mathematics was not his forte, Maupertuis had received a solid education from Johann Bernoulli, who also taught Leonhard Euler. By 1735, however, du Châtelet had turned for her mathematical training to Alexis Clairaut, a mathematical prodigy known best for Clairaut's equation and Clairaut's theorem.

Relationship with Voltaire[edit]

In the frontispiece to Voltaire's book on Newton's philosophy, du Châtelet appears as Voltaire's muse, reflecting Newton's heavenly insights down to Voltaire.

Du Châtelet and Voltaire may have met in her childhood at one of her father's salons; Voltaire himself dates their meeting to 1729, when he returned from his exile in London. However, their friendship began in earnest in May 1733, upon her re-entering society after the birth of her third child.[6]

Du Châtelet invited Voltaire to live in her country house at Cirey-sur-Blaise in Haute-Marne, northeastern France, and he became her long-time companion (under the eyes of her tolerant husband). There she studied physics and mathematics and published scientific articles and translations. To judge from Voltaire's letters to friends and their commentaries on each other's work, they lived together with great mutual liking and respect. As a literary rather than scientific person, Voltaire implicitly acknowledged her contributions to his 1738 Elements of the Philosophy of Newton, where the chapters on optics show strong similarities with her own Essai sur l'optique. But she was able to contribute further to the campaign by a laudatory review in the Journal des savants.[12]

While sharing a passion for science, they had scientific collaborations. They set up a laboratory in du Châtelet's home. In a healthy competition, they both entered the 1738 Paris Academy prize contest on the nature of fire, since Émilie disagreed with Voltaire's essay. Although neither of them won, both essays received honourable mention and were published.[13] She thus became the first woman to have a scientific paper published by the Academy.[14]

The chateau of Cirey

Final pregnancy and death[edit]

The chateau of Lunéville

In May 1748, du Châtelet began an affair with the poet Jean François de Saint-Lambert and became pregnant. In a letter to a friend, she confided her fears that she would not survive her pregnancy. On the night of 3 September 1749, she gave birth to a daughter, Stanislas-Adélaïde, but died a week later, at Lunéville, from a pulmonary embolism, at the age of 42. Her daughter died twenty months later.[15]

Scientific research and publications[edit]

Criticizing Locke and the debate on thinking matter[edit]

In her writings, Émilie du Châtelet criticizes John Locke’s philosophy. She emphasizes the necessity of the verification of knowledge through experience: Locke’s idea of the possibility of thinking matter is […] abstruse. Her critique on Locke originates in her Bernard de Mandeville commentary [on the Fable of the Bees]. She confronts us with her resolute statement in favor of universal principles which precondition human knowledge and action, and maintains that this kind of law is innate. […] Du Châtelet claims the necessity of a universal presupposition, because if there is no such beginning, all our knowledge is relative. In that way, Du Châtelet rejects John Locke’s aversion of innate ideas and a priori principles. She also reverses Locke’s negation of the principle of contradiction, which would constitute the basis of her methodic reflections in the Institutions. On the contrary, she affirms her arguments in favor of the necessity of a priori and universal principles. “two and two could then make as well 4 as 6” if a priori principles did not exist.

Pierre Louis Moreau de Maupertuis’ and Julien Offray de La Mettrie’s reference to Du Châtelet's deliberations on motion and free will, on thinking matter and numbers and on the way to do metaphysics indicate the importance of her reflections. She rebuts the claim to finding truth by using mathematical laws, […] and argues against Maupertuis.[16]

Heat and light[edit]

Dissertation Sur La Nature et La Propagation du feu, 1744

In 1737, Châtelet published a paper entitled Dissertation sur la nature et la propagation du feu, based upon her research into the science of fire, that predicted what is today known as infrared radiation and the nature of light.

Institutions de Physique[edit]

Her book Institutions de Physique (“Lessons in Physics”) appeared in 1740; it was presented as a review of new ideas in science and philosophy to be studied by her thirteen-year-old son, but it incorporated and sought to reconcile complex ideas from the leading thinkers of the time.

Forces Vives[edit]

Réponse de Madame la Marquise du Chastelet, 1741

In 1741, du Châtelet published a small book entitled Réponse de Madame la Marquise du Chastelet, a la lettre que M. de Mairan. Dortous de Mairan, secretary of the Academy of Sciences, had published a set of arguments addressed to her regarding the appropriate mathematical expression for forces vives. Du Châtelet presented a spirited point by point rebuttal of de Mairan's arguments, which caused him to withdraw from the controversy.[17]

Immanuel Kant’s first publication in 1747 'Gedanken zur wahren Schätzung der lebendigen Kräfte' focuses on Du Châtelet's pamphlet against the secretary of the French Academy of Sciences, Mairan. Beyond this, it is also an interesting fact that Kant’s opponent, Johann Augustus Eberhard, is accusing Kant of having taken ideas from Du Châtelet.[18]

Advocacy of kinetic energy[edit]

Although in the early 18th century the concepts of force and momentum had been long understood, the idea of energy, as a transferable currency between different systems, was still in its infancy and would not be fully resolved until well into the 19th Century. It is now accepted that the total mechanical momentum of a system is conserved and none is lost to friction. Simply put, there is no 'momentum friction' and momentum can not transfer between different forms, and particularly there is no potential momentum. Emmy Noether proved this to be true for all problems where the initial state is symmetric in generalized coordinates. Mechanical energy, kinetic and potential, may be lost to another form, but the total is conserved in time. The Châtelet contribution was the hypothesis of the conservation of total energy, as distinct from momentum. Inspired by the theories of Gottfried Leibniz, she repeated and publicized an experiment originally devised by Willem 's Gravesande in which balls were dropped from different heights into a sheet of soft clay. Each ball's kinetic energy - as indicated by the quantity of material displaced - was shown to be proportional to the square of the velocity. The deformation of the clay was found to be directly proportional to the height the balls were dropped from, equal to the initial potential energy. Earlier workers, such as Newton and Voltaire, had all believed that "energy" (so far as they understood the concept at all) was indistinct from momentum and therefore proportional to velocity. In classical physics the correct formula is E_k = \frac{1}{2} mv^2, where E_k is the kinetic energy of an object, m its mass and v its speed.) Energy must always have the same dimensions in any form, which is necessary to be able to relate it in different forms (kinetic, potential, heat…). Newton's work assumed the exact conservation of only mechanical momentum. A broad range of mechanical problems are soluble only if energy conservation is included. The collision and scattering of two point masses is one of them. Leonhard Euler and Joseph-Louis Lagrange established a more formal framework for mechanics using the results of du Châtelet.[19][20]

Translation and commentary on Newton's Principia[edit]

In 1749, the year of her death, she completed the work regarded as her outstanding achievement: her translation into French, with her commentary, of Newton’s Principia Mathematica, including her derivation of the notion of conservation of energy from its principles of mechanics. Published ten years after her death, today du Châtelet's translation of Principia Mathematica is still the standard translation of the work into French.

Other contributions[edit]

Development of financial derivatives[edit]

Much later in life, she once lost the huge sum of 84,000 francs—some of it borrowed—in one evening at the table at the court of Fontainebleau, to card cheats.[1][21] To quickly raise the money to pay back her debts, she devised an ingenious financing arrangement similar to modern derivatives, whereby she paid tax collectors a fairly low sum for the right to their future earnings (they were allowed to keep a portion of the taxes they collected for the King), and promised to pay the court gamblers part of these future earnings.[1]

Biblical scholarship[edit]

Du Châtelet wrote a critical analysis of the entire Bible. A synthesis of her remarks on the book of Genesis was published in English in 1967 by Ira O. Wade of Princeton in his book "Voltaire and Madame du Châtelet: An Essay on Intellectual Activity at Cirey" and a book of her complete notes was published in 2011, in the original French, edited and annotated by Bertram Eugene Schwarzbach.

Discourse on happiness[edit]

Du Châtelet also wrote a monograph, Discours sur le bonheur, on the nature of happiness, both in general and specialized to women.

Translation of the Fable of the Bees, and other works[edit]

Du Châtelet translated The Fable of the Bees in a free adaptation. She also wrote works on optics, rational linguistics, and the nature of free will.

Support of women's education[edit]

In her first independent work, the preface to her translation of the Fable of the Bees, du Châtelet argues strongly for women's education, particularly a strong secondary education as was available for young men in the French collèges. By denying women a good education, she argues, society prevents women from becoming eminent in the arts and sciences.[22]


Du Châtelet made a crucial scientific contribution in making Newton's historic work more accessible in a timely, accurate and insightful French translation, augmented by her own original concept of energy conservation. Her scientific role deserves more exposure in educational curricula.[19][20]

A main-belt minor planet and a crater on Venus have been named in her honor, and she is the subject of three plays: Legacy of Light by Karen Zacarías; Émilie: La Marquise Du Châtelet Defends Her Life Tonight by Lauren Gunderson and Urania: the Life of Émilie du Châtelet by Jyl Bonaguro. The opera Émilie of Kaija Saariaho is about the last moments of her life.[23]

Du Châtelet is often represented in portraits with mathematical iconography, such as holding a pair of dividers or a page of geometrical calculations. In the early nineteenth century, a French pamphlet of celebrated women (Femmes célèbres) introduced a possibly apocryphal story of du Châtelet's childhood.[24] According to this story, a servant fashioned a doll for her by dressing up wooden dividers as a doll; however, du Châtelet undressed the dividers and intuiting their purpose, made a circle with them.


  • Dissertation sur la nature et la propagation du feu (1st edition, 1739; 2nd edition, 1744)
  • Institutions de physique (1st edition, 1740; 2nd edition, 1742)
  • Principes mathématiques de la philosophie naturelle par feue Madame la Marquise du Châtelet (1st edition, 1756; 2nd edition, 1759)
  • Examen de la Genèse
  • Examen des Livres du Nouveau Testament
  • Discours sur le bonheur


  1. ^ The Lomont suffix indicates the branch of the du Chastellet family; another such branch was the du Chastellet-Clemont.
  2. ^ The spelling Châtelet (replacing the s by a circumflex over the a) was introduced by Voltaire, and has now become standard. (Andrew, Edward (2006). "Voltaire and his female protectors". Patrons of enlightenment. University of Toronto Press. p. 101. ISBN 978-0-8020-9064-5. )


  1. ^ a b c d e f g h Bodanis.
  2. ^ Hamel (1910: 370)
  3. ^ Jonathan I. Israel (Enlightenment Contested, 2006: 795–796)
  4. ^ Zinsser, pp. 19, 21, 22.
  5. ^ Zinsser, pp. 16–17; for a quite different account, see Bodanis, pp. 131–134.
  6. ^ a b Zinsser.
  7. ^ a b Zinsser (2006: 26–29)
  8. ^ Hamel (1910: 5).
  9. ^ Zinsser, pp. 39 and 58.
  10. ^ Zinsser, pp. 40 and 93.
  11. ^ D. W. Smith, "Nouveaux regards sur la brève rencontre entre Mme Du Châtelet et Saint-Lambert." In The Enterprise of Enlightenment. A Tribute to David Williams from his friends. Ed. Terry Pratt and David McCallam. Oxford, Berne, etc.: Peter Lang, 2004, p. 329-343. See also Anne Soprani, ed., Mme Du Châtelet, Lettres d'amour au marquis de Saint-Lambert, Paris, 1997.
  12. ^ Shank, J. B. (2009). "Voltaire". Stanford Encyclopedia of Philosophy. 
  13. ^ Detlefsen, Karen. "Émilie du Châtelet". Stanford Encyclopedia of Philosophy. Retrieved 2014-06-07. 
  14. ^ Arianrhod, Robyn (2012). Seduced by Logic. Oxford Univ. Press. p. 96. 
  15. ^ Zinsser (2006: 278)
  16. ^ Hagengruber (2011: 8-12,24,53,54)
  17. ^ Smeltzer, Ronald K. (2013). Extraordinary Women in Science & Medicine: Four Centuries of Achievement. The Grolier Club. 
  18. ^ Ruth Hagengruber: "Émilie du Châtelet between Leibniz and Newton: The Transformation of Metaphysics", in: Hagengruber, Ruth 2011: Émilie du Châtelet between Leibniz and Newton, Springer 1-59, p. 1 and 23, footnote 4 and 113.
  19. ^ a b Hagengruber (2011)
  20. ^ a b Arianrhod (2012)
  21. ^ Hamel (1910: 286)
  22. ^ Zinsser, pp. 25–26.
  23. ^ Libretto of Émilie
  24. ^ Zinsser, p. 13.


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