A remarkable French natural philosopher and mathematician who lived in the early eighteenth century, Émilie Du Châtalet, is generally remembered for her translation of Isaac Newton’s *Principia Mathematica*, but her work was much more than a simple translation: she added an extensive commentary in which she included new developments in mechanics, the most important being her formulation of the principle of conservation of energy [TM223 or search for “thatsmaths” at irishtimes.com].

Du Châtalet was born in 1706 in Paris. Her father was an official in the Court of Louis XIV in Versailles. She showed signs of brilliance from an early age, mastering several languages and taking a keen interest in mathematics. Aged just 18, she married the Marquis of Châtalet, with whom she had three children.

Aged 26, she resumed her mathematical studies, being tutored by Pierre-Louis Moreau de Maupertuis, who introduced her to the work of Newton, and later by Alexis Claude Clairaut, also an avid Newtonian. Both of these men had been students of Johann Bernoulli and both were active in the expedition to Lapland to confirm Newton’s theory that the Earth is an oblate spheroid, flattened at the poles.

There were regular mathematical discussions at the Café Gradot in Paris at that time, but they were not open to women. To gain access to these, Du Châtalet dressed in men’s clothes, much to the amusement of Maupertuis. She also had frequent contact with leading international mathematicians, including Leonhard Euler and Johann Bernoulli. Frederick the Great of Prussia was a keen admirer of Du Châtalet. He corresponded regularly with her and introduced her to the work of Leibniz.

In 1733, Du Châtalet became intimate with the renowned writer, historian, and philosopher, Voltaire. The two of them lived together for many years at her house in Haute Marne, east of Paris, collaborating closely on scientific and philosophical projects, each providing great intellectual stimulus to the other.

**Energy Conservation**

** **Newton argued that momentum conservation was the crucial principle of mechanics, and he assumed it in his work. A broad range of problems in mechanics require conservation of energy for their solution, but the concept of energy was not well formulated or clearly defined at that stage. Du Châtalet derived a principle of energy conservation from the fundamental principles of Newton’s mechanics. Momentum is proportional to velocity, whereas kinetic energy varies with the square of velocity.

The focus on energy was central in the later development of mechanics by Lagrange, Hamilton and others. Du Châtalet’s translation of, and commentary on the *Principia* is regarded as her greatest scientific achievement and is still the standard reference in French on Newtonian mechanics.

As a teenager, Du Châtalet resorted to gambling to acquire funds for books and used her mathematical skills to devise gambling strategies. She had a weakness for gambling and later, after a severe loss in a card game, she developed a clever arrangement, very similar a modern financial derivative, to clear her debts. She was a strong supporter of the education of women. She wrote several philosophical essays, an extensive critique of the Bible, and a monograph, *A Discourse on Happiness*.

In 1749, Émilie Du Châtalet died shortly after giving birth to a child fathered by the poet Jean-François de Saint-Lambert. She was just 42 years old. In his Preface to her commentary on the *Principia*, published seven years after her death, Voltaire wrote that “No woman was ever more learned than she was”.

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**That’s Maths II: A Ton of Wonders**

**by Peter Lynch**

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