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Seduced by Logic: Émilie Du Châtelet, Mary Somerville and the Newtonian Revolution

Robyn Arianrhod
Oxford University Press
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The Basic Library List Committee recommends this book for acquisition by undergraduate mathematics libraries.

[Reviewed by
Underwood Dudley
, on

This book is about two women, Émilie du Châtelet (1706–1749) and Mary Somerville (1780–1872), who published translations and popularizations of mathematical and scientific works.

Du Châtelet was born into the minor aristocracy. As a child, she displayed interest and mathematics and science, encouraged by her father and resisted by her mother. She was married to the Marquis du Châtelet in 1725 and had three children with him. After the last was born in 1733, she took up scientific studies again, being tutored at one time or another by Pierre-Louis Maupertius (who measured a degree of latitude in Lapland showing, as Newton had predicted, that the earth was an oblate sphere; he also formulated the principle of least action), Alexis Clairault (who went with Maupertius to Lapland and later computed the orbit of Halley’s comet), and Samuel König (who was a student of Johann Bernoulli). In that day, as in this, it helped to have connections, and money.

She spent several years with Voltaire, helping him with his book on Newton, and she translated Newton’s Principia into French, though the translation was not published until ten years after her death. She also wrote a book of popular physics, and several other works.

She was far from being a nerd. She had an energetic sex life (in what I suppose was the fashion of the time and place, her husband did not mind), she gambled, and, as Lynn Osen says in Women in Mathematics, “she lived a life at a full tilt like a spirited healthy child”. She died from complications following childbirth. The baby, not her husband’s, lived only a year.

Somerville, as many women of the time (those who received any education, that is) was educated mostly at home, by tutors and by self-study. Her marriage in 1804 lasted only three years, her husband dying prematurely. After his death she had the time and means to study essentially full-time. Her second husband, William Somerville, whom she married in 1812, supported her in her interests. Her most important work was The Mechanism of the Heavens (1831), a translation, expansion, and simplification of Laplace’s Mécanique Céleste, a very difficult work. Nathaniel Bowditch, another translator of Laplace, said that whenever he read “Thus it plainly appears” in the book he was sure “that hours and perhaps days of hard study will allow me to discover how it plainly appears.” Her book was a great success and was used as a text for decades. She wrote other books, though none in mathematics, that were also successful. She received many honors, tangible (a government pension of £300 a year in 1835, equivalent to around $60,000 today) and intangible.

Here is an excerpt, written in 1870 when she was ninety years old, from her fascinating memoir, Personal Recollections, that illustrates her character:

I wrote to Mr. Spottiswoode, asking his advice as to the books that would be of use, and he sent me Serret’s “Cours d’Algèbre Supérieure,” Salmon’s “Higher Algebra,” and Tait on “Quaternions;” so now I got exactly what I wanted, and I am very busy for a few hours every morning; delighted to have an occupation so entirely to my mind. I thank God that my intellect is still unimpaired. I am grateful to Professor Peirce for giving me an opportunity of exercising it so agreeably. During the rest of the day I have recourse to Shakespeare, Dante, and more modern light reading, besides the newspapers, which always interested me much. I have resumed my habit of working, and can count the threads of a fine canvas without spectacles. I receive every one who comes to see me, and often have the pleasure of a visit from old friends very unexpectedly. In the evening I read a novel, but my tragic days are over; I prefer a cheerful conversational novel to the sentimental ones. I have recently been reading Walter Scott’s novels again, and enjoyed the broad Scotch in them. I play a few games at Bézique with one of my daughters, for honour and glory, and so our evenings pass pleasantly enough.

Robyn Arianrhod gives details of the life and works of du Châtelet and Somerville and also provides a good deal of the history of physics in their times. We do not appreciate, if we think of it at all, how difficult it is for new ideas to be accepted, and how long it takes. We say, “Of course gravity varies as the inverse square of distance, everyone knows that.” However, even well after Newton not everyone knew that. There’s another term needed, with a 1/r4 in it, some people said. They quieted down eventually, but time and effort was needed to show them the error of their ways. The author gives several such examples, which are good to have.

The book contains hardly any mathematics — the author finds it necessary to explain that v2 means v × v — though there is a 36-page appendix that contains equations and explanations for anyone who can recall elementary calculus. There are 43 pages of notes, sources, and bibliography, so this is a book of respectable scholarship.

The writing, though, is not dry and scholastic. The author sometimes goes a bit too far in the other direction for my taste — too many things are “cutting-edge”. She refers to her subjects as “Émilie” and “Mary”, a familiarity that they might not have permitted in the flesh.

The index is quite good. The indexer knew, as the author and her editors didn’t, that Jean le Rond’s name is “d’Alembert” and not “D’Alembert”.

The book will be of most interest, I think, to those interested in the place of women in mathematics and science, especially in the eighteenth and nineteenth centuries. But all readers will find new things in it and have their worlds correspondingly enlarged.

After teaching mathematics for a living in each of six different decades, Woody Dudley hung up his blackboard eraser for good in 2004. He now lives and reads books in Florida.

1 Madame Newton du Chatelet
2 Creating the theory of gravity: the Newtonian controversy
3 Learning mathematics and fighting for freedom
4 Emilie and Voltaire's Academy of Free Thought
5 Testing Newton: the'New Argonauts'
6 The danger in Newton: life, love and politics
7 The nature of light: Emilie takes on Newton
8 Searching for 'energy': Emilie discovers Leibniz
9 Mathematics and free will
10 The re-emergence of Madame Newton du Chatelet
11 Love letters to Saint-Lambert
12 Mourning Emilie
13 Mary Fairfax Somerville
14 The long road to fame
15 Mechanism of the Heavens
16 Mary's second book: popular science in the nineteenth century
17 Finding light waves: the 'Newtonian Revolution' comes of age
18 Mary Somerville: a fortunate life
Epilogue: Declaring a point of view