It might seem surprising that biographical portraits of ?milie du Ch?telet and Mary Somerville should feature together in the same book: after all, their historical backgrounds, social origins and personal lives could not have been more remote from one another. The Marquise du Ch?telet was a French aristocrat who lived in the first half of the 18th century, frequented the court and the most fashionable circles, and is better known for her scandalous liaisons with Voltaire and with the Marquis de Saint-Lambert than for her own intellectual achievements. Born near Edinburgh almost 90 years later, Mary Fairfax Somerville was born to a naval officer and raised in genteel poverty, and she went on to lead the quiet, industrious life of a respectable married woman.

But what Ch?telet and Somerville had in common was their passion for mathematics and their commitment to the popularisation of scientific doctrines. Ch?telet produced a translation of and commentary on Sir Isaac Newton¡¯s The Principia: Mathematical Principles of Natural Philosophy, making this groundbreaking work accessible to the French public for the first time; Somerville performed a similar service for English readers when she translated from the French and edited Pierre-Simon Laplace¡¯s Celestial Mechanics. The pair also shared bitter experience of the prejudices that, across space and time, have been entertained against those rare women who presumed to intrude into the traditionally male domain of scientific research: indeed, in this respect liberal, progressive 19th-century Scotland proved scarcely more advanced than ancien regime France.

Robyn Arianrhod, a mathematician, was inspired to write this book in part by the awareness that even today women are a minority (between one in four and one in five) of all researchers in mathematics and the natural sciences, a fact that suggests that prejudices are even more tenacious than the material and legal obstacles to women¡¯s education and academic careers. Although Seduced by Logic is by no means a feminist tract, the author clearly feels sympathy for her subjects¡¯ predicaments and is full of justifiable admiration for their talent, tenacity and courage.

One of the most striking aspects of Ch?telet¡¯s and Somerville¡¯s stories is how they managed to become proficient in a challenging domain such as mathematics without formal training. Both were educated at home: what this meant in practice was some casual reading, and possibly lessons in music, drawing and other ¡°feminine¡± pursuits. Ch?telet discovered philosophy and logic in her twenties via an epiphany that made her see herself as a ¡°thinking creature¡±. She found it astonishing that, in her time, women (Catherine II of Russia, for example) could rule an empire but were not allowed to think for themselves. Her intellectual ambitions exposed her to the ridicule that aristocratic society attached to the ¡°femme savante¡± caricatured by Moli¨¨re in his plays. When she tried to recruit a tutor to help her in her studies, she became the object of yet more malicious gossip, with her request seen as a pretext to find herself alone with a man.

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For her part, Somerville discovered mathematics as a teenager when she noticed the mathematical puzzles published in a magazine of sewing patterns and was intrigued by their mysterious symbols and formulae. As no one in her circle of acquaintances was interested in science, she encountered considerable difficulty simply obtaining books that might enable her to teach herself. Even much later, when after the death of her first husband she married a cousin who shared her passion for science, she drew criticism for cultivating odd intellectual fancies instead of devoting herself to her family. Unsurprisingly, both Ch?telet and Somerville became strong advocates of women¡¯s education. Killed tragically at 42 by a late pregnancy, Ch?telet did not live to see this issue brought to the fore of political debate during the French Revolution. But Somerville, who died in 1872 at the age of 91, saw the establishment of Girton College for women at the University of Cambridge and missed by only a few years the creation of the Oxford college named in her honour.

While Ch?telet and Somerville were attracted to mathematics by its logical rigour and the ¡°beauty¡± of its formulations, the field into which they had strayed was by no means a purely academic and abstract subject. Instead, it was a highly controversial ground, not just because of disagreements within the scientific community but because the doctrines set forth by Newton and his followers were seen as subversive by religious and political establishments. This revolutionary dimension of science was especially apparent in early 18th-century France. In the absence of any prospect of political change - as France had no elective institutions through which political dissent could be expressed - the opposition to absolute monarchy focused on issues such as religious toleration, civil rights and freedom of thought. The innovative potential of Newton¡¯s writings was readily apparent to Voltaire, who saw that the attempt to formulate a mathematical theory that gave unity and structure to the whole field of experimental science represented not just a scientific revolution but a challenge to a whole tradition of thought based on religious revelation and authority. Moreover, Newton was an English scientist, and England was associated in the mind of the French public with revolution, Protestantism and political freedom. As they sat in Ch?telet¡¯s chateau at Cirey-sur-Blaise, labouring away at the popularisation of Newton¡¯s work, Voltaire and ?milie found themselves on the front line of a dangerous battle against the established powers.

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Things were obviously different in Britain in Somerville¡¯s time, as the impact of the French Revolution had given more concrete targets to political and social reform. Causes such as parliamentary reform, popular education and the rights of women were espoused by political groups and scores of civic associations (Somerville, for her part, agitated for the abolition of the slave trade and for women¡¯s suffrage). This did not mean, however, that scientific debates had lost their subversive potential. Since 1789, Newton¡¯s school had given rise in France to a brilliant new generation of mathematicians and physicists. Somerville, who had met one of the most distinguished, Laplace, in Paris, was surprised and thrilled when in 18 she was asked to provide an English edition of Celestial Mechanics, his major work on astronomy. The request came from Lord Brougham, one of the founders of the Edinburgh Review and a Whig politician. As an advocate of reform, Brougham believed that Laplace¡¯s work should be made available to a wider public, to promote useful knowledge on a more democratic basis; from this perspective scientific progress was directly associated with the extension of political rights to the masses.

Seduced by Logic offers the lay reader an easy and agreeable introduction to the evolution of some crucial scientific debates in the 18th and 19th centuries (and for the mathematically minded, the formal details of the arguments can be found in the appendix). Although Arianrhod¡¯s decision to focus on Ch?telet¡¯s and Somerville¡¯s lives is not the only possible approach - one could argue the merits of a more comprehensive historical view - her biographical perspective makes the narrative especially lively and engaging. Although the author¡¯s emotional response to her subjects may seem on occasion a little naive, one cannot help but be captivated by her intellectual honesty and enthusiasm.

The Author

A former lecturer in mathematics and now adjunct research fellow at Monash University in Melbourne, Robyn Arianrhod recalls ¡°falling in love with mathematics as a language of proof, and with physics as a way of understanding the natural world¡± at high school.

¡°But at university, I became part of the Radical Science movement, which critiqued science¡¯s involvement with nuclear weapons (as well as) the capitalist growth model that relied on technology to fuel consumption regardless of environmental and social costs. I was more interested in helping to bring about social change than a career. I spent some years living off the grid in communities that focused on living simply.

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¡°Unexpectedly, that reignited my interest in science: I saw at first hand how important the appropriate use of technology is. Life is very hard without it. Living in the wilderness with its vast sky and brilliant stars also awakened an almost primeval curiosity about the Universe, which transformed itself into a study of general relativity (by candlelight).

¡°I became excited about the power of mathematics as a language of nature that enabled physicists to discover astounding things about our Universe; it lured me back to university to do a PhD in relativity.

¡°Around this time, I discovered self-taught women such as Ch?telet and Somerville, who inspired me in my own study,¡± says Arianrhod. ¡°At school, I lost confidence because I was told that girls could never be as good at maths and physics as boys, so I felt I understood what they had gone through. Because of my new passion for Einstein¡¯s theories, I also understood why they were so captivated by mathematics. All these years later, I wanted to write a book that celebrated not only these extraordinary women but also the science that excited them.¡±