Passionate Minds: the great Enlightenment love affair, by David Bodanis

A pretty pair of polymaths

Fifty years ago, Nancy Mitford softened the image of the leader of the French Enlightenment with a witty little book called Voltaire in Love. Mitford took pleasure in showing that the celebrated reformer was much more than a desiccated brainbox. He had a heart as well, and one day in 1733 he lost it to a brilliant, strong-minded and alluring young countess called Emilie du Châtelet.

Émilie already had two children and a husband, but was impatient with superstition and convention, and she had enough money to do what she liked. Apart from that, as Mitford put it, "she always had something of the whore", and after several celebrity love affairs she decided, at 27, to ally herself with Voltaire. He was 12 years older, and a political trouble-maker familiar with the inside of the Bastille, but also Europe's most glamorous and best-dressed poet, and one of the world's richest financiers.

Thoroughly in love, but bored with courtly life, Voltaire and Mme du Châtelet built a sumptuous love nest in a vast dilapidated château at Cirey, deep in rural Champagne. When that began to pall they threw themselves into another extravagant exercise in house-improvement in the middle of Paris. But both had wandering eyes and towering tempers, and they eventually tired of each other's tantrums and infidelities. Yet they went on living and travelling together, providing each other with a comprehensive and absolute love - a love that lasted until her sudden death (after giving birth to another man's child) at the age of 44.

Mitford had a good story and she told it well; but it was seriously incomplete. Readers of David Bodanis's bestselling work of popular science, E=mc2: a biography of the world's most famous equation, will know that Émilie was much more than a society beauty who died too young. She was also a serious mathematician whose work on the nature of energy - specifically, why simple velocity is not such an interesting quantity as velocity squared - marks one of the first steps on the path that led to Einstein and the triumphs of 20th-century physics.

Bodanis's new book is a combination of brain-teaser and bodice-ripper, designed to bring Voltaire's mistress out of the shadows at last. Perhaps he gushes too much about the lovers who could not "keep their hands off each other", adding little except patronising vulgarity to Nancy Mitford's well-judged love story, but he makes up for it with his busy descriptions of their turbulent attempts to lead a life of intellectual partnership. In 1737 Voltaire decided that he could be a great natural scientist as well as businessman, playwright and poet.

Taking advice from Mme du Châtelet, he instructed agents to sleuth among the leading experimenters, and bought himself masses of the finest scientific instruments. For several months he supervised a band of servants at Cirey as they heated huge blocks of metal and wood in furnaces and tried, without much success, to detect any gains or losses in weight. He then reported his results to a competition run by the French Academy of Sciences. But Voltaire's scintillating prose could not conceal the fact that his scientific efforts were theoretically aimless and experimentally empty: he came nowhere near winning a prize.

Voltaire had been too busy with his schemes to notice that when Émilie kept retreating to her boudoir, it was not in order to recline on her cushions and read a novel, but to sit at her desk and labour over a set of post-Newtonian problems, solving equations that took her beyond the accepted boundaries of the physics of the time. In the end she submitted her results in the same competition, and Voltaire had no choice but to recognise that her scientific prowess far exceeded his own. She too was passed over.

On the other hand, her efforts were noticed by the few fellow scientists who could understand them, and they would be built upon in later generations. Voltaire was shattered by her death in 1749. "I am bereft of half of myself," he wrote, and though he lived on for almost 30 years, a chill had entered his heart.

Jonathan Rée's 'I See a Voice' is published by HarperPerennial