Free Press £20 pp352

René Descartes has always been one of the more appealing philosophers, not least because he was so human, quarrelsome and frequently bone idle. As AC Grayling drily puts it, “He lived at his own pace always, which was by no means a hectic one.” He worked best in a room that was nice and warm, appreciated 10 hours’ sleep a night, and loathed getting up in the morning. One anecdote tells of a friend coming to see him not long before midday and finding him still abed, gazing ceilingwards. The friend anxiously asked if he was ill. “No,” replied the great philosopher. “I’m working.”

Grayling’s account of the man and the thinker, which aims “to engage in conversation with non-specialists”, navigates a careful path between the colourfully anecdotal and the challengingly scholarly, and succeeds admirably in producing an elegant, subtle and historically informed portrait of one of the founding fathers of modernity.

Although a supreme figure in rationalism and early science, Descartes was born in 1596, within living memory of the hideous Massacre of Saint Bartholomew’s Day, and lived through the tumult and horror of the Thirty Years’ war. But we shouldn’t mistake his rationalism for a reaction against religious faction and extremism. He was a devout Catholic all his life, and indeed Grayling makes an intriguing case for his being a Jesuit spy during his early life. This is not so far-fetched as it sounds. Christopher Marlowe was famously involved in spying as well as writing plays, and even comfortable, bourgeois Peter Paul Rubens, Grayling reminds us, doubled as a Habsburg agent at home in Antwerp. The spy-hypothesis might also explain Descartes’s sudden, surprising move to Holland in 1628.

“Glimpses of Descartes as family man are few but tantalising,” Grayling admits. He did get a Dutch maidservant named Helena Jans pregnant, and looked after her and her daughter Francine thereafter, although there is no evidence that they lived with him. Francine died when she was five, and Descartes wrote in a letter, with heartbreaking simplicity, that he was “not the kind of philosopher who thinks that men should not cry”. One of Descartes’s friends suggested that the begetting of Francine was the only time in his life that Descartes behaved “contrary to the honour of his celibacy”, ie had sex; Grayling finds this “humanly improbable”. I don’t know. Newton and Kant both died virgins.

Although remembered today as a philosopher, Descartes was also at the forefront of mathematics, geometry, and gave us the first satisfactory explanation of the rainbow. Less appealingly, he was a keen vivisector, although by the standards of his times whipping a dog while a violin was played, one of his more peculiar experiments, might count as pretty mild stuff. He could be cruelly cutting about philosophical and scientific rivals, dismissing Hobbes as “contemptible” , the work of de Fermat (of Last Theorem fame) as “dung”, and the letters of a certain Beaugrand as fit only for use as lavatory paper.

Meanwhile, Descartes himself left us one of the key axioms in western philosophy — “'I think therefore I am” — and the Method of Doubt by which he arrived at it, a method that has underpinned science ever since. Accept nothing from tradition or revelation: experiment, test, question, and only believe something when it is proven to be true.

In his early fifties, he was invited to Sweden to teach the brilliant Queen Christina. There, in the depths of the Scandinavian winter, he had to stand in her presence, hatless, from as early as 5am, and teach her philosophy. Within two weeks the little Frenchman, 5ft 1in in his stockinged feet, had fallen ill; within a month he was dead of pneumonia.

A useful appendix to this excellent intellectual biography gives readers an overview of other biographies of great philosophers that Grayling can recommend: Rudiger Safranski on Nietzsche, Ray Monk and Brian McGuinness on young Wittgenstein, and so on. For its lucidity, elegance and sweet reasonableness, Grayling on Descartes fully deserves to join the list.

Available at the Sunday Times Books First price of £18 on 0870 165 8585

Times Recommends

• The 100 Best Books of the Decade
• The Times picks the 50 best paperbacks of 2009
• The conversation: James Ellroy