For a computer programmer, or indeed anyone at all, Ada Lovelace had the oddest start in life. She was the only legitimate child of Lord Byron and hence should have been the female incarnation of Poetry and Passion. But instead of feeling things, Ada Lovelace preferred to work them out. Numbers, facts, proofs and rules – these were what she used to make herself feel safe, while her mad, bad Dad cavorted around Italy and Greece following his fancy.

As with all the best defences, Ada’s stern approach to life yielded great creative rewards. She was virtually unique amongst Victorian women; her mentor and model Mary Somerville was the obvious exception in working alongside some of the most interesting scientists of the day. In 1843 Ada wrote a paper about Charles Babbage’s Analytical Engine which incorporated the first published example of a computer program, a century before the emergence of the technology needed to run it. And just in case that sounds like an over-hopeful revision of women’s contribution to the history of science and technology, in 1980 the US Department of Defense named its programming language ‘Ada’, out of respect to Lady Lovelace.

The science bit in Ada’s life came from her mother, Annabella, who had been known in her youth as ‘The Princess of Parallelograms’. Annabella Milbanke was twenty years old when she first set eyes on Lord Byron – the closest thing the Regency had to a rock star ­– and decided that she was destined to be his Redeemer. Normally Byron wouldn’t have looked twice at the dumpy daughter of a north-country baronet, but in 1812 he was desperately trying to extricate himself from the exhausting and deranged business with Lady Caroline Lamb. For if Byron was the first celebrity, then Lamb was the first stalker, sending her idol strands of her pubic hair and, when that failed to do the trick, threatening to set fire to herself ­ or to him. In this storm, the prissy Princess of Parallelograms seemed, at least for the time being, like a safe haven.

The marriage, naturally, didn’t last. By late 1815, when Ada was born, Byron was only four months away from permanent exile. He was famously ghastly to Annabella even while she was pushing their daughter into the world. First he asked hopefully if the child was dead, and then when Ada arrived pink and screaming, declared ‘Oh what an implement of torture have I acquired in you!’ Annabella, having given up on being a Redeemer, now dedicated herself to becoming an Avenging Angel. For the rest of his short life, and long beyond it, she mounted a PR campaign to show the world just how awful Byron was, and so, by contrast, how wonderfully she had behaved in the circumstances.

A big part of that campaign involved making baby Ada into everything that her father was not. The girl was prescribed a diet of maths and science, designed to keep Imagination –­ that besetting sin of poets in general, and Romantics in particular –­ at bay. As a proto-Victorian bourgeoise, Annabella saw science as the hand-maiden of morality, taking the heat out of wild ideas. If Ada could be turned into a scientist, Annabella reckoned, then she would be kept safe from the sins of the father.

Initially Ada seemed to oblige. Instead of making up stories about her dolls, she spent her nursery days designing flying machines. But just as her father could never resist the grand and gorgeous gesture, so Ada’s aeroplanes were built on an heroic scale. Her favourite design included a body in the shape of a horse, with a steam engine inside connected to an immense pair of mechanical wings. The passenger would then mount this cranky Pegasus and flap away to a vivid new world.

Nothing Annabella did could curb her daughter’s rich, dark flow of Imagination. She instructed the adolescent Ada to read texts with titles like Useful Knowledge and the girl responded by becoming temporarily blind. She hired a tutor to teach her daughter the neat logic of shorthand, whereupon Ada immediately ran off with him. What Annabella missed, of course, was that it was precisely because Ada had inherited her father’s vision as well as her mother’s rationality that she developed the kind of intellect which could grasp the implications of Babbage’s work and take them to a new place entirely. Rather like one of the cross-breeds designed to suit the new conditions in English farming, Ada Byron Lovelace (she married a dull, useful peer in 1835) was the perfect creature for early Victorian science. With a neat symbolism beloved of biographers, she died in 1852, just at the point when the Great Exhibition was taking science and technology out of the studies and sheds of individual men, and occasionally women, and making them a public, corporate business.

Benjamin Woolley has written a magnificent book, incorporating the best methods of biography and narrative history. The Bride of Science has none of the text-bookishness of Longitude and its hundred followers, yet it knows its subject just as well. Indeed, in many ways it knows it better. For by choosing to write about a female scientist Woolley gives up his chance to write a straight-line story of individual endeavour and circumstances heroically overcome. As he is well aware, Ada Byron Lovelace did not create herself or her own story, but was as much a designed product as Babbage’s Analytic Engine. But unlike the Engine, she refused to tick over quietly and to infinity. And it is in the odd rhythms and missed beats of Ada’s life – the legacy of her mismatched parentage – that Woolley finds his extraordinary story.