‘It’s not easy being the daughter of a celebrity mad genius deviant sex god,’ remarks Sydney Padua at the start of the wittiest, best-researched and most original tribute yet paid to the achievements of Lord Byron’s brilliant, tearaway and tragically short-lived child, Ada Lovelace.

Padua is a Canadian-born, London-based visual-effects artist whose annoyingly cryptic author’s biography states that she started drawing comics by accident ‘and is still trying to figure out how to stop’. On the strength of this astonishing debut, she needs to drop that idea of early retirement. What she’s done here, in a book that ought to be ordered in triplicate by every school in the land, is to give another nudge up the literary ladder to a genre that still – even after Sandman, Ghost World, Persepolis, Fun Home and Maus – produces the sneering dismissal from some that serious readers don’t stoop to ‘comic books’.

Lovelace, reared by scientists and mathematicians (Padua mischievously deletes ‘wolves’ with a thin line), first encountered Babbage while admiring a silver automaton in the enormous north London house where the prodigiously intelligent inventor was in the habit of entertaining – among others – Florence Nightingale, Charles Dickens, Alfred, Lord Tennyson and the Duke of Wellington. A world-class mathematician (he held the Lucasian Chair of Mathematics later occupied by Stephen Hawking), Babbage was perpetually trying to raise funds to build the awesomely elaborate calculating machines that he forever envisaged but never completed. A significant contributing cause to the delay was the fact that an exasperated British government finally cut off the funding upon which the inventor depended. Babbage, despite his brilliant mind, possessed a filthy temper, along with a penchant for shooting himself in the foot. (Neither flaw was mitigated by the ferocity with which he regularly denigrated his colleagues.) Efforts to obtain extended financial credit through such eminences as Lord Melbourne (Padua frankly trades that influential peer in for Wellington, because she finds Melbourne ‘totally not entertaining at all’) were wrecked by Babbage’s rudeness.

Enter Lovelace. A letter written by an American professor, which thanks to Padua’s extensive research is published here for the first time since 1867, records Babbage telling an admirer that only Lovelace possessed the ‘peculiar capability – higher he said than of any one he knew, to prepare … the descriptions connected with his calculating machine’. But Lovelace also possessed charm, charisma (she wasn’t Byron’s daughter for nothing), social status and access – through a long-suffering mother and a devoted husband – to large amounts of cash. Better still, she was forceful enough to threaten Babbage when he grew dilatory (which was frequently) and imaginative enough to look beyond her friend’s relatively prosaic machine-dreams to our own computer-driven age. Hardware and software is the analogy adopted here: Babbage’s rigid hardware found its perfect complement in the well-conceived software of mercurial, airy Ada, his self-styled fairy, patron and creative goad.

Padua grounds her adventurous tale in fact – there isn’t a detail that doesn’t sport at least one footnote, and sometimes, dizzyingly, enough of them to proliferate into tiny essays of their own – before taking off into a world of delectably improbable (but always meticulously referenced) hypotheses. Babbage, frog-mouthed and square of jaw, accompanies his dashingly uniformed colleague (Padua’s choice of a military look matches the swashbuckling personality evoked by Lovelace’s liveliest letters) on an illustrated series of madcap schemes. These fantastical frolics bring the intrepid pair into contact with everybody from Queen Victoria (not amused at all) to Brunel and Coleridge (Lovelace takes a time-jump back to morph into the Person from Porlock, a village close to her real-life marital home).

The grain of truth upon which each extravagant fantasy is founded is sometimes microscopic. Yes, Babbage and Lovelace did admire the plans for Brunel’s atmospheric railway; no, they absolutely did not have anything to do with the banking crises of their day (an excuse for Padua to draw upon those of our own times and to insert Tenniel’s wonderful illustration of a row of bare-kneed banker boys being scolded by the Old Lady of Threadneedle Street). Yes, Babbage did have a weakness for mad inventions (including a new telegraphic postal system). But no, he did not build a cocktail-serving robot. And Lovelace – who developed a fatal fondness for betting on horses – never relied upon her colleague’s rigid calculations for her speculative racing handicaps.

Pedants may grumble. Surely, Lovelace’s magnificent sixty-five-page addition to her translation of General Menabrea’s notes related not to the ‘Difference Engine’ (Babbage’s original, abandoned calculating machine), but to the yet more ambitious ‘Analytical Machine’? Padua notes the fact and breezily discards it: ‘honestly, Difference Engine just sounds way cooler.’ How ridiculous to suggest that George Eliot would have subjected her sole manuscript of Adam Bede to the trials of a punch-card computing machine – with obvious results. Improbable, maybe, but who’s to complain, when the adventure enables Padua to offer a dashing mini-life of Eliot, whisking her from a stint in the editor’s chair at the Westminster Review into the enigmas of John Searle’s 1980 conundrum of the Chinese Room (beautifully explained along the way). ‘Chinoiserie,’ sighs an unfazed Eliot. ‘How 1820!’

What Padua has created – enlisting Babbage and Lovelace as her questing detectives – is a rip-roaring dash through the labyrinthine world of Victorian science. Illustrations, notes and asides are employed to provide the mathematically befuddled reader with pellucid expositions of fiendishly complicated theories. Ingenious as a textbook, marvellous fun as inventive biography, The Thrilling Adventures also makes a convincing argument for accepting Lovelace’s frequently disputed role as the very first computer programmer. ‘I am able to manage anything almost,’ Lovelace once wrote (she was boasting about her mastery of an unruly horse). In Padua’s skilfully documented account, that ‘almost’ gradually recedes. The incredible imaginative leap of a young 19th-century woman into an invisible 21st-century future seems entirely within the capability of a dauntlessly unpredictable genius.