There is to me something ineffably grand, romantic and ambitious about the idea of a seven-metre diameter, 150-metre-long machine eating its way slowly under London to make the tunnel for the vast Crossrail project that will unclog the city’s tubes and whizz passengers from east to west from 2018. So when I saw a competition to name one of these engines, Ada seemed an appropriate handle, for Ada, Countess of Lovelace was one of the grandest, most romantic and most intellectually ambitious women of the 19th century. Boris Johnson, the Mayor of London, apparently agreed; so Ada, in her latest incarnation, has spent the past two years munching her way through the subsoil of southern England, and has emerged just in time for the 200th anniversary of her birth.

It isn’t just tunnel-boring machines that are named after the remarkable woman some say was the world’s first computer programmer. There are less eccentric memorials, too: a computer language, a scientific medal, a day, an international conference, a film, a building, a blog and so on. Ada has garnered the attention not just because of her mathematical achievements but because she is a great story. When she was a month old her mother, Anne, wife of George Gordon, Lord Byron, had had enough of her husband’s profligacy (he disposed of her vast inheritance within a year), promiscuity (he had an affair with his half-sister Augusta among many, many others) and general horridness (he would send his wife up to bed while he dallied with Augusta downstairs), and stole away from the marital home with her baby. Neither mother nor daughter ever saw the mad and bad poet-peer again, but when he died at the age of 36 he was such a celebrity that Ada was, royalty aside, London’s most famous child.

Anne Byron was worried that her daughter’s mind would be tainted by what she regarded as an excess of imagination in the Byron family. In order to keep Ada’s intellect on the straight and narrow, she hired a tutor at the generous salary of £300 a year to teach her maths. Ada, who was already planning to build a flying machine, took to the discipline with enthusiasm initially for instrumental reasons – “my wish is to make myself well acquainted with Astronomy, Optics, & c; but I find that I cannot study these satisfactorily for want of a thorough acquaintance with the elementary parts of Mathematics” — but found herself increasingly entranced by its beauty.

When Ada was 17 she met the 41-year-old Charles Babbage at a party. She was impressed by his growing reputation as a brilliant scientist; he by her sharp intellect and interest in his subject. Babbage and Ada started to correspond. There was perhaps a hint of romance in the air, but the dominating, snobbish Anne married her daughter off to the Earl of Lovelace, and Ada’s relationship with Babbage turned into an intense and affectionate collaboration. Babbage was clearly enthralled by Ada: he described her to the scientist Michael Faraday as “that Enchantress who has thrown her magical spell around the most abstract of Sciences and has grasped it with a force which few masculine intellects (in our own country at least) could have exerted over it”.

Babbage pioneered computing a century before it happened. He half-built the Difference Engine, a machine for doing complex calculations. He designed the even more ambitious Analytical Engine, to be based on the Jacquard loom — a machine which was operated by instructions written on punched cards and made far more elaborately patterned cloth far more efficiently than human weavers ever could. The Analytical Engine was never built, but Federico Menabrea, an Italian mathematician (and later prime minister), wrote a paper on the design. Ada translated the paper and appended notes that were three times as long as the original.

There are two remarkable aspects to Ada’s notes. One is her visionary understanding of the engine’s potential: “a new, vast and powerful language”, she wrote, “is developed for the future use of analysis, in which to wield its truths so that these may become of more speedy and accurate practical application for the purposes of mankind than the means hitherto in our possession have rendered possible.” She understood the breadth of its implications: “Supposing, for instance, that the fundamental relations of pitched sounds in the science of harmony and of musical composition were susceptible of such expression and adaptations, the engine might compose elaborate and scientific pieces of music of any degree of complexity or extent.” The other startling aspect of this work is Note G, which concerns the creation of a sequence called the Bernoulli numbers, and contains a table showing the punch-card flow for these numbers. This is regarded as the first computer algorithm – hence the claim that Ada was the first computer programmer.

Whether she really was or not is a matter of some dispute. Note G is written in her hand, but Babbage may have been responsible for many or most of the numbers in it. Their correspondence is unclear on this point. He was certainly responsible for some, because he wrote in his memoirs that when he sent them to her, she “detected a grave mistake which I had made”. So if she wasn’t the first computer programmer, she was certainly the first debugger.

Doubts about the extent of her contribution along with Ada’s celebrity status have led to claims that she has been over-promoted. “She was”, wrote Bruce Collier, one of Babbage’s biographers, “a manic-depressive with the most amazing delusions about her own talents, and a rather shallow understanding of both Charles Babbage and the Analytical Engine…I guess someone has to be the most overrated figure in the history of computing.” But the world will continue to give Ada the benefit of the doubt – because it needs her. Computing is short of female heroines, and historical role models demonstrate that even in the days when it was hard for clever women to use their brains to great effect, there were female scientists passionate enough to overcome the barriers society placed in their way.

Yet about her contribution to one aspect of the digital revolution there is no doubt. She was — blood will out — one of the best writers about computing ever. “The Analytic Engine”, she wrote, “weaves algebraic patterns, just as the Jacquard loom weaves flowers and leaves.” There are irresistible echoes of the muscular passion of her father’s poetry: “this brain of mine is something more than merely mortal…before ten years are over, the Devil’s in it if I have not sucked out some of the life-blood from the mysteries of this universe.”■