Ada Lovelace: A Simple Solution to a Lengthy Controversy

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The fact that the statement “Ada Lovelace was the first computer programmer” is controversial says a lot more about modern attitudes toward women in computing than it does Lovelace’s abilities or achievements. While recent reappraisals of Lovelace’s mathematical education and knowledge have gone some way toward setting the record straight, further work to recontextualize Lovelace’s achievements is still needed. And even more work will be required to repair the misconceptions about her that are still prevalent in popular discourse. A re-examination of many other women in STEM is essential if we are to shed biased and factually inaccurate portraits of historic figures, and thus the influence such portraits have on the perceived abilities of contemporary women.

In October 1843, a hundred years before the first modern computers, Augusta Ada King, Countess of Lovelace, published a set of instructions for a mechanical general-purpose computing machine in Taylor’s Scientific Memoirs. The machine was Charles Babbage’s Analytical Engine, and Lovelace’s instructions—which we would now call a computer program—would have calculated the Numbers of Bernoulli.

Over the winter of 1842–1843, Lovelace had translated a paper by Italian mathematician Luigi Menabrea describing the workings of the Analytical Engine. At Babbage’s suggestion, and in collaboration with him,¹ she added her own thoughts in a series of footnotes, which, together, tripled the length of the original.

Although Lovelace was the first person to publish a computer program, that wasn’t her most impressive accomplishment. Babbage had written snippets of programs before, and while Lovelace’s was more elaborate and more complete, her true breakthrough was recognizing that any machine capable of manipulating numbers could also manipulate symbols. Thus, she realized, the Analytical Engine had the capacity to calculate results that had not “been worked out by human head and hands first,” separating it from the “mere calculating machines” that came before, such as Babbage’s earlier Difference Engine. Such a machine could, for example, create music of “any degree of complexity or extent”, if only it were possible to reduce the “science of harmony and of musical composition” to a set of rules and variables that could be programmed into the machine.²

Lovelace’s peers held her in high regard. In a letter to Michael Faraday in 1843, Babbage referred to her 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”.³

Sophia De Morgan, who had tutored the young Lovelace, and Michael Faraday himself were both impressed with her understanding of Babbage’s Analytical Engine. Augustus De Morgan, Sophia’s husband and another of Lovelace’s tutors, described her as having the potential, had she been a man, to become “an original mathematical investigator, perhaps of first-rate eminence” (De Morgan, cited in Hollings et al.⁴).

But by the final quarter of the 20^th century, the knives were out. In 1985, Dorothy Stein wrote a biography that begins with a preface arguing that Lovelace’s reputation underwent a “process of mystification” based on Babbage’s “generous tribute” to her in his memoirs, and that, “In the manner of all mythology, elements have accreted to the story that have only tenuous connection with the original”. One of these elements, Stein argues, was Lovelace’s mathematical abilities, which she believed were, in reality, too poor for her to have been responsible for the Bernoulli program.⁵

Stein perhaps drew her inspiration from Doris Langley Moore (1977) or Anthony Hyman (1982), neither of whom were impressed by Lovelace. But she was soon joined by Bruce Collier (1990), Allan Bromley (1990), Doron Swade (2000), and Benjamin Woolley (2000) in her excoriation of Lovelace’s abilities. By the advent of the internet age, these criticisms of Lovelace had entered into canon and were seen by many as incontrovertible facts. Lovelace simply could not have written the Bernoulli program, it must have been Babbage, and thus the claims that Lovelace was the “first computer programmer” not only must not stand but are also an insult to the real pioneers of computing, particularly Babbage himself.

But the contention that Lovelace’s mathematical skills were lacking is based a misdating of letters and a misunderstanding of how her education unfolded.⁶

In the summer of 1840, Lovelace began what might be best described as an 18-month correspondence course in maths with one of the era’s foremost mathematicians and logicians, Augustus De Morgan. The two exchanged many letters, of which only 63 now survive. These letters were sometimes undated or misdated, making it hard for the cataloguers to put them into an accurate chronological order.

A core plank of Stein’s argument is that letters from Lovelace dated the 16^th and 27^th of November 1842 show that she was still “wrestling with an elementary problem in functional equations”, two years after beginning her studies with De Morgan and shortly before she translated Menabrea’s paper.⁵

“The impression given [by Stein] is thus of a young lady, whose mathematical skills have barely progressed over a period of seven years, including two years of intensive study with one of the foremost British mathematicians of the age—an image that hardly fits our picture of Lovelace as someone capable of finding derivatives from first principles by early 1841,” wrote Hollings, Martin, and Rice in their 2017 reanalysis of the letters.⁶

Hollings et al.’s paper examines not just the date evidence but the content of Lovelace’s and De Morgan’s letters and finds that Lovelace’s conversation about functional equations happened two years earlier than Stein assumes—in 1840. This shows that Lovelace had plenty of time to conquer the functional equation “will-o’-the-wisp” that had at one point frustrated her so much and to develop her calculus skills well beyond the elementary.

Hollings et al. also provide a more accurate picture of how Lovelace’s skills progressed over the course of her study with De Morgan, describing how she developed “good habits of study, a grounding in certain areas of higher mathematics, a critical attitude towards foundational principles, the ability to make perceptive mathematical observations, and exposure to ideas then current in British mathematical research”.⁶

They conclude that Lovelace “was capable of moments of great insight and understanding that belied her lack of formal training. Indeed, certain questions and remarks evince an intellectual acuity that has tantalised and beguiled scholars from De Morgan to the present day”.⁶

When Lovelace’s mathematical education is further recontextualized by a more detailed exploration of her childhood schooling, her achievements become more impressive rather than less.

Lady Anne Isabella Byron, Lovelace’s mother, was keen for her daughter to have a solid education, but as a girl, a formal schooling would be denied to young Ada. Instead, she studied whatever her mother, who was herself a proficient mathematician, or her tutor thought she ought. Although Lady Byron sought assistance and advice from her friends William Frend and Dr. William King, there was no carefully constructed syllabus designed to build her knowledge by introducing concepts in a logical order.

Instead, young Ada studied books like CW Pasley’s Practical Geometry, which “covered the basics of geometry, of the kind needed by soldiers, surveyors or engineers, entirely through practical instructions for making technical drawings, and stopping short of any explicit algebra or Euclidean geometry,” and Euclid’s then over 2,100-year-old Elements. Lovelace corresponded directly with King, asking him questions to clarify her understanding, but she reached the limits of his expertise in just seven weeks.⁴

Lovelace was soon introduced to Mary Somerville, who took a more modern and analytical approach to mathematics. Lovelace writes to Somerville of her studies in basic trigonometry and cubic and quadratic equations.⁴ Even with this additional assistance, she had significant gaps in her understanding when she came to study with De Morgan. She had to go back to basics, particularly to algebra, so that she could progress to calculus. But progress, she did.

Yet, there is more context missing from the modern conception of Lovelace’s abilities, significantly, the popular understanding in the Victorian era of the limits of a machine’s capabilities.

Lovelace’s vision of a general-purpose computing machine—and the impact it would have on fields as diverse as mathematics, music, and art—was extraordinary. It simply had no parallel. While we are used to tapping numbers into a calculator and getting a correct answer in return, in Lovelace’s time, mathematicians would have relied on tools such as slide rules and mathematical tables.

Indeed, it was the desire to produce perfect mathematical tables entirely free from the human error that had inspired Babbage to design first the Difference Engine and then the Analytical Engine. This wasn’t just a matter of perfectionism—these tables were used in navigation, and ships were wrecked and lives were lost because of mathematical mistakes.

While calculating devices have a long history, the idea that a machine might be able create music or graphics was contrary to all experience and expectation. Lovelace and her peers would have been familiar with the artifice of the automaton, clockwork machines which looked and acted like humans or animals but were driven by complex arrangements of cams and levers. And indeed, Babbage is said to have owned one called the Silver Lady, which could “bow and put up her eyeglass at intervals, as if to passing acquaintances”.⁷ But the Analytical Engine would have been in a category all its own.

One of the biggest leaps the human mind can make is extrapolating from current capabilities to future possibilities. The “art of the possible”, as it has been called, is an essential skill for innovators and entrepreneurs, but envisioning an entirely new class of machine is something for which few people have the capacity. Babbage’s design for the Analytical Engine was astounding, but none of his peers seemed to truly grasp its meaning. None except Lovelace.

When the threads of Lovelace’s education, gender, and culture—and all the limitations and barriers inherent in her experience—are woven together, an inspiring picture emerges. If the impact of the modern casting of Lovelace as a delusional charlatan were merely that there were a few misinformed people on the internet, it wouldn’t matter so much. But it’s not.

The importance of role models to girls and women in STEM cannot be overstated. The stories of famous women in these traditionally male-dominated fields prove that women are capable of great success and provide not just inspiration, but also the sense that it is possible for girls and women to belong in STEM.

The modern denigration of historic women and the undermining of their achievements tells quite the opposite story. It says that women are still not welcome in STEM, and that no matter how hard you work to overcome the barriers placed in your path, you will never be accorded the respect given to men. You will never be capable of becoming a great woman, on a par with history’s great men.

The scales need to be rebalanced. We need more scholarship exploring women’s contributions in STEM. Such work can be difficult, particularly with historic figures because women’s documents were often not seen as worthy of preservation. We have only a fraction of Lovelace’s documents, for example, and will have to learn to live with ambiguity and unanswered questions as a result. But even so, a simple analysis and re-dating of her letters has already paid dividends, refuting a decades-old accusation and providing a clearer understanding of Lovelace’s life and achievements. How many other women’s legacies could benefit from such attention?