Ada’s interest in applied science was further stimulated when she met one of Britain’s few noted female mathematicians and scientists, Mary Somerville. Somerville had just finished writing one of her great works, On the Connexion of the Physical Sciences, in which she tied together developments in astronomy, optics, electricity, chemistry, physics, botany, and geology.^I Emblematic of the time, it provided a unified sense of the extraordinary endeavors of discovery that were under way. She proclaimed in her opening sentence, “The progress of modern science, especially within the last five years, has been remarkable for a tendency to simplify the laws of nature and to unite detached branches by general principles.”

Somerville became a friend, teacher, inspiration, and mentor to Ada. She met with Ada regularly, sent her math books, devised problems for her to solve, and patiently explained the correct answers. She was also a good friend of Babbage’s, and during the fall of 1834 she and Ada would often visit his Saturday-evening salons. Somerville’s son, Woronzow Greig, aided Ada’s efforts to settle down by suggesting to one of his former classmates at Cambridge that she would make a suitable—or at least interesting—wife.

William King was socially prominent, financially secure, quietly intelligent, and as taciturn as Ada was excitable. Like her, he was a student of science, but his focus was more practical and less poetic: his primary interests were crop rotation theories and advances in livestock breeding techniques. He proposed marriage within a few weeks of meeting Ada, and she accepted. Her mother, with motives that only a psychiatrist could fathom, decided it was imperative to tell William about Ada’s attempted elopement with her tutor. Despite this news, William was willing to proceed with the wedding, which was held in July 1835. “Gracious God, who has so mercifully given you an opportunity of turning aside from the dangerous paths, has given you a friend and guardian,” Lady Byron wrote her daughter, adding that she should use this opportunity to “bid adieu” to all of her “peculiarities, caprices, and self-seeking.”¹⁹

The marriage was a match made in rational calculus. For Ada, it offered the chance to adopt a more steady and grounded life. More important, it allowed her to escape dependence on her domineering mother. For William, it meant having a fascinating, eccentric wife from a wealthy and famous family.

Lady Byron’s first cousin Viscount Melbourne (who had the misfortune of having been married to Lady Caroline Lamb, by then deceased) was the prime minister, and he arranged that, in Queen Victoria’s coronation list of honors, William would become the Earl of Lovelace. His wife thus became Ada, Countess of Lovelace. She is therefore properly referred to as Ada or Lady Lovelace, though she is now commonly known as Ada Lovelace.

That Christmas of 1835, Ada received from her mother the family’s life-size portrait of her father. Painted by Thomas Phillips, it showed Lord Byron in romantic profile, gazing at the horizon, dressed in traditional Albanian costume featuring a red velvet jacket, ceremonial sword, and headdress. For years it had hung over Ada’s grandparents’ mantelpiece, but it had been veiled by a green cloth from the day her parents had separated. Now she was trusted not only to see it but to possess it, along with his inkstand and pen.

Her mother did something even more surprising when the Lovelaces’ first child, a son, was born a few months later. Despite her disdain for her late husband’s memory, she agreed that Ada should name the boy Byron, which she did. The following year Ada had a daughter, whom she dutifully named Annabella, after her mother. Ada then came down with yet another mysterious malady, which kept her bedridden for months. She recovered well enough to have a third child, a son named Ralph, but her health remained fragile. She had digestive and respiratory problems that were compounded by being treated with laudanum, morphine, and other forms of opium, which led to mood swings and occasional delusions.

Ada was further unsettled by the eruption of a personal drama that was bizarre even by the standards of the Byron family. It involved Medora Leigh, the daughter of Byron’s half sister and occasional lover. According to widely accepted rumors, Medora was Byron’s daughter. She seemed determined to show that darkness ran in the family. She had an affair with a sister’s husband, then ran off with him to France and had two illegitimate children. In a fit of self-righteousness, Lady Byron went to France to rescue Medora, then revealed to Ada the story of her father’s incest.

This “most strange and dreadful history” did not seem to surprise Ada. “I am not in the least astonished,” she wrote her mother. “You merely confirm what I have for years and years felt scarcely a doubt about.”²⁰ Rather than being outraged, she seemed oddly energized by the news. She declared that she could relate to her father’s defiance of authority. Referring to his “misused genius,” she wrote to her mother, “If he has transmitted to me any portion of that genius, I would use it to bring out great truths and principles. I think he has bequeathed this task to me. I have this feeling strongly, and there is a pleasure attending it.”²¹

Once again Ada took up the study of math in order to settle herself, and she tried to convince Babbage to become her tutor. “I have a peculiar way of learning, and I think it must be a peculiar man to teach me successfully,” she wrote him. Whether due to her opiates or her breeding or both, she developed a somewhat outsize opinion of her own talents and began to describe herself as a genius. In her letter to Babbage, she wrote, “Do not reckon me conceited, . . . but I believe I have the power of going just as far as I like in such pursuits, and where there is so decided a taste, I should almost say a passion, as I have for them, I question if there is not always some portion of natural genius even.”²²

Babbage deflected Ada’s request, which was probably wise. It preserved their friendship for an even more important collaboration, and she was able to secure a first-rate math tutor instead: Augustus De Morgan, a patient gentleman who was a pioneer in the field of symbolic logic. He had propounded a concept that Ada would one day employ with great significance, which was that an algebraic equation could apply to things other than numbers. The relations among symbols (for example, that a + b = b + a) could be part of a logic that applied to things that were not numerical.

Ada was never the great mathematician that her canonizers claim, but she was an eager pupil, able to grasp most of the basic concepts of calculus, and with her artistic sensibility she liked to visualize the changing curves and trajectories that the equations were describing. De Morgan encouraged her to focus on the rules for working through equations, but she was more eager to discuss the underlying concepts. Likewise with geometry, she often asked for visual ways to picture problems, such as how the intersections of circles in a sphere divide it into various shapes.

Ada’s ability to appreciate the beauty of mathematics is a gift that eludes many people, including some who think of themselves as intellectual. She realized that math was a lovely language, one that describes the harmonies of the universe and can be poetic at times. Despite her mother’s efforts, she remained her father’s daughter, with a poetic sensibility that allowed her to view an equation as a brushstroke that painted an aspect of nature’s physical splendor, just as she could visualize the “wine-dark sea” or a woman who “walks in beauty, like the night.” But math’s appeal went even deeper; it was spiritual. Math “constitutes the language through which alone we can adequately express the great facts of the natural world,” she said, and it allows us to portray the “changes of mutual relationship” that unfold in creation. It is “the instrument through which the weak mind of man can most effectually read his Creator’s works.”