She is mainly known for having written a description of Charles Babbage's early mechanical general-purpose computer, the analytical engine. She is today appreciated as the "first programmer" since she was writing programs—that is, manipulating symbols according to rules—for a machine that Babbage had not yet built. She also foresaw the capability of computers to go beyond mere calculating or number-crunching while others, including Babbage himself, focused only on these capabilities.
On 16 January 1816, Annabella, at Byron's behest, left for her parents home at Kirby Mallory taking one-month-old Ada with her. Although English law gave fathers full custody of their children in cases of separation, Byron made no attempt to claim his parental rights. On 21 April, Byron signed the Deed of Separation, although very reluctantly, and left England for good a few days later.
Lovelace was often ill starting in her early childhood. At eight she experienced head aches that obscured her vision. Later in 1824, Byron died, but he did not have a relationship with his daughter, as her mother was the only significant parental figure in her life. In June 1829, she was paralyzed after a bout of the measles. She was subjected to continuous bed rest for nearly a year, which may have extended her period of disability. By 1831 she was able to walk with crutches. Throughout her illnesses, Lovelace continued her education. In 1832, she started to display her mathematical abilities.
Lovelace never met her younger half-sister, Allegra Byron, daughter of Lord Byron and Claire Clairmont, who died at the age of five in 1822. Lovelace did have some contact with Elizabeth Medora Leigh, the daughter of Byron's half-sister Augusta Leigh. However, Augusta purposely avoided Lovelace as much as possible when she was soon introduced at Court. By 1834, Lovelace was a regular at Court and started attending various events. She danced often and was able to charm many people and was described by most people as being dainty. However, John Hobhouse, Lord Byron's friend, was the exception and he described her as "a large, coarse-skinned young woman but with something of my friend's features, particularly the mouth". This description followed their meeting on 24 February 1834 in which Lovelace made it clear to Hobhouse that she did not like him, which was probably the influence of her mother that taught her to dislike all of her father's friends; this impression of each other was not to last, and they later would become friends.
Lovelace's interest in mathematics dominated her life even after her marriage. Her obsession with rooting out any of the insanity of which she accused Lord Byron was one of the reasons that her mother taught Lovelace mathematics at an early age. Lovelace was privately home schooled in mathematics and science by William Frend, William King and Mary Somerville . One of her later tutors was Augustus De Morgan.
She knew Mary Somerville, noted researcher and scientific author of the 19th century, who introduced her in turn to Charles Babbage on 5 June 1833. Other acquaintances were Sir David Brewster, Charles Wheatstone, Charles Dickens and Michael Faraday.
In 1841, Lovelace and Medora were told by Lovelace's mother that Byron was Medora Leigh's father. Lovelace, 27 February 1841, wrote to her mother: "I am not in the least astonished. In fact you merely confirm what I have for years and years felt scarcely a doubt about, but should have considered it most improper in me to hint to you that I in any way suspected". However, Lovelace did not blame the incestuous relationship on Byron, but instead on Augusta Leigh: "I fear she is more inherently wicked than he ever was". This did not stop Lovelace's mother from attempting to destroy her daughter's image of her father, but instead drove her to attacking Byron's image with greater intensity.
During a nine-month period in 1842–1843, Lovelace translated Italian mathematician Luigi Menabrea's memoir on Babbage's newest proposed machine, the Analytical Engine. With the article, she appended a set of notes. The notes are longer than the memoir itself and include (Section G) in complete detail a method for calculating Bernoulli numbers with the Engine, recognized by historians as the world's first computer program. Biographers debate the extent of her original contributions, with some holding that the programs were written by Babbage himself. Babbage wrote the following on the subject, in his Passages from the Life of a Philosopher (1846):
Lovelace's prose also acknowledged some possibilities of the machine which Babbage never published, such as speculating that "the Engine might compose elaborate and scientific pieces of music of any degree of complexity or extent.
She was buried next to the father she never knew at the Church of St. Mary Magdalene in Hucknall, Nottingham. Over one hundred years after her death, in 1953, Lovelace's notes on Babbage's Analytical Engine were republished after being forgotten. The engine has now been recognized as an early model for a computer and Lovelace's notes as a description of a computer and software.
Lovelace was one of the few people who fully understood Babbage's ideas and created a program for the Analytical Engine. Had the Analytical Engine ever actually been built, her program would have been able to calculate a sequence of Bernoulli numbers. Based on this work, Lovelace is now widely credited with being the first computer programmer.
Babbage was impressed by Lovelace's intellect and writing skills. He called her "The Enchantress of Numbers". In 1843 he wrote of her:
The level of impact of Lovelace on Babbage's engines is the subject of debate. The debate is difficult to resolve due to Charles Babbage's tendency not to acknowledge (either verbally or in writing) the influence of other people in his work.