Ada Lovelace's notes appended to her translation of an Italian paper on Charles Babbage's unbuilt Analytical Engine included a method for calculating Bernoulli numbers using the machine, now widely cited as the first published computer program. She also speculated the engine could one day manipulate music and art, not merely numbers—an extraordinary conceptual leap a century before general-purpose computers existed.
Ada Lovelace, daughter of the poet Lord Byron, had been tutored rigorously in mathematics by her mother, partly out of fear that she might inherit her father's perceived instability. She met Charles Babbage as a teenager and became captivated by his designs for a mechanical calculating engine capable of performing any arithmetical operation given the right instructions.
When asked to translate a French-language description of the Analytical Engine written by Italian engineer Luigi Menabrea, Lovelace didn't merely translate; she added notes nearly three times longer than the original article. Note G contained a step-by-step algorithm for computing Bernoulli numbers, which historians of computing consider the first published program designed for a general-purpose computing machine, though Babbage's engine was never actually built in his lifetime.
More remarkably, Lovelace foresaw that such a machine could go beyond number-crunching entirely, writing that it might compose elaborate pieces of music if numbers could represent the pitch and harmony of sound. It took more than a century, and the arrival of electronic computers, for that insight to be borne out.