Ada Byron was a teenager when she met Cambridge mathematics professor Charles Babbage, who had invented the Difference Engine, a mechanical computer designed to produce mathematical tables automatically and error-free. Babbage never built the actual machine due to personal setbacks and financing difficulty. By 1834 he had moved on to design his Analytical Engine, the first general purpose computer, which used punch cards for input and output. This machine also lacked financing and was never built. (Babbage's Difference Engine was finally constructedin 1985–2002, and it worked.)
Babbage was impressed with the brilliant young woman, and they corresponded for years, discussing math and computing as he developed the Analytical Engine. In 1842, Babbage gave a lecture on the engine at the University of Turin. Luigi Menabrea, a mathematician (and future Italian prime minister), transcribed the lecture in French. Ada, now in her late 20s and known as Countess of Lovelace, was commissioned to translate the transcript into English. Lovelace added her own notes to the lecture, which ended up being three times as long as the actual transcript. It was published in 1843.
Lovelace's notes made it clear that she understood the Analytical Engine as well as Babbage himself, and furthermore, she understood how to make it do the things computers do. She suggested the data input that would program the machine to calculate Bernoulli numbers, which is now considered the first computer program. But more than that, Lovelace was a visionary: she understood that numbers could be used to represent more than just quantities, and a machine that could manipulate numbers could be made to manipulate any data represented by numbers. She predicted that machines like the Analytical Engine could be used to compose music, produce graphics, and be useful to science. Of course, all that came true—in another 100 years.
Babbage was so impressed with Lovelace's contributions, he dubbed her "The Enchantress of Numbers."