Ada Lovelace met and corresponded with Charles Babbage on many occasions, including socially and in relation to Babbage's Difference Engine and Analytical Engine. They first met through their mutual friend Mary Somerville; Ada became fascinated with his Difference Engine and used her relationship with Somerville to visit him as often as she could. In later years, she became acquainted with Babbage’s Italian friend Fortunato Prandi, an associate of revolutionaries.
Babbage was impressed by Ada's intellect and writing skills. He called her "The Enchantress of Numbers". In 1843 he wrote of her:
Forget this world and all its troubles and if
possible its multitudinous Charlatans – every thing
in short but the Enchantress of Numbers.
During a nine-month period in 1842–43, Ada 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. Explaining the Analytical Engine’s function was a difficult task, as even other scientists did not really grasp the concept and the British establishment was uninterested in it. Ada’s notes had to even explain how the Engine differed from the original Difference Engine. The notes are longer than the memoir itself and include (Section G), in complete detail, a method for calculating a sequence of Bernoulli numbers with the Engine, which would have run correctly had the Analytical Engine been built (the first complete Babbage Engine was completed in London in 2002). Based on this work, Ada is now widely credited with being the first computer programmer and her method is recognised as the world's first computer program. Her work was well received at the time: Michael Faraday would describe himself as a fan of her writing.
Babbage and Ada had a minor falling out when the papers were published, when he tried to leave his own statement (a criticism of the government’s treatment of his Engine) as an unsigned preface – which would imply she’d written that too. When ‘’Taylor’s Scientific Memoirs’’ ruled that the statement should be signed, Babbage wrote to Ada asking her to withdraw the paper. This was the first she knew he was leaving it unsigned and she wrote back refusing to withdraw the paper. Historian Benjamin Woolley has theorised that “his actions suggested he had so enthusiastically sought Ada’s involvement, and so happily indulged her… because of her ‘celebrated name’”.
Their friendship would recover after this and they continued to correspond. In August 12, 1851, when she was dying of cancer, Ada wrote to him asking him to be her executor, though this letter did not give him the necessary legal authority.
Part of the terrace at Worthy Manor was known as "Philosopher's Walk", as it was there that Ada and Babbage were reputed to have walked discussing mathematical principles.
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