Ada Lovelace publishes the first algorithm for a machine

Ada Lovelace translated a paper on Charles Babbage's Analytical Engine and added her own notes, which included a method for the machine to calculate Bernoulli numbers. Many historians call it the first published computer program.

Historians debate how much of the method was hers and how much was Babbage's.

Context

Charles Wheatstone asked Lovelace to translate Luigi Menabrea's 1842 French article on the Engine, and Babbage suggested she add appendices. The paper appeared in Taylor's Scientific Memoirs in August 1843 under her initials, A.A.L. Of its 66 pages, 41 are her appendices.

Her notes were labelled A to G. Note G, the last, shows how the Engine would calculate Bernoulli numbers. Bernoulli numbers suit machine calculation because each is defined recursively, so earlier values help find the next. She chose a less simple method on purpose to show the Engine's powers.

She also speculated that the Engine could operate on other things besides number, such as musical notes, if their relations could be expressed in its notation.

The Bodleian authors note that Babbage and Lovelace corresponded intensely while revising the Note G tables. They argue the Note G table is better described as a trace of the machine's successive states than as a program, which would have been the punched card decks. The Analytical Engine itself was never completed.