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>She didn't write the "first program" but she was the first to understand what computers would be capable of doing

Or merely the first to express it? I'm pretty sure Babbage himself, as the inventor, understood well what computers would be capable of doing.

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He was focused on using his machines to efficiently generate mathematical tables. It was Ada who realized the potential of the analytical engine as a universal computer. She even wrote that given a good numeric representation for sound, one could program the analytical engine to generate algorithmic music based on mathematical rules. Babbage himself wrote examples of programs for the engine, but they were all very simple examples of numerical calculations that would be applicable for generating mathematical tables.

Well, the often inaccurate title of "first programmer", which clearly Charles Babbage was for at least his machine. Perhaps it would be better to describe Ada Lovelace as an early enthusiast / evangelist / adopter.

I'm not sure that inventors always understand the consequences of their inventions. Often, they are either focused on first-order capabilities and neglect the larger significance; or focused on visions of the future but unable to turn them into useful products in the short term.

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