Ada Lovelace (1815-1852) is generally credited with being the first computer programmer: specifically, after Charles Babbage wrote down the plans for his Analytical Engine (which Britannica calls "a general-purpose, fully program-controlled, automatic mechanical digital computer"), Lovelace wrote down a set of instructions that would allow the machine to calculate the "numbers of Bernoulli" (for discussion, see here and here). Suw Charman-Anders gives an overview of the episode and some surrounding historical controversy in "Ada Lovelace: A Simple Solution to a Lengthy Controversy" (Patterns, October, 9, 2020, volume 1, issue 7).
The historical controversy is whether Lovelace really truly deserves credit for the program, or whether her contemporaries who gave her credit for doing so were just being chivalrous to a fault (and perhaps being generous to the only daughter of Lord Byron and his wife). For example:
In a letter to Michael Faraday in 1843, Babbage referred to her as “that Enchantress who has thrown her magical spell around the most abstract of Sciences and has grasped it with a force which few masculine intellects (in our own country at least) could have exerted over it”. Sophia De Morgan, who had tutored the young Lovelace, and Michael Faraday himself were both impressed with her understanding of Babbage’s Analytical Engine. Augustus De Morgan, Sophia’s husband and another of Lovelace’s tutors, described her as having the potential, had she been a man, to become “an original mathematical investigator, perhaps of first-rate eminence” ...
Apparently, some modern writers have pored over what remains of the imprecisely dated correspondence between Lovelace and her tutor Augustus de Morgan, and decided that Lovelace didn't know enough math to have written the program. (Personally, I shudder to think of what judgments would be reached about my own capabilities if I was judged by the questions I sometimes felt the need to ask!) But Charman-Anders makes a persuasive case that the whole controversy is based in a mis-dating of Lovelace's mathematical education in general and her correspondence with de Morgan in particular; that is, critics of Lovelace were mistakenly treating early questions she asked her tutor as if they were questions asked several years later.
For me, the more interesting point that Charman-Anders makes is to emphasize that writing a computer program was its own conceptual breakthough. There had long been mechanical computing machines, where you plugged in a problem and it spit out an answer. But the breakthrough from Lovelace was to see that the Babbage's Analytical Engine could be viewed a set of rules for working out new results; indeed, Lovelace hypothesized that such a machine could write music based on a set of rules. Charman-Anders writes (quotations in first paragraph from Lovelace's 1843 notes, footnotes omitted):
Although Lovelace was the first person to publish a computer program, that wasn’t her most impressive accomplishment. Babbage had written snippets of programs before, and while Lovelace’s was more elaborate and more complete, her true breakthrough was recognizing that any machine capable of manipulating numbers could also manipulate symbols. Thus, she realized, the Analytical Engine had the capacity to calculate results that had not “been worked out by human head and hands first,” separating it from the “mere calculating machines” that came before, such as Babbage’s earlier Difference Engine. Such a machine could, for example, create music of “any degree of complexity or extent”, if only it were possible to reduce the “science of harmony and of musical composition” to a set of rules and variables that could be programmed into the machine. ...
While calculating devices have a long history, the idea that a machine might be able create music or graphics was contrary to all experience and expectation. Lovelace and her peers would have been familiar with the artifice of the automaton, clockwork machines which looked and acted like humans or animals but were driven by complex arrangements of cams and levers. And indeed, Babbage is said to have owned one called the Silver Lady, which could “bow and put up her eyeglass at intervals, as if to passing acquaintances”. But the Analytical Engine would have been in a category all its own.
One of the biggest leaps the human mind can make is extrapolating from current capabilities to future possibilities. The “art of the possible”, as it has been called, is an essential skill for innovators and entrepreneurs, but envisioning an entirely new class of machine is something for which few people have the capacity. Babbage’s design for the Analytical Engine was astounding, but none of his peers seemed to truly grasp its meaning. None except Lovelace.