Ada Lovelace is widely considered to be the first computer programmer. She worked with Charles Babbage on his proto-computer designs, and translated an academic paper about Babbage's Analytical Engine from French to English. In the process, she discovered errors in Babbage's design, fixed them, and added a pile of new commentary in a series of notes that were longer than the original paper itself.
Among Lovelace's contributions was "Note G." In it, she wrote an algorithm intended to be implemented by the machine. This algorithm is what many consider to be the first computer program. She wrote:
We will terminate these Notes by following up in detail the steps through which the engine could compute the Numbers of Bernoulli, this being (in the form in which we shall deduce it) a rather complicated example of its powers. ...
(And then it's formulae all the way down.)
If you've ever been curious about what Lovelace did, or why she was such a strong mathematician, let this six-minute mini-biography be your guide:
If you're curious about her translation of that paper, it's online.