Ada Lovelace
A century before a working computer existed, Lovelace read Charles Babbage's plans for the Analytical Engine and saw further than its inventor did. In her notes she wrote out a step by step method for the machine to compute Bernoulli numbers, the thing we now recognize as the first published program. She also drew the line the rest of this page keeps returning to: the machine has no pretensions to originate anything; it can only do what we know how to order it to perform.
She is first in this ledger because she was first to imagine the computer as an instrument for human ideas rather than a calculator. The vision came before the hardware. It usually does.