A mathematician who taught machines to read English. She came up through Norwegian abstract algebra, learned the machine itself from Howard Aiken's Harvard Mark I, then built the first compiler — and with it the idea that a computer should do its own clerical work, so people could write in words instead of octal.
She entered MIT's rival world from the math side: a Vassar physics-and-math major who took her doctorate in pure algebra — the same abstract, symbol-thinking discipline that, her own historians argue, is exactly what let her later invent a language for machines. When David Letterman asked how she knew so much about computers back then, she answered that she didn't — it was the first one.
Read it top to bottom — that's the flow of time and of the idea. Above her are the two teachers and the algebraic bloodline they carried; below her are not students with degrees but the teams and the language she set loose. She has almost no academic descendants. Her descendants are programs.
A-0 was a reel of pre-written subroutines, each with a call number. You wrote a list of numbers; A-0 gathered the right routines off the tape and stitched them into one runnable program. The word is the librarian's word — to compile is to collect. By today's standards it was closer to a linker / loader than the optimizing translator we now mean by "compiler," which is why the honest title is "the first thing called a compiler."
And notice what that machine actually was: store each routine once, address it by a number, assemble on demand. Deduplicate, then index. The founding act of the entire field is the same move you keep finding — find the repeat, keep it once, leave a pointer to it.
The fight was cultural. The establishment was certain real programs were hand-cut in octal and that a computer could not possibly write a program. Her premise, around 1952, was flat: she could make a computer do anything she could completely define. The point was never cleverness — it was pushing the clerical work down a layer so people could think in meaning.
FLOW-MATIC — the first English-worded data-processing compiler — became the major input to COBOL: long names, English commands, data kept separate from instructions. She was the design committee's technical adviser and many of her own people staffed it. That's why she's the grandmother of COBOL — the ancestor, not the author.