A real first, and a real vision. Note G is a genuine, complete algorithm (loop, variables, a computed table) published in 1843; and her insight that the engine could operate on symbols of any kind is the conceptual seed of general-purpose computing.
Shared, not solo. Babbage designed the engine and sketched earlier routines; the Notes grew from his work and their collaboration. Historians argue how much of Note G is hers. Her authorship of the Notes and the visionary leap, though, are firmly hers.
Ahead of any hardware. The Analytical Engine was never completed in her lifetime; her algorithm ran only on paper for a century. She also tempered the hype — the engine "has no pretensions to originate anything."
Note G's task: have the engine compute the Bernoulli numbers, a deep sequence of fractions from number theory, using only the engine's operations — add, subtract, multiply, divide — driven by a loop with stored variables. Step the engine forward and watch it produce each Bernoulli number exactly (as a true fraction, computed live by the recurrence Note G implements). This is a program: it has working storage, a repeated cycle, and a computed result.
Σ C(n+1,k)·Bₖ = 0, solving for the newest Bₙ — exactly the kind of repeated, variable-driven computation Note G lays out across its 25 operations. ⚑ Loops, stored variables, a computed table of results: by any modern definition, this is code — written in 1843, for a machine that did not yet exist."The Analytical Engine weaves algebraic patterns, just as the Jacquard-loom weaves flowers and leaves." — A. A. L., Note A, 1843
Babbage saw a calculator. Ada saw something none of her contemporaries did: that the engine's numbers could stand for anything — and so the machine could operate on symbols of any kind, by rule. Pick what the engine's operations might represent.
A complete machine procedure for the Bernoulli numbers, with loop and variables (1843). The first program published for a general computing machine.
The insight that a number-machine is really a symbol-machine — able, in principle, to do music, logic, language. The concept of general-purpose computing.
Gate kept on. The honest reckoning cuts both ways and lands firmly in her favour. Against the legend: she did not build the engine (Babbage did), she did not invent computing alone, and Babbage had sketched routines before her — so "the world's first programmer" is a contested honorific, and a few historians argue Babbage shaped Note G heavily. For the reality: the Notes are unquestionably hers (signed "A. A. L."), they run three times the length of the original paper, Note G is a genuine and correct algorithm, and the conceptual leap — that the machine operates on symbols, not numbers, and could therefore do far more than sums — is hers alone and is the single most prescient idea in the prehistory of the computer. She was also clear-eyed against hype, warning the engine "has no pretensions to originate anything" — a caution AI still needs. The woman: daughter of the poet Byron (whom she never knew), raised relentlessly on mathematics by a mother determined to suppress any inherited "poetic" madness, she fused the two into what she called "poetical science"; she died of cancer at 36, the same age as the father she never met. The machine was built in full only in our century — and her algorithm ran. ⚑ She is the face of this universe for a reason: the ancestry of the algorithm runs through her. [[alfred-tarski]] ← · next → Christine Ladd-Franklin.