Before the word, there were the machines. Crash Course Computer Science #1: Early Computing — from the abacus to Herman Hollerith's punch cards.

A short answer, in under three minutes — BBC Ideas: Why algorithms are called algorithms.

Muhammad ibn Musa al-Khwarizmi, a 9th-century Persian scholar working in Baghdad's House of Wisdom, wrote a treatise on systematic methods for solving equations.

His name, Latinized centuries later as "algorithmi," became attached to the step-by-step methods he described — and eventually to the general concept itself.

(His other book's title gave us a second word: al-jabr — "algebra.")

Rewind two centuries. Long before Babbage, long before steam, the same ancient appetite for mechanizing the mind was already stirring — in the Baroque.

In 1642, at nineteen, Blaise Pascal built the Pascaline to help his father with tax calculations — a gear-driven adding machine, among the first of its kind ever built and sold.

A generation later, Gottfried Wilhelm Leibniz — one of the last true polymaths, equally at home in philosophy, law, and mathematics — went further still, designing the Stepped Reckoner: a machine that could multiply and divide, not merely add and subtract.

Leibniz wanted more than a calculator. He dreamed of a calculus ratiocinator — a universal symbolic method by which any dispute, of any kind, could in principle be settled by calculation alone: "Let us calculate."

Cogs and steam would eventually belong to Babbage's century. But the dream — that reasoning itself might be mechanized — is, properly speaking, Baroque.

Charles Babbage (1791–1871) — mathematician, philosopher, mechanical engineer, and by most accounts a thoroughly restless Victorian gentleman.

His Difference Engine was a mechanical calculator, designed to compute polynomial values automatically — and to print the results, removing human error from mathematical tables.

His far more ambitious Analytical Engine was something else entirely: a general-purpose, programmable computer — a century before electronics made one practical. It had a "mill" (processor), a "store" (memory), and was to be fed instructions on Jacquard-style punched cards.

He never finished building it. But he had, in effect, designed a computer.

Augusta Ada King, Countess of Lovelace (1815–1852), daughter of Lord Byron, was trained rigorously in mathematics from childhood — and became Babbage's closest intellectual collaborator.

In 1843, translating an Italian paper on the Analytical Engine, she added her own notes — three times longer than the original text. Among them: a step-by-step method for the Engine to compute Bernoulli numbers.

That method is widely considered the first published algorithm written specifically for a machine — making Lovelace, by most accounts, the first computer programmer, over a century before there was a computer to run it on.

She also saw further than Babbage himself: the Engine, she wrote, might one day manipulate not just numbers, but music and symbols of any kind. Others called her the Enchantress of Numbers.

One more figure worth knowing, even briefly: George Boole (1815–1864), who in 1854 published The Laws of Thought — reducing logical reasoning itself to a kind of algebra, with only two values: true and false.

Boolean algebra sat unused for decades as a philosophical curiosity. In the 20th century it became the literal switching logic inside every digital circuit ever built.

Babbage's engine, Lovelace's program, Boole's logic — three separate threads in the 1800s, waiting nearly a hundred years for electronics to braid them together. We'll pick that thread up again later in this course.

Today: a definition, a history, a name.

Next week: Alan and his Enigma — the story of Alan Turing, his machine(s), and his test(s).

We'll meet the Turing machine that finally gave "algorithm" a single, rigorous, universal meaning — and ask what happens when the body running one never gets tired, never gets bored, and never stops.