Al-Khwarizmi · Algebra
How do you find a number you don't know?
That time, that place
Baghdad under the Abbasids. Al-Khwarizmi worked at the House of Wisdom, and the problems he handled were not abstract: how an inheritance is divided among siblings, what tax is owed, how much land this parcel holds.
Why this question
Such problems mostly take one shape: there is an unknown quantity, and doing something to it makes it equal to something else. What is the quantity?
People solved each one by knack. But knacks differ from person to person, and a new problem stops you again. Al-Khwarizmi asked whether there could be a procedure that works no matter how the problem changes.
What was found
He sorted these problems into a few standard shapes and wrote out, in order, the steps that solve each.
Two moves are central. One is shifting a subtracted term to the other side to remove it — al-jabr in Arabic, which became algebra. The other is deleting what appears identically on both sides to simplify.
What matters is not the answer but the procedure. Anyone following the same steps arrives at the same answer. You need not understand it; you need only follow it. His name, carried into Latin, is our word algorithm.
Each problem was solved by its own knack
Al-jabr wa'l-muqabala, setting out solution steps by standard form
A thousand years later, Turing's question about what a machine cannot compute stands on exactly this notion of procedure