From al-Khwarizmi to the Genoa ledger: how did accounting change in the Middle Ages?

Try adding CCCLXXV to MDCCCXLVIII in Roman numerals. Hard? Now work out 1848 + 375: 2223. The biggest revolution in medieval accounting began with exactly this difference.

Key facts

1. Al-Khwarizmi and numerals. According to Britannica, al-Khwarizmi's main works introduced Hindu-Arabic numerals and the concepts of algebra into European mathematics. The nisba "al-Khwarizmi" in his name itself points to Khwarazm.
2. The word "algorithm". His work on arithmetic became known in Latin as "Algoritmi de numero Indorum". The Latin form of his name, "Algoritmi", gave us today's word "algorithm". Every accounting program works on the basis of algorithms.
3. Fibonacci and the merchants. Leonardo of Pisa (Fibonacci) completed his book "Liber Abaci" in 1202. The book showed how to apply the new numerals to commercial bookkeeping: exchanging currencies, calculating profit and interest.
4. Why does this matter? With positional numerals (0 to 9, with place value), adding, subtracting and multiplying in columns can be done on the paper itself. This makes bookkeeping much faster.
5. The first double-entry ledgers. The ledger of the Florentine Farolfi firm's branch in Provence (in the south of present-day France) for 1299–1300 was studied by the researcher G. A. Lee in 1977. According to his findings, the ledger has a debit and a credit for every entry, and a serious attempt was made to balance the accounts at the end of the year. For this reason the ledger is cited as one of the earliest known examples of double-entry bookkeeping.
6. Genoa, 1340. The 1340 ledger of the Commune of Genoa (Cartullarium massariorum) was long considered the oldest surviving double-entry ledger. Later research rejected this view: ledgers from an earlier period were also found in Tuscany.
7. Not overnight. In the late 14th and the 15th centuries double-entry bookkeeping spread widely in Italy, but even there not all merchants used it. The method spread gradually, through practice.

Example (prepared by the author, hypothetical)

Imagine an Italian merchant sold a bolt of woollen cloth for 40 florins in cash. With a single entry one could say "40 florins received". Double-entry bookkeeping, however, shows one transaction in two places:

The totals of the two sides are equal. If at the end of the month the total of the debits does not equal the total of the credits, the merchant knows at once that there is a mistake somewhere. Seven centuries later, every journal entry is still made with the same logic.