By 1200, Hindu-Arabic numerals and positional notation, including the zero, had already been described in Latin mathematical treatises circulating among European scholars for centuries. Despite documented advantages over Roman numerals for calculation, adoption among the merchants who stood to benefit most from faster, more reliable arithmetic remained minimal — the treatises argued the system's abstract mathematical merits, not the everyday commercial problems merchants actually needed solved.

Leonardo of Pisa, later known as Fibonacci, was the son of a Pisan merchant and learned the Hindu-Arabic system firsthand while doing business in North Africa, where he observed its practical advantages directly rather than through scholarly description.

In 1202, Fibonacci published Liber Abaci, a roughly 600-page work that introduced Hindu-Arabic numerals and positional notation almost entirely through realistic trade word-problems: splitting profit shares between partners, converting between the roughly two dozen different currencies then circulating among Mediterranean city-states, and calculating interest and prices on goods like pepper and saffron — the exact daily calculations merchants already needed to do, worked in the new system rather than argued for in the abstract.

Fibonacci, a merchant's son, wrote Liber Abaci as trade word-problems—profit splits, currency conversions, pricing—so merchants saw it solve their own tasks.

Merchants saw their own problems solved in the new system, making the benefit tangible.

Worked examples required no translation from abstract principle to practical use.

The practical sections spread and were copied, driving adoption across Europe.

When a better method stalls, translate it into the audience's own daily tasks instead of arguing its abstract merits.

Liber Abaci was widely copied and imitated, and the practical numerical methods it demonstrated for merchants' own daily problems, rather than its more abstract mathematical sections, were what actually spread and were absorbed into the subsequent tradition of European 'abacus books' used to teach practical commercial arithmetic.

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The sources

  1. Fibonacci MacTutor History of Mathematics Archive, University of St Andrews · mathshistory.st-andrews.ac.uk
  2. Fibonacci's real mathematical legacy Nature (Springer Nature) · blogs.nature.com