A new method spreads not just because it is better, but because someone puts it in a readable, practical form and sells it to the people who need it. A single book full of worked business problems became the model for a whole series of copycat teaching manuals, and that genre is what made the new numbers stick.
A culture can possess a powerful technique for centuries and still fail to see what it could do, while an outsider who adopts it reaps the gains. The place-value number system began in India and was long known across the Muslim world, yet it was Western Europe that built its dominance in science, technology and commerce on it.
New knowledge often crosses between cultures through the people who move goods and money, not through scholars. A merchant's son, sent abroad with his father on customs business, picked up the foreign way of counting in the marketplace and brought it home to an audience of traders already waiting for it.
Writing numbers with ten digits and place value, instead of Roman numerals and an abacus board, let ordinary people buy and sell, convert currencies and keep accurate accounts themselves. That spread of everyday calculation fed large-scale international trade and laid the groundwork for later scientific advances.
An idea's success can erase its source: once cheaper versions spread it widely, people stop reading or crediting the work that started it. The original stayed handwritten while imitators printed their books, so its author was all but forgotten until a historian, following a passing mention, tracked down a surviving copy centuries later.