How Zero Reached Europe

[A] A symbol for nothing seems an obvious invention, and it was not. Roman numerals need no zero because each symbol carries its own value, and a system of that kind can record a number without ever asking what occupies an empty column. [B] The zero becomes necessary only once position determines value, which is why it appears in India alongside a place-value system rather than before one. [C]

Its arrival in Europe was slow, and the reasons for the delay were commercial rather than mathematical. Merchants could already calculate quickly with counters on a ruled board, and the board did in physical form the work that the written zero would later do on the page. [D] What changed the balance was the account book. A calculation on a board leaves nothing behind, while a calculation written in the new numerals stays on the page where a partner, an auditor or a court can check it. The advantage that carried the day was not speed but the fact that the working could be read afterwards by somebody who had not been there, and challenged if it was wrong.