Hindu-Arabic Numeral System

Timeline

1. c. 458–628Indian subcontinent · IndiaAncient Indian mathematicians gradually perfected a decimal place-value system including a zero symbol around Brahmagupta (Brahmasphutasiddhanta, 628); nine digit symbols (later joined by zero) could express numbers of any magnitude, laying the mathematical foundation of modern notation.
2. c. 820–825Baghdad, House of Wisdom · BaghdadAbbasid scholar Muhammad ibn Musa al-Khwarizmi wrote On the Calculation with Indian Numerals (Kitāb al-mukhtaṣar fī ḥisāb al-jabr wa-l-muqābala) at the House of Wisdom in Baghdad, systematically introducing the Indian decimal place-value system; its Latin translation later acquainted European scholars with the system, and the word 'algorithm' derives from his Latinized name.
3. 1202Pisa · TuscanyLeonardo Fibonacci, son of a Pisan merchant, learned Indo-Arabic numerals in North Africa and in 1202 wrote Liber Abaci, demonstrating the practical advantages of the new notation through numerous commercial problems, becoming the foundational work for promoting Indo-Arabic numerals in Europe.
4. 1451–1460Mainz · MainzWhile Gutenberg's movable-type workshop operated in Mainz (c. 1450–1460), printers cast lead type sets including Arabic numeral matrices. As printed matter circulated widely, numeral glyphs gradually unified across Europe, accelerating the mass spread of commercial arithmetic manuals (algorismus) and shifting numeral writing from diverse manuscript forms to standardized printed forms.
5. c. 1480–1550Major commercial cities of Europe · Western EuropeWith the mass publication of printed arithmetic textbooks (such as Luca Pacioli's Summa de arithmetica, 1494), Arabic numerals completely replaced Roman numerals as the mainstream tool for European commercial ledgers, scientific calculation, and official records, laying the written foundation for modern mathematics and the scientific revolution.