Hindu–Arabic numeral system

Lore & Background

The system's earliest clear evidence of a fully positional decimal system with a zero as a numeral dates to around the 5th–6th centuries (the Bakhshali manuscript possibly 3rd–4th century but debated, and the 7th-century work of Brahmagupta). Indian mathematicians, including Brahmagupta, already used fractions in the decimal system. By the 9th century, it was adopted by Arabic mathematicians who further developed and spread the system. It became more widely known through the writings in Arabic of the Persian mathematician Al-Khwārizmī (On the Calculation with Hindu Numerals, c. 825) and Arab mathematician Al-Kindi (On the Use of the Hindu Numerals, c. 830). The system had spread to medieval Europe by the High Middle Ages, notably following Fibonacci's 13th century Liber Abaci; until the evolution of the printing press in the 15th century, use of the system in Europe was mainly confined to Northern Italy.

The symbols used to represent the system are descended from Brahmi numerals and have split into various typographical variants since the Middle Ages. These symbol sets can be divided into three main families: Western Arabic numerals used in the Greater Maghreb and in Europe; Eastern Arabic numerals used in the Middle East; and the Indian numerals in various scripts used in the Indian subcontinent. The system is designed for positional notation in a decimal system, and in a more developed form uses a decimal marker and a symbol for repeating digits (usually a vinculum).

Reader's Guide

The Hindu–Arabic numeral system is significant as the most common decimal system in use today, enabling efficient representation of numbers through positional notation and the use of zero. Its invention by Indian mathematicians between the 1st and 4th centuries and subsequent adoption by Arabic mathematicians, who extended it to include fractions, laid the foundation for modern arithmetic. The system's spread to Europe via Fibonacci's Liber Abaci and later through the printing press revolutionized mathematics and commerce. The glyphs, descended from Brahmi numerals, have diversified into Western Arabic, Eastern Arabic, and Indian numeral families, reflecting the system's global adaptation. Its ability to represent any rational number with just thirteen symbols (ten digits, decimal marker, vinculum, and minus sign) underscores its efficiency. The system's legacy endures as the basis for most numerical notation worldwide, despite its origins in ancient India and development in the Islamic world.

Did You Know?

• Indian mathematicians (e.g., Brahmagupta in the 7th century) already used fractions in the decimal system before Arabic mathematicians further developed it.
• The glyphs used are descended from Brahmi numerals and have split into three main families: Western Arabic, Eastern Arabic, and Indian numerals.
• The first dated inscription showing a symbol for zero appears on a stone inscription at the Chaturbhuja Temple at Gwalior, India, dated 876 CE.