Technology & Medicine › Medieval › Islamic Golden Age science and medicine
Hindu–Arabic numerals and zero
zero by 628 (Brahmagupta); al-Khwarizmi c. 825; Europe 1202· Idea, religion or movement· Communication & computing
Mostly agreedGood evidence; some details, dates or numbers uncertain.
The ten-digit, place-value number system with zero, created in India and carried to Europe through Arabic-language scholarship.
See it on the Technology & Medicine map →How it works
Indian mathematicians wrote numbers with nine digits whose value depends on position, plus a symbol for an empty place. In 628 Brahmagupta gave rules for zero as a number in its own right. Around 825 al-Khwarizmi, in Baghdad, wrote a manual on Indian reckoning; his Latinized name gave us the word 'algorithm'. Fibonacci's Liber Abaci (1202) promoted the digits to Italian merchants, but Roman numerals lingered in many accounts until the 1500s.
Why it mattered
Written arithmetic — long multiplication, division, decimals — became fast on paper, enabling bookkeeping, banking, navigation tables and later algebra and calculus.
Think of it like
Like columns on a rent roll: the same digit means $5, $50 or $500 depending on which column it sits in.
How we know
Indian inscriptions such as Gwalior (876), Brahmagupta's text, the Bakhshali manuscript, Latin translations of al-Khwarizmi, and Fibonacci's book.
Still unknown or debated
When the zero symbol first appeared is debated; contested radiocarbon dates on the Bakhshali manuscript range from the 200s to the 900s AD.
Connections (3)
▸House of Wisdom and the translation movement spread Hindu–Arabic numerals and zeroWell documented
The connection
Indian astronomy texts reached Baghdad around 770. Al-Khwarizmi, a scholar at the House of Wisdom, wrote a book around 825 explaining Indian place-value numbers and zero. Translated into Latin in the 1100s, it carried the system to Europe, and his name, Latinized as Algoritmi, became 'algorithm'.
When and how
Baghdad, about 770–825; Latin translations made in Spain in the 1100s.
How we know
Al-Khwarizmi's Arabic original is lost, but Latin versions survive, opening 'Dixit Algorizmi' ('Thus spoke al-Khwarizmi').
Debates and open questions
The digit shapes changed on the way; Western 'Arabic' numerals descend from forms used in North Africa and Spain, not Baghdad's Eastern Arabic digits.
▸Hindu–Arabic numerals and zero made possible Mechanical calculators (Schickard, Pascal, Leibniz)Mostly agreed
The connection
Mechanical calculators turn written arithmetic into gears: one wheel for each decimal place, 0 to 9, with automatic carrying. That design copies the place-value system with zero that came from India through the Arab world. Roman numerals, which lack place value, would have made such a machine far harder to design.
When and how
Indian mathematicians used zero by 628; al-Khwarizmi spread the system around 825; Fibonacci popularized it in Europe in 1202; calculators appeared in Germany and France from 1623.
How sure are we?
Every early calculator's wheels are decimal place-value dials; the link is a logical dependency visible in the machines' own design.
Debates and open questions
The abacus also works by place value, so how much calculator builders drew on written numerals versus counting boards is an open question.
▸Hindu–Arabic numerals and zero supplied the arithmetic of the Scientific RevolutionMostly agreed
The connection
Place-value numbers made heavy calculation practical on paper. Merchants adopted them first; by the 1500s scientists had too. Simon Stevin popularized decimal fractions (1585), John Napier invented logarithms (1614), and Kepler crunched Tycho Brahe's planetary data with both. Without fast written arithmetic, the number-crunching behind the new astronomy and physics would have been impractical.
When and how
Italy from 1202 (Fibonacci); Leiden (Stevin, 1585); Scotland (Napier, 1614); Prague and Linz (Kepler, early 1600s).
How sure are we?
Scientific books of the 1500s–1600s use Hindu–Arabic numerals and decimal tables throughout; Kepler's Rudolphine Tables (1627) were computed with logarithms.
Debates and open questions
Adoption was slow; historians debate whether the numerals drove the change or simply spread alongside commerce, printing and new mathematics.