A timeline of numerals and arithmetic

## Before 2000 BC

 Further information: Prehistoric numerals

## 1000–1500

• c. 1000 — Pope Sylvester II introduces the abacus using the Hindu–Arabic numeral system to Europe.
• 1030 — Ali Ahmad Nasawi writes a treatise on the decimal and sexagesimal number systems. His arithmetic explains the division of fractions and the extraction of square and cubic roots (square root of 57,342; cubic root of 3, 652, 296) in an almost modern manner.
• 12th century — Indian numerals have been modified by Persian mathematicians al-Khwārizmī to form the modern Arabic numerals (used universally in the modern world.)
• 12th century — the Arabic numerals reach Europe through the Arabs.
• 1202 — Leonardo Fibonacci demonstrates the utility of Hindu–Arabic numeral system in his Book of the Abacus.
• c. 1400 — Ghiyath al-Kashi “contributed to the development of decimal fractions not only for approximating algebraic numbers, but also for real numbers such as pi. His contribution to decimal fractions is so major that for many years he was considered as their inventor. Although not the first to do so, al-Kashi gave an algorithm for calculating nth roots which is a special case of the methods given many centuries later by Ruffini and Horner.” He is also the first to use the decimal point notation in arithmetic and Arabic numerals. His works include The Key of arithmetics, Discoveries in mathematics, The Decimal point, and The benefits of the zero. The contents of the Benefits of the Zero are an introduction followed by five essays: “On whole number arithmetic”, “On fractional arithmetic”, “On astrology”, “On areas”, and “On finding the unknowns [unknown variables]”. He also wrote the Thesis on the sine and the chord and Thesis on finding the first degree sine.
• 15th century — Ibn al-Banna and al-Qalasadi introduced symbolic notation for algebra and for mathematics in general.
• 1427 — Al-Kashi completes The Key to Arithmetic containing work of great depth on decimal fractions. It applies arithmetical and algebraic methods to the solution of various problems, including several geometric ones.
• 1478 — An anonymous author writes the Treviso Arithmetic.