- Jabir ibn Aflah writes works on mathematics which, although not as good as many other Arabic works, are important since they will be translated into Latin and become available to European mathematicians.
- Bhaskara II (sometimes known as Bhaskaracharya) writes Lilavati (The Beautiful) on arithmetic and geometry, and Bijaganita (Seed Arithmetic), on algebra.
- Gherard of Cremona begins translating Arabic works (and Arabic translations of Greek works) into Latin.
- Al-Samawal writes al-Bahir fi'l-jabr (The brilliant in algebra). He develops algebra with polynomials using negative powers and zero. He solves quadratic equations, sums the squares of the first natural numbers, and looks at combinatorial problems.
- Arabic numerals are introduced into Europe with Gherard of Cremona's translation of Ptolemy's Almagest. The name of the "sine" function comes from this translation.
- Chinese start to use a symbol for zero. (See this History Topic.)
- Fibonacci writes Liber abaci (The Book of the Abacus), which sets out the arithmetic and algebra he had learnt in Arab countries. It also introduces the famous sequence of numbers now called the "Fibonacci sequence".
- Fibonacci writes Liber quadratorum (The Book of the Square), his most impressive work. It is the first major European advance in number theory since the work of Diophantus a thousand years earlier.
- Jordanus Nemorarius writes on astronomy. In mathematics he uses letters in an early form of algebraic notation.
- John of Holywood (sometimes called Johannes de Sacrobosco) writes on arithmetic, astronomy and calendar reform.
- Qin Jinshao writes Mathematical Treatise in Nine Sections. It contains simultaneous integer congruences and the Chinese Remainder Theorem. It considers indeterminate equations, Horner's method, areas of geometrical figures and linear simultaneous equations.
- Li Yeh writes a book which contains negative numbers, denoted by putting a diagonal stroke through the last digit.
- Campanus of Novara, chaplain to Pope Urban IV, writes on astronomy and publishes a Latin edition of Euclid's Elements which became the standard Euclid for the next 200 years.
- Yang Hui writes Cheng Chu Tong Bian Ben Mo (Alpha and omega of variations on multiplication and division). It uses decimal fractions (in the modern form) and gives the first account of Pascal's triangle.