900 - 1100


  • Sridhara writes the Trisatika (sometimes called the Patiganitasara) and the Patiganita. In these he solves quadratic equations, sums series, studies combinations, and gives methods of finding the areas of polygons.
  • Abu Kamil writes Book on algebra which studies applications of algebra to geometrical problems. It will be the book on which Fibonacci will base his works.


  • Al-Battani writes Kitab al-Zij a major work on astronomy in 57 chapters. It contains advances in trigonometry.


  • Gerbert of Aurillac (later Pope Sylvester II) reintroduces the abacus into Europe. He uses Indian/Arabic numerals without having a zero.


  • Al-Uqlidisi writes Kitab al-fusul fi al-hisab al-Hindi which is the earliest surviving book that presents the Hindu system.


  • Abu'l-Wafa invents the wall quadrant for the accurate measurement of the declination of stars in the sky. He writes important books on arithmetic and geometric constructions. He introduces the tangent function and produces improved methods of calculating trigonometric tables.


  • Codex Vigilanus copied in Spain. Contains the first evidence of decimal numbers in Europe.



  • Ibn al-Haytham (often called Alhazen) writes works on optics, including a theory of light and a theory of vision, astronomy, and mathematics, including geometry and number theory. He gives Alhazen's problem: Given a light source and a spherical mirror, find the point on the mirror were the light will be reflected to the eye of an observer.


  • Al-Biruni writes on many scientific topics. His work on mathematics covers arithmetic, summation of series, combinatorial analysis, the rule of three, irrational numbers, ratio theory, algebraic definitions, method of solving algebraic equations, geometry, Archimedes' theorems, trisection of the angle and other problems which cannot be solved with ruler and compass alone, conic sections, stereometry, stereographic projection, trigonometry, the sine theorem in the plane, and solving spherical triangles.


  • Ibn Sina (usually called Avicenna) writes on philosophy, medicine, psychology, geology, mathematics, astronomy, and logic. His important mathematical work Kitab al-Shifa' (The Book of Healing) divides mathematics into four major topics, geometry, astronomy, arithmetic, and music.


  • Ahmad al-Nasawi writes al-Muqni'fi al-Hisab al-Hindi which studies four different number systems. He explains the operations of arithmetic, particularly taking square and cube roots in each system.


  • Hermann of Reichenau (sometimes called Hermann the Lame or Hermann Contractus) writes treatises on the abacus and the astrolabe. He introduces into Europe the astrolabe, a portable sundial and a quadrant with a cursor.


  • Al-Khayyami (usually known as Omar Khayyam) writes Treatise on Demonstration of Problems of Algebra which contains a complete classification of cubic equations with geometric solutions found by means of intersecting conic sections. He measures the length of the year to be 365.24219858156 days, a remarkably accurate result.


  • Shen Kua writes Meng ch'i pi t'an (Dream Pool Essays), which is a work on mathematics, astronomy, cartography, optics and medicine. It contains the earliest mention of a magnetic compass.