Abu Abd Allah Muhammad ibn Muadh al-Jayyani

Abu Abd Allah Muhammad ibn Muadh al-Jayyani was an Andalusian mathematician, astronomer, and optical scientist born in 989 CE in Jaen, in the southern Iberian Peninsula. He lived and worked during the golden age of Islamic Spain — al-Andalus — when the cities of Jaen, Cordoba, and Seville were centres of scientific and philosophical inquiry that rivalled any in the medieval world. Al-Jayyani spent most of his life in his native Jaen, where he served in administrative or judicial roles while pursuing mathematical and scientific research.

His most celebrated mathematical work is the Kitab Majhulat Qisi al-Kura, known in Latin translation as the Liber de Arcubus Similaribus (The Book on Unknown Arcs of a Sphere). In this treatise, al-Jayyani presented a systematic and fully general treatment of spherical trigonometry — the mathematics of triangles drawn on the surface of a sphere — independent of astronomy. He introduced and proved the general law of sines for spherical triangles, a theorem of fundamental importance for navigators, astronomers, and mathematicians. This work predates and clearly anticipates the later European developments in trigonometry by several centuries.

In optics, al-Jayyani engaged with the foundational questions of the science of vision. He composed a commentary on or response to the optical tradition that circulated in al-Andalus, contributing to the transmission of optical knowledge in the western Islamic world.

Al-Jayyani also wrote on the total solar eclipse, on meteorological phenomena, and on Euclid's parallel postulate — showing a philosophical and foundational interest in mathematics that went well beyond computational needs. He died in Jaen in 1079 CE, leaving a mathematical legacy that, through Latin translations, would shape the development of trigonometry in medieval and Renaissance Europe. Historians of mathematics regard his Kitab Majhulat Qisi al-Kura as one of the key texts in the history of trigonometry.