The transmission of Greek mathematical and scientific knowledge to medieval Europe through Arabic translations is one of the great intellectual relay races of history, involving Greek scholars, Syrian Christians, Arab translators, and Latin medievals across a span of nearly a millennium.

The translation movement in Abbasid Baghdad during the 8th-10th centuries AD was state-sponsored intellectual work of enormous scale. The Caliph's House of Wisdom (Bayt al-Hikma) supported the systematic translation of Greek philosophical, medical, and scientific texts into Arabic, often via Syriac intermediate translations. Works of Aristotle, Galen, Euclid, Ptolemy, and Archimedes were translated and made available to Islamic scholars.

The Arabic scholarly tradition did not merely transmit Greek knowledge but substantially extended it. Al-Khwarizmi's Algebra (from whose name we derive 'algorithm') developed general methods for solving linear and quadratic equations beyond what the Greek tradition had. Ibn al-Haytham's Kitab al-Manazir (Book of Optics) fundamentally revised the Greek theory of vision. Avicenna's Canon of Medicine was the dominant medical textbook in both the Islamic world and medieval Europe for centuries.

The return transmission to Latin Europe came through two primary routes: the translations made in Toledo in the 12th century (from Arabic to Latin, under the patronage of the Archbishop of Toledo) and the translations made in southern Italy and Sicily where Greek communities preserved direct access to Greek texts. The 12th-century translation movement that brought Aristotle, Euclid, Ptolemy, and medical texts into Latin was the material foundation of the scholastic philosophy and the proto-scientific work of the medieval universities.