What was the byzantines' most important contribution to mathematics and science?

Thanks to the Byzantines, ancient and early medieval Greek works of astronomy, philosophy and mathematics were transmitted to the Arab world. Byzantium turned into a major learning center at the beginning of the Middle Ages. Though it isn´t accounted for many innovations or discoveries, the Byzantine Empire served as vehicle of transmission of the classical culture, laying the ground for later innovator and inventors. Much of its science and philosophy was based on Christian theology. A major heritage in archictecture is the Haga Sophia cathedral, splendid and magnificent; it was designed by mathematicians/architects Isidore and Anthemius. Much later, it was  turned into a large mosque by the Turks and so it remains until today. Byzantium also served as a means of transmission of Arabic culture and learning for Europe.

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