I recently read a fun little retold fairytale set in Constantinople, and this piqued my interest in Byzantine science. Byzantine science continued classical Greek learning, and acted as a bridge to Islamic and Western European science.
The Byzantine Empire was the Greek-speaking continuation of the Roman Empire, which continued until 1453, long after the Western Roman Empire fell. Byzantine scholars included, in mathematics and physics, Anthemius of Tralles (c. 474–c. 534), who studied parabolic and elliptical mirrors and helped design the Hagia Sophia church (see above – it is now a mosque).
Byzantine medicine was well advanced, and the Vienna Dioscurides (one page shown above) dates from the period. In military technology, Greek fire (below) stands out. Nobody knows exactly what it was, but it was a kind of ancient napalm that acted as a powerful defence against naval attack by wooden ships (the technology gets a mention in the book and film Timeline, and in the novel Dark Fire).