In late antiquity the major centres of learning in the empire such as Alexandria, Antioch, Athens and Constantinople cultivated the study of many fields of knowledge, with an emphasis on Philosophy, Rhetoric and Law.

Once Christianity prevailed, debate arose concerning the creation of the world, and how the contents of the Old Testament related to current knowledge and ancient science. Two schools of interpretation emerged, one in Alexandria and the other in Antioch.
 
The school of Alexandria argued that everything in the Book of Genesis was written in an allegorical manner, in other words that it meant something different from what it said. Followers of this school were Philo of Alexandria, a philosopher who lived in Alexandria from 20 BC to 50 AD, and Saint Basil the Great , who expressed his views in nine speeches collected into a book called the Hexameron (The Six Days of Creation). In the book, Basil accepts the Greek astronomical model as described by Claudius Ptolemy (a famous Greek natural philosopher who lived in Alexandria from 127 to151 AD). According to this view, the world is round; the earth is also round and motionless, and is located at the centre of the universe.

Unlike the school of Alexandria, the school of Antioch argued that everything in the Book of Genesis happened exactly as described, word for word. Followers of this school were Theophilus of Antioch and John Chrysostom, who claimed that the world was of various shapes and that the earth was flat. Similar views are expressed by Cosmas Indicopleustes in his book Christian Topography, which presents the earth as the flat bottom of a chest, with the celestial sphere as its vaulted lid.

The Byzantines did not always accept Greek science easily. On the one hand there were those who supported it, such as Emperor Heraclius (610-640), who summoned a follower of Greek science called Stephen of Alexandria to teach in Constantinople, and on the other there were events like the murder of Hypatia, a woman astronomer killed by fanatical Christians in Alexandria in 415.

The difficult centuries
Arab sources report the presence of Byzantine scholars in Baghdad and Damascus, which in the early 9^th century became centres for the study of mathematics (especially algebra) and astronomy.

Theophilus of Edessa († 785) was the personal astronomer-astrologer of Caliph al-Mahdi (775-785), while Leo the Mathematician († ca 869) was invited to Baghdad by Caliph al-Mamoun (813-833), in return for immense riches. Leo, however, preferred to become Archbishop of Thessaloniki and then "protector of the philosophy faculty" in the Magnaura Pandidakterion (University of the Palace Hall of Magnaura). Works by ancient and modern scholars such as Euclid, Archimedes, Apollonius of Perge in Pamphylia, Claudius Ptolemy, Diophantus, Theon Alexandricus (Hypatia’s father) and others were reissued in Constantinople. In general, Byzantium was in constant contact with the Arab caliphate at the time, and their technical expertise in matters of peace and war was largely shared, as can be seen in the case of Greek fire.

The Comnenus and Angelos era
The most important evidence for the impact of Arab science on Byzantine scholars comes from this period, especially regarding the solution of practical mathematical problems and the planning of astronomical tables. These tables contained predictions about the positions of celestial bodies, conjunctions and eclipses, which proved very useful in calculating Easter time and making horoscopes.
 
The only surviving complete translation of a work of Arabic astronomy, the Calculation Method for Diverse Astronomical Hypotheses (about 1060-1072) comes from this period. Anna Comnena mentions that her father Emperor Alexius I had four astrologers in his court -  two Egyptians, an Athenian and Simeon Seth, physician and mathematician, author of the work Conspectus rerum naturalium (“On the Things of Nature”) (c. 1058). In the first half of the 12th century, Byzantine manuscripts containing scientific works by Ancient Greek authors such as Aristotle, Euclid, Heron, Ptolemy and Proclus were translated into rather poor Latin at the Sicilian royal court. A little later, the same works and others were also translated in Spain.

That being said, conservative circles in Byzantium regarded magic, astrology and the occult as a betrayal of Christianity. One of the great unsolved detective stories in Byzantium concerns a complaint made by Michael Psellos in 1058 against Patriarch Michael Cerularius, claiming that the latter had been initiated into Mithraism and other pagan orgiastic cults by two monks, Nikitas and John, and by Dosithea, a woman with a dark past, possibly a former actress and clairvoyant. Cerularius suffered what was probably a stress-induced heart attack, and died minutes before he was due to be questioned.

The Palaeologan Era
After the fall of Constantinople to the Crusaders in 1204, the university and patriarchal school that had been the capital’s educational institutions collapsed, and their significant libraries were scattered and transferred to the Latin West. An attempt to reorganize education was made in Nice, where most of the scholars settled. In fact, in 1239 and 1240 Nicephorus Blemmydes travelled to Mount Athos, Thessaloniki, Larissa and Ohrid to gather books for republication. His Physics is an abbreviated presentation of Aristotle's work of the same name.

So it was that after 1261 the teaching of four maths courses (arithmetic, geometry, music and astronomy) resumed at the University of Constantinople. George Pachmeres’ work Quadrivium is a textbook on those four subjects.

In this last Byzantine period, knowledge of astronomy was enriched both by the Persians and by the West, even if reactions were provoked by negotiations over the union of the Churches.

Special interest was shown in this era in amending Ptolemy’s laws and comparing them with those that derived from the East, i.e. Persia, or from other Western traditions, such as the Arab laws of Toledo, the Alfonsine laws and the laws of the Jews of Provence. George Chioniades was the first apprentice of the famous Shams Al Din Al Mouchari in Tabriz in 1300, and translated Arabic and Persian astronomical texts and tables. Scholars who wrote astronomical studies, among other things, were George Chrysokokkes, Barlaam of Calabria, Nicephorus Gregoras, Theodore Melitiniotis, Theodore Metochites, Nicephorus Choumnos, Demetrius Chrysoloras, Michael Chrysokokkes, Mark of Ephesus (“the Courteous”) and Gemistus Pletho, who all belong to the Byzantine intelligentsia of the time.