The period I will be examining in the present chapter (third to sixth century AD) begins with an Empire still in place and ends after its dissolution in the West. By the fourth century, Christianity had become the religion of the emperor (with the brief exception of Julian), and the Church emerged as a more and more powerful institution, with buildings, books, schools, canonical authors of its own. The interaction between new and old religion, between the various Christian sects, and between church and state are some of the key issues in the history of this period. One of the most dramatic ways in which a mathematician could be affected by religious changes is exemplified by the death of Hypatia of Alexandria, who taught philosophy and mathematics. She was lynched by a Christian mob in AD 415, for reasons that probably had to do with her being an educated, politically visible, pagan woman.2 Other, more subtle, traces of Christianity in the field of mathematics will be explored in the next chapter. Here we devote individual sections to Diophantus, Pappus, and Eutocius, and general ones to ‘Philosophers’ (mainly Iamblichus and Proclus) and ‘Rest of the world’. To begin with, as usual, I will review the material evidence, which will include (new to this chapter) legal sources.