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Achillas had been ordained a presbyter by Pope Theonas of Alexandria with Pierius, and was made the head of the Catechetical School of Alexandria upon the departure of Pierius, who had either left for Rome or been made a martyr at Alexandria. He was apparently very highly thought of for his work in Greek philosophy and theological science, as Athanasius of Alexandria later described him by the honorific "Achillas the Great".
He came to office after the execution of his predecessor, Peter of Alexandria, during the Diocletian Persecution. He inherited the troubles the church was experiencing at the time, including the Meletian heresy and the continuing troubles with Arianism. Upon Achillas' accession to the patriarchate, he was influenced by the supporters of Arius to rescind the orders of excommunication and anathema which had been placed on him. As a result of Achillas' actions, Arius was not only forgiven for his early actions and statements, but even given the position as the priest at the Bucalis, the oldest and among the most influential churches in Alexandria. 
Achillas is not recorded as having been involved in any other major activities during his short reign, which lasted only six months. Some of the church have ascribed his early death to his violating the order of his predecessor Peter on never allowing Arius back into the church.
He is commemorated in the Synaxarion of the Coptic Orthodox Church on 19 Ba'ūnah.
|Pope of Alexandria