Patriarch of Alexandria in the context of "Archbishop"

Hypatia (born c. 350–370 – March 415 AD) was a Neoplatonist philosopher, astronomer, and mathematician who lived in Alexandria, at that time in the province of Egypt and a major city of the Eastern Roman Empire. In Alexandria, Hypatia was a prominent thinker who taught subjects including philosophy and astronomy, and in her lifetime was renowned as a great teacher and a wise counselor. Not the only fourth century Alexandrian female mathematician, Hypatia was preceded by Pandrosion. However, Hypatia is the first female mathematician whose life is reasonably well recorded. She wrote a commentary on Diophantus's thirteen-volume Arithmetica, which may survive in part, having been interpolated into Diophantus's original text, and another commentary on Apollonius of Perga's treatise on conic sections, which has not survived. Many modern scholars also believe that Hypatia may have edited the surviving text of Ptolemy's Almagest, based on the title of her father Theon's commentary on Book III of the Almagest.

Hypatia constructed astrolabes and hydrometers, but did not invent either of these, which were both in use long before she was born. She was tolerant toward Christians and taught many Christian students, including Synesius, the future bishop of Ptolemais. Ancient sources record that Hypatia was widely beloved by pagans and Christians alike and that she established great influence with the political elite in Alexandria. Toward the end of her life, Hypatia advised Orestes, the Roman prefect of Alexandria, who was in the midst of a political feud with Cyril, the bishop of Alexandria. Rumors spread accusing her of preventing Orestes from reconciling with Cyril and, in March 415 AD, she was murdered by a mob of Christians led by a lector named Peter.

Pentarchy (from Ancient Greek Πενταρχία (Pentarchía), from πέντε (pénte) 'five' and ἄρχειν (archein) 'to rule') was a model of Church organization formulated in the laws of Emperor Justinian I (r.  527–565) of the Roman Empire. In this model, the Christian Church is governed by the heads (patriarchs) of the five major episcopal sees of the Roman Empire: Rome, Constantinople, Alexandria, Antioch, and Jerusalem.

The idea came about because of the political and ecclesiastical prominence of these five sees, but the concept of their universal and exclusive authority was attached to earlier Hellenistic-Christian ideas of administration. The pentarchy was first legally expressed in the legislation of Emperor Justinian I, particularly in Novella 131. The Quinisext Council of 692 gave it formal recognition and ranked the sees in order of preeminence, but its organization remained dependent on the emperor, as when Leo the Isaurian altered the boundary of patriarchal jurisdiction between Rome and Constantinople. Especially following Quinisext, the pentarchy was at least philosophically accepted in Eastern Orthodoxy, but in the West, the Rome based patriarchy evolved into the Roman Catholic Church, which would reject the Council as well as the concept of the pentarchy, considering itself the supreme church with universal jurisdiction.

Cyril of Alexandria (Ancient Greek: Κύριλλος Ἀλεξανδρείας; Coptic: Ⲡⲁⲡⲁ Ⲕⲩⲣⲓⲗⲗⲟⲩ ⲁ̅ or Coptic: Ⲡⲓⲁⲅⲓⲟⲥ Ⲁⲃⲃⲁ Ⲕⲩⲣⲓⲗⲗⲟⲥ ⲡⲓⲥⲧⲩⲗⲗⲟⲥ ⲛ̀ⲧⲉ ⲡⲓⲛⲁϩϯ or ⲡⲓ̀ⲁⲅⲓⲟⲥ Ⲕⲓⲣⲓⲗⲗⲟⲥ; c. 376–444) was the Patriarch of Alexandria from 412 to 444. He was enthroned when the city was at the height of its influence and power within the Roman Empire. Cyril wrote extensively and was a major player in the Christological controversies of the late 4th and 5th centuries. He was a central figure in the Council of Ephesus in 431, which led to the deposition of Nestorius as Patriarch of Constantinople.

Cyril is counted among the Church Fathers and also as a Doctor of the Church, and his reputation within the Christian world has resulted in his titles Pillar of Faith and Seal of all the Fathers. The Nestorian bishops at their synod at the Council of Ephesus declared him a heretic, labelling him as a "monster, born and educated for the destruction of the church".

Christianity in the Middle Ages covers the history of Christianity from the fall of the Western Roman Empire (c. 476). The end of the period is variously defined - depending on the context, events such as the conquest of Constantinople by the Ottoman Empire in 1453, Christopher Columbus's first voyage to the Americas in 1492, or the Protestant Reformation in 1517 are sometimes used.

In Christianity's ancient Pentarchy, five patriarchies held special eminence: the sees of Rome, Constantinople, Jerusalem, Antioch, and Alexandria. The prestige of most of these sees depended in part on their apostolic founders, or in the case of Byzantium/Constantinople, that it was the new seat of the continuing Eastern Roman, or Byzantine Empire. These bishops considered themselves the successors of those apostles. In addition, all five cities were early centres of Christianity, losing their importance after the Levant was conquered by the Sunni Caliphate.

Pope is a religious title traditionally accorded to the Bishop of Rome / Pope of Rome, the Coptic and the Greek Orthodox bishops of Alexandria, and some leaders of other ecclesial communities. Popes may also claim the title patriarch. Both terms come from the Greek πάππας (English: father). The female equivalent of the term 'Pope' is "popess/papess".

The Church of Alexandria in Egypt was the Christian Church headed by the patriarch of Alexandria. It was one of the five sees of the pentarchy, alongside Rome, Antioch, Constantinople and Jerusalem.

Tradition holds that Saint Mark the Evangelist founded the Church of Alexandria c. 49 AD. Alexandrian Christianity greatly influenced the early Church in much of Africa.Alexandria claims jurisdiction over all Christians on the African continent.

The Nestorian schism (a.d. 431–544) was a split between the Christian churches of Sassanid Persia, which affiliated with Nestorius, and those that later became the Catholic and Orthodox churches. The schism rose out of a Christological dispute, notably involving Cyril (Patriarch of Alexandria) and Nestorius (Patriarch of Constantinople).

The First Council of Ephesus in 431 and the Council of Chalcedon in 451 condemned Nestorius and his doctrine, which emphasized the radical distinctness between Christ's human and divine natures. That forced a breach between the churches that defended Nestorius and the state church of the Roman Empire, which caused the Church of the East, the Christian church of Sassanid Persia, to become known as the Nestorian Church, as it took the side of Nestorius.