Cyril of Alexandria in the context of "Ecumenical Patriarch of Constantinople"

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.

Orestes (fl. 415 AD) was a Roman state official serving as governor of the diocese of Egypt (the Augustal prefect) in 415. During his term of office, he was engaged a violent feud with the bishop of Alexandria, Cyril, and their struggle precipitated the death of the philosopher and scientist Hypatia.

The Chalcedonian schism, also known as the Monophysite schism, is the break of communion between the Oriental Orthodox Churches and the Great Church (which later became the Eastern Orthodox Church and Catholic Church) in the aftermath of the Council of Chalcedon. Although the bishops at Chalcedon greatly respected Cyril of Alexandria and used his writings as a benchmark for orthodoxy, opponents of the council believed that the Chalcedonian Definition, which states that Christ is "acknowledged in Two Natures", was too close to Nestorianism and contradicts Cyril's formula "one nature of God the Word incarnate". The Council had also deposed the Pope of Alexandria, Dioscorus, but his supporters continued to consider him their rightful Pope, refusing to recognise the council-appointed Proterius.

The anti-Chalcedonian strongholds were in Egypt, Palestine and later Syria. Over the next century, their communities gradually separated from the official church of the Byzantine Empire, eventually becoming the Oriental Orthodox Churches. The imperial government made many attempts to mend the schism, generally by trying to compromise between the two positions, but these attempts only created further heresies and schisms. The Arab conquests of the Levant and of Egypt in the 7th century fossilised the schism, but ecumenical dialogue between Chalcedonian and non-Chalcedonian Christians has been renewed since the 20th century.

The Council of Ephesus was a council of Christian bishops convened in Ephesus (near present-day Selçuk in Turkey) in AD 431 by the Roman Emperor Theodosius II. This third ecumenical council, an effort to attain consensus in the church through an assembly representing all of Christendom, confirmed the original Nicene Creed, and condemned the teachings of Nestorius, Patriarch of Constantinople, who preferred that the Virgin Mary be called Christotokos, "Christ-bearer" over Theotokos, "God-bearer"; in contrast to Cyril of Alexandria who deemed that Theotokos is enough on its own. It met from 22 June to 31 July 431 at the Church of Mary in Ephesus in Anatolia.

The Second Council of Constantinople is the fifth of the first seven ecumenical councils recognized by both the Eastern Orthodox Church and the Catholic Church. It is also recognized by the Old Catholics and others. Protestant opinions and recognition of it are varied. Some Protestants, such as Calvinists, recognize the first four councils, whereas Lutherans and most Anglo-Catholics accept all seven. Constantinople II was convoked by the Byzantine Emperor Justinian I under the presidency of Patriarch Eutychius of Constantinople. It was held from 5 May to 2 June 553. Participants were overwhelmingly Eastern bishops—only sixteen Western bishops were present, including nine from Illyricum and seven from Africa, but none from Italy—out of the 152 total.

The main work of the council was to confirm the condemnation issued by edict in 551 by the Emperor Justinian against the Three Chapters. These were the Christological writings and ultimately the person of Theodore of Mopsuestia (died 428), certain writings against Cyril of Alexandria's Twelve Anathemas accepted at the Council of Ephesus, written by Theodoret of Cyrrhus (died c. 466), and a letter written against Cyrillianism and the Ephesian Council by Ibas of Edessa (died 457).

Monothelitism, or monotheletism, is a theological doctrine in Christianity that was proposed in the 7th century, but was ultimately rejected by the sixth ecumenical council. It held Christ as having only one will and was thus contrary to dyothelitism, the Christological doctrine accepted by most Christian denominations, which holds Christ as having two wills (divine and human). Historically, monothelitism was closely related to monoenergism, a theological doctrine that holds Jesus Christ as having only one energy. Both doctrines were at the center of Christological disputes during the 7th century.

Monothelitism is from Greek: μονοθελητισμός, romanized: monothelētismós, lit. 'doctrine of one will'. Theological notions related to the oneness of Christ's will emerged as a result of some earlier Christological controversies that were related to monophysitism as formulated by Eutyches (d. 456) and miaphysitism as formulated by non-Chalcedonian followers of Cyril of Alexandria (d. 444). Since the notion of Christ's one nature implied the oneness of his will, ecclesiastical and political elites of the Eastern Roman Empire tried during the 7th century to promote monothelitism as a unifying doctrine that would reconcile divided Christian factions. In spite of strong imperial support, those attempts failed, and monothelitism was consequently rejected and denounced as heresy in 680–681 at the Third Council of Constantinople, the sixth ecumenical council.

The Alexandrian rites are a collection of ritual families and uses of Christian liturgy employed by three Oriental Orthodox churches (the Coptic Orthodox Church, the Eritrean Orthodox Tewahedo Church, and the Ethiopian Orthodox Tewahedo Church), and by three Eastern Catholic Churches (the Coptic Catholic Church, the Eritrean Catholic Church, and the Ethiopian Catholic Church).

The Alexandrian rite's Divine Liturgy contains elements from the liturgies of Saints Mark the Evangelist (who is traditionally regarded as the first bishop of Alexandria), Basil the Great, Cyril of Alexandria, and Gregory of Nazianzus. The Alexandrian rites are sub-grouped into two rites: the Coptic Rite and the Ge'ez Rite.

Nestorius of Constantinople (/ˌnɛsˈtɔːriəs/; Ancient Greek: Νεστόριος; c. 386 – c. 451) was an early Christian prelate who served as Archbishop of Constantinople from 10 April 428 to 11 July 431. He was a Christian theologian from the Catechetical School of Antioch, and several of his teachings in the fields of Christology and Mariology were seen as controversial and heretical, causing major disputes. In 431, he was condemned and deposed from his see by the Council of Ephesus, presided over by his archrival Cyril of Alexandria, but the counter-council led by John I of Antioch vindicated him and deposed Cyril in return. Nestorius refrained from attending both of these councils and instead sought retirement from the Byzantine Emperor.

Nestorius himself used the title Theotokos and did not advocate for its ban. His teachings included cautious usage of Theotokos ("God-Bearer"), used for Mary, mother of Jesus, in order that Christ's human and divine natures not be confused, as he believed Christ was born according to his humanity and not his divinity, which indicated his preference for the concept of the prosopic union of two natures (divine and human) of Christ, over the concept of a hypostatic union. He proposed instead the title of Christotokos ("Christ-bearer"). This brought him into conflict with Cyril of Alexandria and other prominent diophysite and miaphysite churchmen of the time, who accused him of heresy.