Hypatia (370-416 A.D.) was a Greek neoplatonic philosopher, astronomer and mathematician. He lived and taught in Alexandria where he was murdered by a mob made up of fanatical Christians.
Daughter of mathematician and astronomer Theon, she received very good education with her father’s care and traveled to Athens and Italy. In Athens he attended classes at the neoplaton school of Plutarch the Younger and his daughter Asclepinity but also learned near Proclos and Ieroklis.
Returning to Alexandria, he became head of the Platonist school there (400 A.D.), taught philosophy and mathematics and was an attraction for the intellectuals of the time and made extensive and essential comments on the mathematical works of Diofantos and Apollonius.
Unfortunately, although Hypatia itself has been very much a polygraph, none of her works survives and we only have references to them. Many of her students belonged to the upper circles of the city’s aristocracy and became important personalities, such as Bishop Kyrinis Syesios and the prefect of Alexandria Orestes. She was philosophically influenced by the neoplatons Plotino and Iambliho.
Although many believe that Hypatia was purely Greek, there are many who claim that she was half Greek and half Egyptian. This is because a) her father Theon has been recognized as Greek and Egyptian and b) most of the inhabitants of Alexandria were Greeks and Egyptians. Due to its geographical exclusion from the rest of Egypt, Alexandria was free from misogynistic traditions known to the rest of the Roman Empire. Although the Romans forced the conquered areas to follow their own laws, the conquered had a relative autonomy, so the law was a mixture of local and Roman laws, especially in Alexandria, where Greek, Roman and Egyptian laws were confused. Hypatia, as a woman of mixed nationality, could choose to follow the Greek or Egyptian without any intervention of the Romans. That’s why she could own land and run her own business without a supervisor. The laws, along with her education, contributed to her public sermons, teaching and advising men, moving around the city without someone supervising her and owning her own home. The strange thing is that with these actions it did not provoke, but on the contrary the inhabitants of Alexandria must have been accustomed to such situations.
The mathematician and philosopher Hypatia lived in Alexandria from the middle of the 4th century. A.D. until her violent death by a Christian mob in 415. Her date of birth is not confirmed, but it is believed she was born in 370 AD. This is known because of the eclipse her father was studying in 364 AD. She was pure and worthy of respect, a professor of mathematics and neoplaton philosophy in Alexandria. Wearing the classical chlamydia of philosophers, he taught in public to an audience made up of pagans and Christians. Evidence of the life and work of Hypatia can be found in various historical texts, for example in the works of Socrates the School.
According to sources, in addition to a philosopher, mathematician and astronomer, he also held the presidency of the Neoplatonic School of Alexandria and was a person worthy of respect, who exerted influence on the important lords of Alexandria and the Mediterranean. One of them was Orestes, the Roman prefect. They met very often and talked mainly about political issues. Hypatia exerted influence not only in Alexandria, but also in Istanbul, Syria and Kyrini. Unfortunately, works of Hypatia have not been salvaged. Some analysts believe her works were written in Arabic, while others argue that her work consisted of mathematical formulas that she had created herself. Hypatia is important for the rhetorical rule, because it proves that women also participated in the social and spiritual activities of the ancient world. Hypatia taught publicly about Plato and Aristotle, indicating her education in philosophy and rhetoric. There are many texts that validate her involvement as a teacher in addition to mathematical philosophy and rhetoric.
Hypatia probably did two kinds of lessons. A special one, for the elite of its students and its public sermons, in which it exerted influence on Alexandrian officials. She was beloved from all over the world and the various leaders consulted her very often. Hypatia commented on the Arithmetic of Diofantos, wrote the Astronomical Rule and perfected the Canon of Apollonius (see below). She also collaborated with her father on the commentary of the 3rd volume of Almagesti and also helped the student of Syesio in the construction of an astrolabe and a water meter. Of course, although we cannot deny that she was a great mathematician and philosopher of her time, Hypatia became known more for her teaching. Hypatia was a respected and eminent teacher, quite charismatic and dear to her students. Sources say she had natural beauty and was wearing simple clothes. He was giving public lectures and maybe he was in some kind of public office. Hypatia taught and became known for both philosophy and mathematics. The philosophy developed by Hypatia is known as Neoplaton. Although there were different versions of Neoplatonism, it is said that Hypatia preached one of its own, different. The letters and poems provide conclusions about the Neoplaton philosophy of Hypatia but do not provide important information. Moreover, while the writings of the philosopher successors of Hypatia come to shed light on her contributions to Neoplatonism, there are no surviving mathematical works of her own.
What we know about her Mathematics is only a small subset of her work. He is widely regarded as a teacher and scholar. He curated works of Geometry, Algebra and Astronomy and knew how to make astrolabes and hygroscopes. . Although her work was lost, the tradition in which she worked and the texts she commented on proved to be the exact basis for the next step in the history of mathematics. When in the seventeenth century Vieta and Fermat began to explore the conical incisions, the works of Diofantos and Apollonius were vital. Further conclusions about Hypatia’s mathematics remain in the realm of conjecture, a full assessment of her contribution remains beyond any historical definition. Her contributions to Alexandrian philosophy and her exploration of the possible expansion and creation of advanced mathematics in antiquity deserve careful treatment.
It is considered that there is a connection between Neoplaton Philosophy and Mathematics. The nature of mathematics is to create ideas made from material objects. That’s Geometry. Although it has origins in the world of practical topography and inspectors of weights and measures, it goes beyond these principles. Elements deal with a world that is no longer the world of practice, but the world of ideas. Thus, Mathematics could be seen as an example of this transcendence over the material that Neoplatonism called. The fact that Hypatia was a mathematician is not in doubt. Hypatia learned mathematics from her father Theon. He managed to overcome him in this field and teach many students. One source states that “Isidore was greatly overshadowed by Hypatia, not only because he was a man and a woman, but in the way that a true philosopher would amount to a mere geometer.” In addition to Souda (a Byzantine dictionary based on the works of Damascus), she is assigned the writing of three works. All he is known to have written are related to mathematics and astronomy. She is believed to have based her books on Neoplaton Philosophy.
The Astronomical Canon
Souda reveals that Hypatia wrote a volume entitled “The Astronomical Cane” as she sought to study and deepen more in her father’s fields of mathematics than he did. Some scholars believe that the “Astronomical Cane” was just a collection of astronomical paintings others again believe it was a comment on Ptolemy. One of his important books is Almagesti. Comments on Book Three have been made by Theon, where he says that the work is “… in the critical review of the philosopher Hypatia, my daughter. “. There is an assumption that Hypatia had written parts of these Comments. An additional note from Souda mentions the titles of the works of Hypatia, while parts of them have been lost where Hypatia analyzed the knots of Apollonius and the arithmetic of Diofantos. Both works face representations of the upper order of equations but because the approach of Apollonius was arithmetic and Diofant geometric, we understand that Hypatia was familiar with both algebraic and geometric representations of higher order equations.
The hearths of Apollonius are considered among the most difficult works of antiquity and they were the ones that laid the foundations for many of what in the future became known as projective geometry.
Commentary of Diofantos
The algebraic works of Diofantos were much more sophisticated than the previous ones. In any case, the mathematicians of Alexandria in the fourth and fifth centuries developed the mathematics that would be used for the solution of upper-class equation systems. Through these Comments it would be possible to see which work, among all the others, is hers. This thought is created as it is said that a scribe tried to mix the original text of Diofantus with her own works. However, it is more likely that Hypatia’s interference is two “student exercises” at the beginning of Book II. The first asks for the solution of the pair simultaneous equations:
x – y= a, x2 – y2 = (x – y) + b where a, b is known. The next one is a little generalization. Requires the solution of the pair of simultaneous equations:
x – y = a, x2 – y2 = m (x – y) + b,where a, b and m are known. There is some evidence linking this problem to Hypatia: a nine-word phrase in the original Greek is identified with one of euclid’s elements, which her father had elaborated.
Another source of information about the mathematical activities of Hypatia is the correspondence of the Association which reveals that he studied philosophy and astronomy under the guidance of Hypatia and mentions the creation of some scientific instruments such as the astrolabe and the hygrometer. There is a theory of stereographic projection, that the road is open for the construction of a more practical two-dimensional device. This is given to us by the story of The Astrolavos, who, writing about Paion, states that he had designed the astrolabe himself with the help of Hypatia and had been created from the best materials of silversmithing. The conclusion is that the theory of the astrolabe and the details of its construction had passed under Ptolemy, through Theon, to reach Hypatia, which in turn taught the Cossios.
The Students of
Her reputation attracted students from all over the Mediterranean. In fact, it is believed that at the time hypatia died she was the best mathematician in the Greco-Roman world, and quite possibly the rest, thus overshadowing her father in her reputation as a teacher. While we can’t identify all of her students, there are signs that they were generally rich and powerful. Her best-known disciple is the Conesium of Kyrenia, who tried to link early Christianity with Neoplatonism. Some of his letters to her have been preserved, as have some other emissaries to his classmates, where he expresses his admiration and the influence he had exerted on him. In the letters of the Cossios we are given some names of students of Hypatia who validate her talent and reputation. In addition to Syfy, students were also his younger brother (Euoptius) and his uncle (Alexander), his best friend (Herculian) with his brother (Olympiaus), as well as others (Hessychius, Athanasius,Theodosius). To understand the strength and education of its students, Syesios became the Bishop of Constantinople, while his brother became his successor. Olympian was a wealthy landowner from Selefia and was well connected to Alexandria, which probably also applied to his brother, although later I became prefect of Constantinople. Isychos was governor of Upper Libya, Athanasios was a well-known Alexandrian sophist and Theodosius was a grammarist, who wrote rules for verbs and nouns.
For her death there are many theories about who was responsible and what the motives were, but nothing is certain. Her death is perhaps the reason hypatia has remained immortal over the centuries. Many researchers even divide the era of Paganism with Christianity according to the date of her death, in 415, compared to 529 when Justinian closed the Athenian School. Many hold Archbishop Kirill and the orders responsible for her death. The most reliable source for her death is from Socrates the School, who wrote about him some 25 years later. At that time, there was a lot of tension and hatred between the Jews and the Christians of Alexandria; is the time when the prefect Orestes and Archbishop Kirill (known by the harsh way in which he managed the heretic Nektarios) were at odds. About 500 monks arrived in the city to join the Archbishop. They accused Orestes (who was a baptized Christian) of being a pagan and of making sacrifices to the Greek gods contrary to the law of Theodosius that prohibited all kinds of idolatry. When a monk named Ammonius died because he had thrown a stone at the prefect, Cyril and the other Christians turned against Hypatia, who was at that time his assistant. Calling her the pagan witch and priestess, they stripped her and dragged her to the Cathedral, where they killed her by skinning and dismembering her with sharp shells. Her broken body was transported to Kynarion where she was burned. Although the prevailing view is that Cyril gave the order for her death, there is no evidence that he gave the order or knew the mob’s intent. Hypatia was eventually murdered, according to Socrates meticulously, by a portion of many Christians who believed that they were responsible for the non-reconciliation of the prefect Orestes and the Bishop of Alexandria Cyril ecclesiastical history Socrates the Scrupulous states: “The women in Alexandria, the name of The Land; This was the God of the philosopher’s daughter; And in the case of such an education, as if they were in the hands of the philosophers, and in the case of Platoniki from Plotinos, the theses were to be succeeded, and always the philosophical lessons of those who were willing to come; And all the philosophies who were all over the world were in the same way. For they gave her a modest presence from the child, and the lords came safely to the person; And it was not the men who were in the midst of it; For all of them, for they have now put them in a state of silence, and they have been amazed. Then the envy of the ↔; For it was more often the case that the Oreste, the devil, moved against her in spite of the church of the people, as if this were not the case, and I did not forgive Orest in friendship with the bishop. And the wise men of the spirit were warm, and Peter led the unknowns, and they saw the man who had died in the house; And in the church, when they were in the church, they were in the name of Caesarion, and they were in the middle of the night, and they were in the church, and they were in the church, and they were in the church, and they were in the church, and they were in the church, and they were in the church, and they were in the church, and they were in the church, and they were in the church, and they were in the church, and they were in the church, and they were in the church, and they were in the church, and they were in the church, and they were in the church, and they were in the church, and they were in the church, and they were in the church, and they were in And the members of the group broke up on the so-called Kinaron, and the members came under fire. This is not my little Cyril, and the Alexandrian church was in the work; for all the people who believe in Christ’s murders, and who fight and the like. And this is what happened in the fourth year of Cyril’s visit, in the presence of the Tenth, and Theodosius, in the month of March, who were in conflict, and even though he had many Christian friends. The fantasized mob stripped her naked, cut her down with fragments of vessels or sharp shells, and then burned its scattered and bloodthirsty members, a practice followed by the local mob in other cases, as in the case of Patriarch Preterios.
Various views have been expressed about the motives of her murder and the involvement of Kirill of Alexandria. According to Socrates the Meticulous, “the murder of this little man is against Cyril”, but without going into more detail.
- Asteroid 238 Hypatia, discovered in 1884, is named after this historical form.
- Numbers of Diofantos (comments)
- Comments on the Astronomical Rule of Ptolemy
- About the Conicals of Apollonius.