The first woman mathematician of whom we have reasonably secure and detailed knowledge



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The first woman mathematician of whom we have reasonably secure and detailed knowledge

  • The first woman mathematician of whom we have reasonably secure and detailed knowledge

  • Daughter of Theon of Alexandria, mathematician, astronomer, and member of the Museum

  • Taught mathematics and Neoplatonist philosophy in Alexandria

  • Most famous for her brutal murder (c.415 AD) by a group of zealous monks







One of the Fayum portraits: realistically painted portraits on wooden boards from Roman Egypt

  • One of the Fayum portraits: realistically painted portraits on wooden boards from Roman Egypt

  • They date from 1st century AD until about the middle of the 3rd century

  • a little early for our purpose, but gives an idea of what Hypatia might have looked like!

  • Other more modern pictures have been offered, and one or two Fayum portraits have been used

  • I chose this one because she's obviously scholarly!



as a martyr for women intellectuals

  • as a martyr for women intellectuals

  • as a martyr for liberated women generally

  • as a martyr for science and/or freedom of thought amid ‘restrictive’ Christianity

  • as a romantic heroine

  • journals, galleries etc named for her

  • romantic novels and even a film



Much of what has been written about her says more about the writer than it does about her

  • Much of what has been written about her says more about the writer than it does about her

  • Little of the above based on firm evidence...

  • These are the modern publications I’ve found most helpful:



Michael Deakin, Hypatia of Alexandria, Mathematician and Martyr (2007)

  • Michael Deakin, Hypatia of Alexandria, Mathematician and Martyr (2007)

  • Maria Dzielska, Hypatia of Alexandria (tr. F. Lyra, 1996)

  • Edward J. Watts, City and School in late antique Athens and Alexandria (2006)

  • Wilbur Knorr, Textual Studies in Ancient and Medieval Geometry (1989)



Suda Lexicon: 10th C encyclopaedia compiled from a number of sources

  • Suda Lexicon: 10th C encyclopaedia compiled from a number of sources

  • Patrologiae Graecae: collection of early Christian writings in Greek; edited in the 19th C by J. P. Migne (161 vols)

  • Together they cover:



Life of the philosopher Isidorus (c.450—c.520) by his Neoplatonist pupil Damascius (c.458–after 538)

  • Life of the philosopher Isidorus (c.450—c.520) by his Neoplatonist pupil Damascius (c.458–after 538)

  • Socrates Scholasticus Ecclesiastical History (c. 440)



Other sources:

  • Other sources:

  • Hypatia’s pupil Synesius of Cyrene

  • and what has come down to us of the mathematical commentaries of Theon and Hypatia



Complicated political and religious strife

  • Complicated political and religious strife

  • Christian Church still sorting out details of belief

  • Principle of Doctrinal Unity

  • Also:

  • Bitter political rivalry between Roman prefect Orestes (officially Christian) and Bishop Cyril



Neoplatonism

  • Neoplatonism

  • Ammonius Saccas (died c.265), pupil Plotinus (c.205–c.270), and later Iamblichus (c.245–c.325)

  • Plato’s Being-in-itself: the One extended to the Doctrine of “The One Beyond Being"

  • Intellectual, mystical, optional ritual

  • Three elements to it: Unity, Intelligence, Soul (interpretations of these very)



Founded (c.330 BC) by Alexander the Great

  • Founded (c.330 BC) by Alexander the Great

  • Greek in language and right from the start an intellectual tradition that was firmly Greek

  • Became the world’s first centre for learning

  • Cosmopolitan: Alexander (the Great) himself decreed equality of Greeks and non-Greeks



Euclid (c. 240 BC) Elements, Data, Optics

  • Euclid (c. 240 BC) Elements, Data, Optics

  • Apollonius of Perga (c. 200 BC) Conics

  • Eratosthenes c.276-c.195 BC

  • Ptolemy (c.100-c.170 AD) Geography, Astronomy (Almagest, Handy Tables)

  • Diophantus (fl.250 AD) Arithmetic

  • Pappus (c.290-c.350 AD-observed eclipse in 320) Collection, commentaries



Change of emphasis from primary research to conservation and explanation

  • Change of emphasis from primary research to conservation and explanation

  • Theon and Hypatia in the same tradition

  • Occurs as Alexandria becoming more turbulent and Museum under threat

  • Theon in introduction to Handy Tables complains that he is giving a more elementary account, “for the majority of his students are unable to understand geometrical proofs”



Observed eclipses of Sun and Moon in 364

  • Observed eclipses of Sun and Moon in 364

  • Possibly observed a minor conjunction in 377

  • Younger contemporary of Pappus

  • Generally agreed to have lived about 335-400

  • Last attested member of the Museum



Birth generally accepted as 350 – 375

  • Birth generally accepted as 350 – 375

  • Dzielska and Deakin argue for ~355

  • Death generally accepted as March (Lent) 415, although some argue for 416 or 417

  • Scholasticus says “Fourth year of Cyril’s episcopate”

  • Began 412



Taught maths by her father Theon

  • Taught maths by her father Theon

  • Damascius: “Having a nobler nature than her father's, she was not satisfied with his mathematical instruction, but she also embraced the rest of philosophy with diligence”

  • Famous in her time as a teacher of philosophy

  • Scholasticus: “She explained the principles of philosophy to her listeners, many of whom came from a distance to hear her”



Wider than Theon’s – included philosophy

  • Wider than Theon’s – included philosophy

  • Widely respected – none of the ancient sources questions her competence

  • Damascius: “Wearing the scholar’s cloak in the centre of the city, she explained publicly to those who wished to hear either Plato or Aristotle or any other of the philosophers”

  • “Skillful and eloquent in words and prudent and civil in deeds”



“The city loved and honored her exceptionally”

  • “The city loved and honored her exceptionally”

  • “Those who were appointed at any time as rulers of the city came first to attend her lectures”

  • “On account of the self-possession and ease of manner, which she had acquired through the cultivation of her mind, she not infrequently appeared in public in presence of the magistrates”



“Neither did she feel abashed in going to an assembly of men”

  • “Neither did she feel abashed in going to an assembly of men”

  • “For all men on account of her extraordinary dignity and virtue admired her the more”

  • “Attaining the height of practical virtue, becoming just and prudent, she remained a virgin”



“She was so very beautiful and attractive that one of those who attended her lectures fell in love with her. He was not able to contain his desire, but he informed her of his condition”

  • “She was so very beautiful and attractive that one of those who attended her lectures fell in love with her. He was not able to contain his desire, but he informed her of his condition”

  • “Ignorant reports say that Hypatia relieved him of his disease by music; but truth proclaims that music failed to have any effect”





It’s not known whether the young man continued as a student, worshipping her more chivalrously from afar...

  • It’s not known whether the young man continued as a student, worshipping her more chivalrously from afar...

  • One who did worship her with intellectual respect was her pupil Synesius



Came of patrician family in Cyrene

  • Came of patrician family in Cyrene



Great letter writer – about 160 survive, along with other works

  • Great letter writer – about 160 survive, along with other works

  • Many are directly relevant to his Alexandrian circle, including Hypatia, whom he calls

  • “mother, sister, teacher, benefactress in all things”



Born in the 370s, he studied in Alexandria in early 390s

  • Born in the 370s, he studied in Alexandria in early 390s

  • Mid 390s he spent some time in Athens

  • In 398 he was chosen as an envoy to the imperial court in Constantinople, to obtain tax remissions for his country

  • About 403 returned to Alexandria, where he married and started a family, before returning to Cyrene c. 405.



There he spent his time, “studying philosophy, mathematics, astronomy, everything; farming, hunting, having many a brush with hordes of pilfering Libyans; and every now and then upholding the cause of someone who had undeservedly fallen into difficulties”

  • There he spent his time, “studying philosophy, mathematics, astronomy, everything; farming, hunting, having many a brush with hordes of pilfering Libyans; and every now and then upholding the cause of someone who had undeservedly fallen into difficulties”

  • About 410 consecrated Bishop by the Patriarch Theophilus of Alexandria

  • Against his will, but he did the job faithfully



Throughout, he writes to his friends recalling good times as students under Hypatia

  • Throughout, he writes to his friends recalling good times as students under Hypatia

  • Consulted Hypatia on philosophy, publication of books, asked for her help for his friends (she had influence in high places)

  • Praises her highly in his dedication of a gift of an astrolabe to an influential official

  • Asks her, on his sickbed, to supply him with a hydroscope (hydrometer)

  • Addresses his last letter to her

  • Cuts a rather tragic figure...



It’s through Synesius that we know that her pupils came from far and wide

  • It’s through Synesius that we know that her pupils came from far and wide

  • They came for a cultural training

  • They made friends for life

  • Many were Christian

  • They became bishops, government officials, estate owners with a high interest in culture...

  • ...i.e. good solid members of the establishment



This training suited their diverse backgrounds and interests

  • This training suited their diverse backgrounds and interests

  • A philosophy that aimed to reveal deep truths about God and the nature of the world

  • Involved no ritual

  • Did not openly conflict with Christian thought

  • In a city with a Christian majority she remained a popular teacher

  • Students’ lasting bonds of friendship encouraged them in intensive contemplation and personal temperance



Suda: She wrote a commentary on Diophantus (Arithmetic), the Astronomical Canon, and a commentary on the Conics of Apollonius

  • Suda: She wrote a commentary on Diophantus (Arithmetic), the Astronomical Canon, and a commentary on the Conics of Apollonius

  • Theon: commentary on Book III of Almagest, proudly wrote of contribution of “my daughter Hypatia, the philosopher”

  • Synesius mentions Astrolabe, hydroscope (hydrometer)







Synesius, in a long flattering letter to a influential official Paeonius:

  • Synesius, in a long flattering letter to a influential official Paeonius:

  • “I am therefore offering you a gift most befitting for me to give, and for you to receive. It is a work of my own devising, including all that she, my most revered teacher [Hypatia], helped to contribute, and it was executed by the best hand to be found in our country in the art of the silversmiths.”



Since we don’t know what Hypatia’s contribution may have been, we can only describe the instrument as it was known in her time

  • Since we don’t know what Hypatia’s contribution may have been, we can only describe the instrument as it was known in her time

  • An astrolabe is a two-dimensional model of the celestial sphere

  • Often attributed to Hipparchus (c.180 BC)

  • Theon wrote about it; Ptolemy (c.100-c.170 AD) used it in his astronomical observations

  • Hypatia taught Synesius about it





Used to make accurate measurements of the following things:

  • Used to make accurate measurements of the following things:

  • position of celestial objects

  • the time of the night (or the day)

  • the season of the year

  • compute what part of the sky is visible at any time

  • determine the altitude of any object above the horizon

  • determine the current latitude







Eight books (c. 200 BC)

  • Eight books (c. 200 BC)

  • Books I-IV have come down to us in Greek via a commentary by Eutocius (early 6th C)

  • Books V-VII through Arabic translations

  • Book VIII is lost

  • It’s thought that Eutocius only covered the first four



Introduced the names ellipse, parabola, hyperbola for the three cases

  • Introduced the names ellipse, parabola, hyperbola for the three cases

  • He showed that all three varieties can be obtained from a single cone, by varying the angle.

  • Used an oblique cone

  • Introduced double napped cone



Material in I-IV already known, but he arranged it more systematically and added some original material. The other books contain his own discoveries

  • Material in I-IV already known, but he arranged it more systematically and added some original material. The other books contain his own discoveries

  • The Suda says that Hypatia wrote a commentary – no more detail and nothing survives, but it’s possible that Eutocius had access to it for his work.

  • Knorr’s studies of style and language support this idea, i.e.

  • Author with access to text, revised by an editor



Sometimes called "the father of algebra“

  • Sometimes called "the father of algebra“

  • Series of 13 books, the Arithmetica

  • First to recognise fractions as numbers

  • Deals with algebraic equations, usually with integer coefficients, for which integer solutions are sought

  • Both determinate and indeterminate equations

  • Pierre de Fermat: certain equation had no solutions, hence famous marginal note



Six books of the Arithmetica have come down to us in Greek (Byzantium), and another four recently (1968) identified in Arabic translation

  • Six books of the Arithmetica have come down to us in Greek (Byzantium), and another four recently (1968) identified in Arabic translation

  • Enormous stylistic differences:

  • Greek sparse and to the point, Arabic prolix and repetitive

  • One of these may be based on Hypatia’s commentary (Suda). If so, which?



Greek:

  • Greek:

  • In Book II, the early problems repeat material from Book I

  • But problems 6 and 7 are thought to be later additions because they look like a couple of student exercises

  • i.e. simple revision of material before advancing to something more difficult

  • Problem 7 contains a nine-word phrase identical with one in Theon’s edition of Euclid’s Data



Arabic:

  • Arabic:

  • Concludes each problem with a check that the answer is indeed correct, and adds a recapitulation of the work done

  • The style of a good teacher writing for a weaker generation of students who need all the help they can get?



In keeping with his teaching, Theon produced a commentary

  • In keeping with his teaching, Theon produced a commentary

  • Heading of Book III announces that it is his commentary, “the edition having been prepared by the Philosopher, my daughter, Hypatia”

  • Precise meaning unclear, has been disputed



The Almagest is the only surviving comprehensive ancient treatise on astronomy

  • The Almagest is the only surviving comprehensive ancient treatise on astronomy

  • Mathematical treatise on the apparent motions of the stars and planets

  • Original title Mathēmatikē Syntaxis; later Hē Megalē Syntaxis. Thus Arabic name al-majisṭī, from which the English name Almagest derives



Mathematician, astronomer, geographer, astrologer, and poet of a single epigram in the Greek Anthology:

  • Mathematician, astronomer, geographer, astrologer, and poet of a single epigram in the Greek Anthology:

  • I know that I am mortal by nature, the creature of a day.

  • But when I trace at my pleasure the windings to and fro of the heavenly bodies,

  • I no longer touch the earth with my feet.

  • I stand in the presence of Zeus himself,

  • And take my fill of ambrosia, the food of the gods.



Like many Greek works on science and philosophy, preserved for us by Arabic scholars at Baghdad

  • Like many Greek works on science and philosophy, preserved for us by Arabic scholars at Baghdad

  • Translated into Latin by Gerard of Cremona c. 1114–1187, working in Toledo

  • One of the most influential scientific texts of all time

  • Remained popular until the time of Copernicus, Kepler, and Galileo



  • The student from The Milleres Tale:

  • His alms geste, and bokes gret and smale,

  • His astrelabe, longing for his art,

  • His augrim stones, layen faire aparte

  • On shelves couched at his beddes hed...



“The edition having been prepared by the Philosopher, my daughter, Hypatia”

  • “The edition having been prepared by the Philosopher, my daughter, Hypatia”

  • 1. Did Hypatia (more menially) prepare an edition of the text, while her father prepared the commentary? (Cameron)

  • 2. Is this an improved edition of the commentary, superseding one of Theon’s own? (Deakin, Knorr)



A. Rome (1943) put forward the idea of comparing Book III of the commentary (with Hypatia’s involvement) with Books I and II (presumably Theon alone)

  • A. Rome (1943) put forward the idea of comparing Book III of the commentary (with Hypatia’s involvement) with Books I and II (presumably Theon alone)

  • Stylistically inconclusive, but

  • A method for “long division” in Book III (length of the year and the motion of the Sun) differs from that explained in Book I in that it’s more systematic



Knorr continues this kind of analysis into the later books, and sees Hypatia’s hand in calculations also in Book IV, but not in Book IX

  • Knorr continues this kind of analysis into the later books, and sees Hypatia’s hand in calculations also in Book IV, but not in Book IX

  • This approach is obviously speculative and has been criticised, but there’s something reasonable to it as well



Book III covers the length of the year and the motion of the Sun

  • Book III covers the length of the year and the motion of the Sun

  • Greek value for the number of days in a year was: 365.24666 (cf. 365.242199)

  • The question was to determine the number of degrees of arc swept out in a single day, i.e. 360 ÷ 365.24666





While Theophilus was bishop (384-412), things were fairly safe for Hypatia

  • While Theophilus was bishop (384-412), things were fairly safe for Hypatia

  • He had no love for pagans and could be a ruthless and violent opponent

  • Many riots in his time between Christians and Pagans, including Neoplatonist teachers

  • In 391 these more “muscular” Neoplatonists occupied the Serapeum, the main Pagan temple, dedicated to the Alexandrian patron god Serape



It seems that Hypatia and Theon distanced themselves from this disturbance – they were of a more intellectual, less ritualistic brand

  • It seems that Hypatia and Theon distanced themselves from this disturbance – they were of a more intellectual, less ritualistic brand

  • The occupiers were granted an amnesty by Emperor Theodosius provided all pagan images were destroyed, and Theophilus razed the temple



However, Theophilus seemed content to let Hypatia be:

  • However, Theophilus seemed content to let Hypatia be:

  • Tolerated her school, her “product” (all good solid members of the establishment) - made 2 of them bishops

  • Tolerated her connections with local power structures, including government prefects

  • This all changed with his death in 412



Violent conflict over succession between his nephew Cyril and his archdeacon Timothy

  • Violent conflict over succession between his nephew Cyril and his archdeacon Timothy

  • After three days of street fighting, Cyril won

  • Cyril immediately set about settling scores: Timothy’s supporters, the Jews, the Pagans



This violence angered the Prefect Orestes, who wrote to the Emperor about it

  • This violence angered the Prefect Orestes, who wrote to the Emperor about it

  • Orestes was nearly killed in a riot by Cyril’s supporters. Orestes had ringleader arrested and tortured

  • He didn’t survive the experience

  • Power struggle spiralled



Hypatia, along with moderate city officials (Christian, like Orestes, and probably supported Timothy) was in Orestes’ camp

  • Hypatia, along with moderate city officials (Christian, like Orestes, and probably supported Timothy) was in Orestes’ camp

  • She had international influence through her students

  • Synesius was dead by then, succeeded by brother Euoptius



Damascius: Cyril driving through the city

  • Damascius: Cyril driving through the city

  • “When he learned this, his soul was bitten with envy”

  • Rumours were spread that it was Hypatia who prevented Orestes from being reconciled to the bishop

  • Damascius, “Many close-packed ferocious men, truly despicable, fearing neither the eye of the gods nor the vengeance of men... rushed at her and killed her”







Both Cyril and Orestes wrote to the Emperor

  • Both Cyril and Orestes wrote to the Emperor

  • One of the Emperor’s officials got bribed

  • No-one was brought to book

  • Cyril hailed as “New Theophilus, for he had destroyed the last remains of idolatry in the city” - and was later made a saint

  • Scholasticus: inflicted very great pollution and shame on their homeland

  • Damascius: blood-guilt and disgrace

  • Intellectuals drifted away to Athens



More famous and more highly honoured than her persecutor

  • More famous and more highly honoured than her persecutor

  • Might not have been so well remembered if she hadn’t been brutally murdered

  • We know we owe much to her for what has come down to us of Euclid, Apollonius, Diophantus, Ptolemy and others







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