Hypatia of Alexandria: Sifting the Myths Fenny Smith

1. Hypatia of Alexandria: Sifting the MythsFenny Smith Part of Women in Mathematics: The Bicentenary of Ada Lovelace BSHM/Gresham College, Thursday 29 October 2015

2. Hypatia (c.355-415 AD) • 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

3. The pictures

4. The Fayum PortraitsEgypt,1st to 3rd Century AD

5. The picture • 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!

6. Much “iconised” • 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

7. “Sources” • 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:

8. Secondary sources • 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)

9. Ancient 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:

10. Ancient sources • Life of the philosopher Isidorus (c.450—c.520) by his Neoplatonist pupil Damascius (c.458–after 538) • Socrates Scholasticus Ecclesiastical History (c. 440)

11. Ancient sources Other sources: • Hypatia’s pupil Synesius of Cyrene • and what has come down to us of the mathematical commentaries of Theon and Hypatia

12. 4th/5th C AlexandriaQuick background summary • 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

13. 4th/5th C AlexandriaReligious background • 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)

14. 4th/5th C AlexandriaIntellectual background • 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

15. 4th/5th C Alexandria Mathematical background • 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

16. 4th/5th C Alexandria Mathematical background • 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”

17. Dates: Theon • 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

18. Dates: Hypatia • 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

19. Hypatia’s maths • 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”

20. Hypatia’s teaching • 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”

21. Hypatia’s teaching • “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”

22. Hypatia’s teaching • “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”

23. Hypatia’s teaching • “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”

25. Hypatia’s teaching • 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

26. Synesius • Came of patrician family in Cyrene

27. Synesius • 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”

28. Synesius • 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.

29. Synesius • 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

30. Synesius • 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...

31. Hypatia’s teaching • 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

32. Hypatia’s teaching • 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

33. Hypatia’s maths • 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)

34. Hydroscope (Letter 15) I am in such evil fortune that I need a hydroscope. See that one is cast in brass for me and put together. The instrument in question is a cylindrical tube, which has the shape of a flute and is about the same size. It has notches in a perpendicular line, by means of which we are able to test the weight of the waters. A cone forms a lid at one of the extremities, closely fitted to the tube...

35. Hydroscope (Letter 15) ... The cone and the tube have one base only. This is called the baryllium. Whenever you place the tube in water, it remains erect. You can then count the notches at your ease, and in this way ascertain the weight of the water.

36. Astrolabe • 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.”

37. Astrolabe • 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

39. Astrolabe 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

40. Astrolabe

41. Astrolabe

42. Apollonius and conic sections • 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

43. Apollonius and conic sections • 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

44. Apollonius and conic sections • 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

45. Diophantus (c. 275 AD) • 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

46. Diophantus (c. 275 AD) • 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?

47. Diophantus (c. 275 AD) 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

48. Diophantus (c. 275 AD) 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?

49. Book III of Almagest • 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

50. Claudius Ptolemy (c. 150 AD) • 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. ThusArabic name al-majisṭī, from which the English name Almagest derives