HYPATIA

(d. Alexandria, 415), mathematical commentaries, philosophy. For the original article on Hypatia, see DSB, vol. 6.

Hypatia was the daughter of Theon of Alexandria and the only woman in antiquity for whom historians have some positive evidence of her mathematical activities. However, the information about her achievements in this and other fields is particularly scanty, and comes either from authors, such as Christian writers, that were overtly hostile to her or from sources not favorably oriented. The latter is the case of Damascius’ testimony, making up the bulk of the entry of the Suidas lexicon. Such biased reports have exposed even the reasons and the oft-repeated circumstances of her murder to scholarly romancing.

Hypatia was renowned as a philosopher, but only conjectures can be made about her philosophical allegiances and her teaching. The former have been characterized either as Cynic, on the basis of tendentious and caricatural remarks by Damascius, or Neoplatonic with a strong Iamblichean tinge, mainly because of analogous doctrines embraced in the works of her pupil Synesius of Cyrene. No testimony about her philosophical writings has survived, and it is reasonable to doubt that any such writings ever existed. It seems sufficiently established that a circle of pupils of remarkable intellectual level gathered around her, but it is not clear whether her teaching was a public or a private one, whether formal or informal, and there is not the slightest hint that she held an official chair. She was never the head of the Neoplatonic school in Alexandria.

Damascius asserts that his master Isidorus was superior to Hypatia as a philosopher is to a mathematician. At best this suggests that Hypatia was probably no first-rank philosopher, and Isidorus was definitely a very bad mathematician. To be sure, it is no great virtue to be a good mathematician in a period in which this meant being able

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to understand and expound the mathematical proofs in the treatises of the canonical authors.

In fact, the only two sources mentioning Hypatia’s mathematical achievements attest that she was engaged in composing commentaries. The Suidas, drawing from Hesychius, reports that she “Here wrote a commentary on Diophantus, the astronomical table, a commentary on Apollonius’ Conics” (Adler, 1935, 644.3-5). The inscription of Theon’s commentary on Almagest III reads “Commentary of Theon of Alexandria on the third of Ptolemy’s Mathematical Syntaxis, the edition having been proof-read by the philosopher Hypatia, my daughter” (Rome, 1943, p. 807). Both testimonies raise serious problems. The wording of the former probably requires emendations and does not allow the reader to decide whether Hypatia wrote an astronomical table or a commentary on such a work (in this case almost surely Ptolemy’s Handy Tables). The latter option can be doubted, because Theon already had written two commentaries on the same work. However, writing an astronomical table is not the same as editing the text of the Handy Tables and the latter proposal too should be dismissed. Even more implausible is the hypothesis that Hypatia compiled new tables of which nothing has survived.

As for the second testimony, one interpretation pictures Hypatia as proofreading the text of the Almagest itself in assistance to her father’s effort as a commentator, thereby procuring a reliable edition of Ptolemy’s treatise. Yet, the minimal interpretation that Hypatia simply checked the final version of Theon’s commentary on book III appears by far the most plausible one. Theon’s exegeses were first performed as lectures and then redacted in due form, and a checking was necessary-given the presence of non-trivial calculations. Such an authorized copy was the edition alluded to by the inscription. Parallel passages in Eutocius’ commentaries confirm that this was the current practice. There have been attempts to detect stylistic differences between the third and the other books of Theon’s commentary, but the result is that no differences subsist. A recent and thorough search for Hypatia’s own contributions to book III itself rests on arbitrary assumptions about her style and is at bottom circular. Attempts, based on the same stylistic criteria, at assigning Hypatia a role in the very complex tradition of Archimedes’ Dimensio circuli and at singling out relics from her commentary in the extant commentary by Eutocius on Apollonius’ Conics, must be regarded as highly hypothetical speculations as well.

Many of the above proposals rest on the questionable assumption that a wide-ranging enterprise of editing and commenting on mathematical texts was undertaken by Theon and his circle. On the contrary, Theon apparently wrote no commentaries on the only two works historians can be reasonably sure he edited, the Elements and the Data, whereas he commented on treatises that researchers have not the slightest reason to suspect he edited. An analogous net of conjectures has been built upon Hypatia’s alleged commentary on Diophantus’ Arithmetica. The Greek text is incomplete. To explain this, it can be surmised that Hypatia procured a revised and commented text; her commentary arrived as far as the sixth book only and this entailed that the remaining seventh book got lost. The discovery of an Arabic version, containing four more books, disproves such a hypothesis. In its turn, the Arabic text, fairly different in its format, has led to conjecture that it is the translation of a text commented by Hypatia. Difficulties with this proposal are that the Arabic version is a new recension of the treatise, not a commentary, and normally a commentary does not interfere with the text in such a way. Moreover, the modifications with respect to the format of the Greek text are extensive but of no mathematical relevance. It is more charitable to deny than to affirm any Hypatian authorship to such worthless and pedantic additions.

In a letter to a certain Paeonius, Synesius provides a rather clumsy description of a plane astrolabe. As Theon is reported to have written a treatise on the construction of the astrolabe, it is likely that Synesius directly drew from that work, even if he mentions Hypatia as his teacher on the matter. A reference to a hydroscope in a letter of Synesius to Hypatia is too obscure to be explained except arbitrarily. Such a quantity of entirely conjectural reconstructions is self-perpetuating, as any new hypothesis is allegedly supported by all the others taken as established facts, and very often they consist in questionable projections of doctrines and textual formats typical of some of the works of Hypatia’s pupils or relatives.

SUPPLEMENTARY BIBLIOGRAPHY

Adler, A. ed. Lexicographi Graeci. Vol. I. Suidae Lexicon A-W.Index. Pars 4: P-Y. Leipzig: B.G. Teubner, 1935, 644–646. The entry in Suidae Lexicon, vol. IV: 644–646 is the main source on Hypatia. Adler draws in part from Damascius (hence a portion of the entry is edited as fragments 102–105 of Damascius, Vita Isidori (see following citation).

Damascius. Vita Isidori. Edidit Adnotationibusque Instruxit C. Zintzen. Hildesheim: Georg Olms Verlag, 1967, fragments. 102–105. A part of the S uidas entry on Hypatia comes from this work and is here re-edited in the form of fragments.

Cameron, Alan. “Isidore of Miletus and Hypatia: On the Editing of Mathematical Texts.” Greek, Roman and Byzantine Studies 31 (1990): 103–127. This article contains the analysis of the inscription to Theon’s Commentary, Book III and the proposal that Hypatia edited the Almagest.

Cameron, Alan, and Jacqueline Long. Barbarians and Politics at the Court of Arcadius. Berkeley: University of California Press, 1993, 39–62. The authors present a detailed discussion of the extant evidence, still over-optimistic in its assessment of the sources.

Charles, R.H. (trans.), The Chronicle of John, Bishop of Nikiu. Oxford: Oxford University Press, 1916, 100–102. A further source on Hypatia. The text is currently available only as an English translation of an Ethiopian version of a (lost) Arabic translation.

Dzielska, Maria. Hypatia of Alexandria. Cambridge, MA: Harvard University Press, 1996. Presents an extensive discussion of the extant evidence and contains a very rich bibliography.

Jones, Alexander. “Uses and Users of Astronomical Commentaries in Antiquity.” In Commentaries – Kommentare, edited by Glenn W. Most. Aporemata: Kritische Studien zur Philologiegeschichte, Band 4.Göttingen: Vandenhoeck und Ruprecht, 1999, 149–172. Alan Cameron’s conclusions are criticized in this article.

Knorr, Wilbur R. Textual Studies in Ancient and Medieval Geometry. Boston: Birkhäuser, 1989, 753–84. Hypatia’s contributions to several extant commentaries and edited works are here singled out.

Rome, Adolphe. Commentaires de Pappus et de Théon d’Alexandrie sur l’Almageste. Tome III: “Théon d’Alexandrie,” Commentaire sur les livres 3 et 4 de l’Almageste. Texte établi et annoté par A. Rome. Città del Vaticano: Biblioteca Apostolica Vaticana, 1943: cxvi-cxxi. The introduction contains the first stylistic analysis of Theon’s Commentary.

Saffrey, Henri D. “Hypatie d’Alexandrie.” In Dictionnaire des Philosophes Antiques, edited by Richard Goulet. Paris: CNRS Editions, 2000. A first orientation, with bibliography, on Hypatia’s possible philosophical affiliations.

Sesiano, Jacques, trans. Books IV to VII of Diophantus’ Arithmetica. Attributed to Qustâ ibn Lûqâ. New York: Springer-Verlag, 1982, 68–75. Hypatia’s role in the tradition of Diophantus’ Arithmetica is discussed here.

Socrates. Historia Ecclesiastica. In Patrologiae Cursus Completus, Accurante J.-P. Migne. Patrologiae Graecae Tomus 67. Paris: 1864, VII.13–15. A well-balanced exposition of Hypatia’s life by a her contemporary.

Synésios de Cyrène, Tome II: Correspondance: Lettres I-LXIII; Tome III: Correspondance: Lettres LXIV–CLVI. Texte établi par A. Garzya, traduit par D. Roques. Paris: Les Belles Lettres, 2000.

Tannery, Paul. “L’article de Suidas sur Hypatia.” Annales de la Faculté des Lettres de Bordeaux, 2 (1880): 197–201, reprinted in Mémoires Scientifiques, tome I (1912), no. 7: 74–79. This first critical discussion of the Suidas entry was valuable into the early 2000s.

Fabio Acerbi

Hypatia

(b. Alexandria, Egypt, ca. 370; d. Alexandria, 415)

mathematics, philosophy.

Hypatia, the first woman in history to have lectured and written critical works on the most advanced mathematics of her day, was the daughter and pupil of the mathematician Theon of Alexandria. It is believed that she assisted him in writing his eleven-part treatise on Ptolemy’s Almagest and possibly in formulating the revised and improved version of Euclid’s Elements that is the basis of all modern editions of the work. According to Suidas she composed commentaries not only on the Almagest but also on Diophantus’ Arithmetica and Apollonius’ Conic Sections. None of them survives.

Although accurate documentation of Hypatia’s activities is lacking, it is known that she lectured in her native city on mathematics and on the NeoPlatonic doctrines of Plotinus and Iamblichus and that about A.D. 400 she became head of the Neoplatonic school in Alexandria. Her classes attracted many distinguished men, among them Synesius of Cyrene, later bishop of Ptolemais. Several of his letters to Hypatia are extant, They are full of chivalrous admiration and reverence. In one he asks her how to construct an astrolabe and a hydroscope.

In spite of her association with Synesius and other Christians, Hypatia’s Neoplatonic philosophy and the freedom of her ways seemed a pagan influence to the Christian community of Alexandria. Prejudice was strengthened by her friendship with Orestes, Roman prefect of the city and political enemy of Cyril, bishop of Alexandria. The mounting hostility culminated in her murder by a fanatic mob. None of her writings was preserved; but the general loss of Hellenic sources must be blamed on repeated book-burning episodes rather than on lynching. The great Alexandrian library had been burned by Roman soldiers long before Hypatia’s day, and during her lifetime the valuable library in the temple of Serapis was sacked by an Alexandrian mob.

Hypatia has been the subject of much romantic drama and fiction, including the 1853 novelHypatiaor New Foes With an Old Face, by Charles Kingsley. Such works have perpetuated the legend that she was not only intellectual but also beautiful, eloquent, and modest.

BIBLIOGRAPHY

See T. L. Heath, History of Greek Mathematics, II (Oxford, 1921), 528-529; A. W. Richeson, “Hypatia of Alexandria,” in National Mathematics Magazine, 15, no 2 (Nov. 1940), 74-82; Socrates Scholastics, Ecclesiastical History, VII (London, 1853), 15; Suidae Lexicon, Ada Adler, ed., I (Leipzig, 1928), 618; B. L. van der Waerden,Science Awakening (New York, 1961), 290.

Edna E. Kramer

Hypatia

Greek Philosopher and Mathematician
370–415 c.e.

Hypatia of Alexandria was a leading mathematician and philosopher of the ancient era. Her father, Theon, was the last known head of the Museum at Alexandria, Egypt, an ancient center of classical learning. He tutored Hypatia and passed on to her his love of mathematics. Eventually her reputation as a mathematician exceeded and outlasted his.

Only fragments of Hypatia's work and a list of several titles of her treatises on mathematics remain. She translated and popularized the works of Greek mathematicians, including Diophantus's (third century) Arithmetica, a book noted for integral solutions to linear equations , and Apollonius's Conic Sections. Hypatia also edited the Almagest, an important work by the Greek astronomer and mathematician Claudius Ptolemy. She taught and wrote about a number of math topics on which further progress was not made until centuries later.

One of Hypatia's most eminent students, Synesius, wrote her letters asking her advice on scientific matters, and these letters are one of the key sources about her work. He credits her with detailed knowledge of the astrolabe and the hydroscope , as well as other devices used for studies in astronomy and physics. Historians living in her time praised her learning, as well as her beauty and character.

Hypatia's ties to a politician who disagreed with Alexandria's Christian bishop led to Hypatia's death in 415 c.e., when she was murdered by a mob of religious fanatics. Following Hypatia's murder, many of her students migrated to Athens, which by 420 c.e. acquired a considerable reputation in mathematics.

All of Hypatia's works are believed to have been lost in the seventh century, when the books of the library at Alexandria were burned by Arab invaders.

see also Apollonius of Perga.

Shirley B. Gray

Bibliography

Deakin, Michael. "Hypatia and Her Mathematics." American Mathematical Monthly 101 (1994): 234–243.

Narins, Brigham, ed. World of Mathematics. Detroit: Gale Group, 2001.

Olsen, Lynn M. Women in Mathematics. Cambridge, MA: MIT Press, 1974.

Hypatia (c.370–415), Greek philosopher, astronomer, and mathematician. Head of the Neoplatonist school at Alexandria, she wrote several learned treatises as well as devising inventions such as an astrolabe. She was murdered by a Christian mob opposed to her Neoplatonist philosophy.

Hypatia (Neo-Platonic philosopher): see CYRIL, ST.