Hypatia's work on Diophantus

Hypatia's work on Diophantus


In the 10th century Suda Lexicon, Hesychius' 6th century material was summarized: "She wrote a commentary on Diophantus, the Canon of Astronomy and a commentary on the conics of Appolonius".

From The Primary Souces for the Life and Work of Hypatia of Alexandria, by Michael A.B. Deakin

It was once thought that the surviving Greek text of Diophantus' Arithmetic held portions due to Hypatia, but this hypothesis is no longer tenable. Further portions of this work have recently been unearthed, in Arabic translation. Comparison of the Greek and the Arabic versions make it clear that if any of Hypatia's work survives it is in the Arabic rather than the Greek. The most likely Hypatian material is the detailed checking that the solutions are valid.

For more discussion with translation of the original text, see J. Sesiano's Books IV to VII of Diophantus' Arithmetica (New York: Springer, 1982) and R. Rashed's Diophante: Les Arithmé tiques, Tome III, Livre IV; Tome IV, Livres V, VI, VII (Paris: Socié té d'é dition "Les belles lettres", 1984). Sesiano and Rashed are the two foremost authorities on this material, but they differ deeply and acrimoniously over many points. The question of Hypatia's involvement in this material is still very much under discussion.

From Hypatia's Mathematics: A Review of Recent Studies, by Edith Prentice Mendez

"She wrote a commentary on Diophantus. . ." Historians have debated the existence, nature, and extent of Hypatia's commentary. Tannery, disagreeing with an earlier editor Bachet (1621), who supposed that Hypatia must have written on an astronomical work of Diophantus, asserted that her commentary must have been on the Arithmetica [46]. Heath declared that Tannery misread Bachet and that Bachet had also concluded that Hypatia wrote on Diophantus' Arithmetica. Heath in 1885 was doubtful that Hypatia wrote on Diophantus at all. He felt that the citation from the Suda could not be trusted because of its mention that Hypatia wrote an astronomical canon when "we know of no astronomical work after that of Claudius Ptolemy" [16, 9-10]. . Heath also dismissed the conjecture of Kuster (1705) that the Suda passage implied that Hypatia's commentary was on an astronomical table by Diophantus, since there is no evidence of astronomical work by Diophantus [16, 8]. By 1921, Heath spoke more positively of both Hypatia, as the first Diophantus commentator, and of "the attractive hypothesis of Tannery that Hypatia's commentary extended only to our six Books, and that this accounts for their survival when the rest were lost" [17, 453]. According to Sesiano, the existing Greek text of the Arithmetica shows no signs of reworked problems or systematic commentary, so this hypothesis cannot hold. In his view, the recently discovered Arabic text might well be a translation of Hypatia's commentary [42, 71]. Sesiano's hypothesis is that Hypatia, or some other commentator "at about the time of the decline of Greek mathematics" [42, 71], wrote on Books I to VII of Diophantus' thirteen books, that these were translated into Arabic, and that the books IV to VII were eventually copied, in 1198, into the manuscript Sesiano studied [42, 75]. This commentary entailed a complete rewriting at a level for students, showing "relative mediocrity. . .hardly compatible with Hypatia's renown. . .she may simply have been a good mathematician in a bad time" [42, 71-72]. Knorr disputes this hypothesis as demeaning to Hypatia's reputation and inconsistent with the standard transmission of texts in which old works are displaced by newer recensions [23]. Allard and Rashed also disagree, claiming that Sesiano has not proved his hypothesis, but merely restated a conjecture of Tannery's which was continued by Bashmakova [1]. Bashmakova accepts the existence of a Diophantine commentary by Hypatia, but not its preservation [2, 56]. Tannery hypothesized that Hypatia's commentary preserved part of the Arithmetica as Eutocius preserved part of the Conics [47]. He identified some problems as possibly due to Hypatia; Waithe gives an English translation of several of these [54, 177-180].

Classroom Discussion

  • Discuss the above
  • Discuss p. 176-183 from Waithe's A History of Women Philosophers on Tannery's theories and translation of sections from Diophantus Arithmetica that Hypatia possibly worked on. I went over p. 180 II.XVII. and then each student chose some other problem to go thru and then present to the rest of the class.