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Independent writings

Hypatia wrote a commentary on Diophantus 's thirteen-volume Arithmetica, which had been written sometime around the year 250 AD. It set out more than 100 mathematical problems, for which solutions are proposed using algebra. For centuries, scholars believed that this commentary had been lost. Only volumes one through six of the Arithmetica have survived in the original Greek, but at least four additional volumes have been preserved in an Arabic translation produced around the year 860. The Arabic text contains numerous expansions not found in the Greek text, including verifications of Diophantus's examples and additional problems.

Cameron states that the most likely source of the additional material is Hypatia, since Hypatia is the only ancient writer known to have written a commentary on the Arithmetica and the additions appear to follow the same methods used by her father Theon. The first person to deduce that the additional material in the Arabic manuscripts came from Hypatia was the nineteenth-century scholar Paul Tannery. In 1885, Sir Thomas Heath published the first English translation of the surviving portion of the Arithmetica. Heath argued that surviving text of Arithmetica is actually a school edition produced by Hypatia to aid her students. According to Mary Ellen Waithe, Hypatia used an unusual algorithm for division (in the then-standard sexagesimal numeral system), making it easy for scholars to pick out which parts of the text she had written.

The consensus that Hypatia's commentary is the source of the additional material in the Arabic manuscripts of the Arithmetica has been challenged by Wilbur Knorr, a historian of mathematics, who argues that the interpolations are "of such low level as not to require any real mathematical insight" and that the author of the interpolations can only have been "an essentially trivial mind... in direct conflict with ancient testimonies of Hypatia's high caliber as a philosopher and mathematician." Cameron rejects this argument, noting that "Theon too enjoyed a high reputation, yet his surviving work has been judged 'completely unoriginal.'" Cameron also insists that "Hypatia's work on Diophantus was what we today might call a school edition, designed for the use of students rather than professional mathematicians."

Hypatia also wrote a commentary on Apollonius of Perga 's work on conic sections, but this commentary is not extant. She also created an " Astronomical Canon "; this is believed to have been either a new edition of the Handy Tables by the Alexandrian Ptolemy or the aforementioned commentary on his Almagest. Based on a close reading in comparison with her supposed contributions to the work of Diophantus, Knorr suggests that Hypatia may also have edited Archimedes ' Measurement of a Circle, an anonymous text on isometric figures, and a text later used by John of Tynemouth in his work on Archimedes' measurement of the sphere. A high degree of mathematical accomplishment would have been needed to comment on Apollonius's advanced mathematics or the astronomical Canon. Because of this, most scholars today recognize that Hypatia must have been among the leading mathematicians of her day.