No, she bleedin’ weren’t!
That was my buddy the HISTSCI_HULK expostulating whilst he was indulging in his annoying habit of peering over my shoulder whilst I’m reading.
She never was! That’s simply wrong!
Hulky was getting his nickers in a twist about the following claim:
Hypatia was by all accounts, a fine astronomer and a first rank mathematician…[1]
He bleedin’ weren’t either! Exploded Hulky as he read further on:
…her father, an equally formidable mathematician…
Hulky is, of course, totally correct. Hypatia’s father was Theon of Alexandria and although such judgements are to a large extent subjective, in the normal run of things nobody would classify Theon as a formidable mathematician or Hypatia a fine astronomer and a first rank mathematician.
We start with Theon from whom Hypatia appears to have learnt and inherited everything. Theon was the head of a (note, not ‘the’) Neoplatonic school in Alexandria where he taught philosophy, mathematics and astronomy. The latter two being part of a basic Neoplatonic curriculum. Here Theon is a teacher of astronomy and mathematics not in any way a formidable mathematician.
Theon is most well known in the history of mathematics as the editor and commentator of an edition of the Euclid’s Elements. In fact, the only known Greek edition until a different one was found in the nineteenth century. He also produced commentaries on Euclid’s Data, his Optics and Ptolemaios’ Mathēmatikē Syntaxis. All of these are works of elucidation for students and it is more correct to call Theon a textbook editor.
Turing to Hypatia, she appears to have studied under her father and then went on to take over his position as head of his school, also teaching Neoplatonic philosophy with astronomy and mathematics as subsidiaries. Once again, a teacher not a fine astronomer and a first rank mathematician. Unlike Theon there are no known surviving publications by Hypatia.
The Suda, a tenth-century Byzantine encyclopaedia of the ancient Mediterranean world list three mathematical works for her, which it states have all been lost. The Suda credits her with commentaries on the Conic Sections of the third-century BCE Apollonius of Perga, the “Astronomical Table” and the Arithemica of the second- and third-century CE Diophantus of Alexandria. Alan Cameron, however, argues convincingly that she in fact edited the surviving text of Ptolemaeus’ Handy Tables, (the second item on the Suda list) normally attributed to her father Theon as well as a large part of the text of the Almagest her father used for his commentary. Only six of the thirteen books of Apollonius’ Conic Sections exist in Greek; historians argue that the additional four books that exist in Arabic are from Hypatia, a plausible assumption[2]. So once again, what we have is that Hypatia was like her father a textbook editor.
The MacTutor article on Theon contains the following judgement:
Theon was a competent but unoriginal mathematician.
Although we have no direct evidence in her case, the same can almost certainly be said about his daughter, Hypatia. Both of them are Neoplatonic philosophy teachers, a philosophical direction that includes a basic amount of astronomy and mathematics. They both produced textbooks for students by editing existing standard texts and adding commentaries to aid understanding. There is absolutely no evidence that their mathematical competence went beyond this pedagogical level.
Because they both feature fairly prominently in the history of mathematics, people, and unfortunately, not just the quoted author make the lazy, unfounded assumptions that they are “a fine astronomer and a first rank mathematician” and “an equally formidable mathematician.” Assumptions that have absolutely no foundation in the known historical facts. Theon is famous because of his edition of Euclid’s Elements and Hypatia because she was brutally murdered, and not for their mathematical abilities.
I will, however, add, as a sort of footnote, that textbook authors and editors play a very important role in the history of a scientific discipline, a role that unfortunately, all too often, simply gets ignored in the standard accounts of the history of science.
[1] I’m not going to mention the source on this occasion because the assumption made here turns up time and again and has somehow become gospel. I will however be reviewing the book in question in due course.
[2] This paragraph is borrowed from an early blog post about Hypatia that I wrote.