https://thonyc.wordpress.com/2023/09/21/incorrect-casual-assumptions/ The Renaissance Mathematicus Skip to content * Home * About * Biographies Index * Contact * Early Modern English mathematical practitioners * From ta phusika (ta physika) to physics * Renaissance Garbage * Renaissance Science * Subject Index: * The emergence of modern astronomy - a complex mosaic * The transition to heliocentricity: The Rough Guides * The Trilogies of Christmas Past [cropped-p1010022] - She sought it here, she sought it there, she found elusive longitude everywhere From ta phusika (ta physika) to physics - VII - September 21, 2023 * 8:41 am | Jump to Comments Incorrect casual assumptions 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' Mathematike Syntaxis. All of these are works of elucidation for students and it is more correct to call Theon a textbook editor. [euclid_vat]Theon of Alexandria is best known for having edited the existing text of Euclid's Elements, shown here in a ninth-century manuscript Vatican Library via Wikimedia Commons 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. Share this: * Share * * Twitter * Facebook * Tumblr * Pinterest * Like this: Like Loading... Related 11 Comments Filed under History of Astronomy, History of Mathematics, Myths of Science - She sought it here, she sought it there, she found elusive longitude everywhere From ta phusika (ta physika) to physics - VII - 11 responses to "Incorrect casual assumptions" 1. [f06e4] Michael Wright September 22, 2023 at 1:11 am That is to say, both Hypatia and her father had achieved about the same level in their professions as someone who achieves the middle ranks of academia in a university of middling (but respectable) standing. We know that we are not outstanding intellects: but we also have a suspicion that the outstanding intellects need us to keep the infrastructure chugging and the study alive. HISTSCI_HULK is entertaining, and his contributions are valuable, but I suspect he'd be bugger-all use in a meeting to consider revisions in the syllabus. In one way, this makes her murder even more appalling. Love your work. Reply + [bb553] thonyc September 22, 2023 at 7:28 am That is the sentiment that I hoped to express in my last very short paragraph. It is something that I have repeated several times over the years, in fact the very first substantive post on this blog, more than fourteen years ago, about Christopher Clavius, was about his important role as an educational reformer, textbook, author etc. Reply + [57459] Laurence Cox September 22, 2023 at 8:33 am Around 15 years ago the Royal Society published "The Scientific Century" making the case that we needed more, and different, scientists in the 21st Century. One figure in that book, the leaky pipeline in academia, always struck me. Of all those with a PhD, 54% left science research, 16% went into research in industry and government (my chosen path) and of the remaining 30% of post-docs, only 3.5% achieved tenure and 0.5% full professor status. I tend to imagine Hypatia and her father in that 3% (which was probably higher then as the industrial/government research path did not exist) and we should recognise their value as teachers of others rather than as original thinkers. Reply o [bb553] thonyc September 22, 2023 at 12:19 pm Their's was of course not a state educational institute but rather a private school for philosophy, one of several in Alexandria at the time. They lived from their reputation and from the few references that we have from one time students in letters, Hypatia enjoyed a good reputation as teacher o [57459] Laurence Cox September 27, 2023 at 1:08 pm @Thony As you pointed out in a previous article, universities did not exist until the Middle Ages. However, we can trace what we would now call Higher Education back to the Ancient Greeks and Hypatia and her father were firmly part of that tradition. 2. [cb92f] Michael Weiss September 22, 2023 at 5:22 pm The progress of mathematics (and other fields) obviously depends heavily on far more than the top tier. If we compare, say, European mathematics in the span from 100CE to 500CE with the span from 1600CE to 1900CE--well, there's no comparison. It's hard to believe that the "rate of inborn talent" was much different. Even accounting for population, social factor have to have played the dominant role. OTOH, imagine we are writing an extremely internalist history of European mathematics: just the results (with names), not even any anecdotes about Gauss as a kid or the Newton-Leibniz brouhaha. How many names would figure? Well, more than the top-tier: Archimedes, Newton, Gauss, Poincare and Hilbert account for, I dunno, 5% of the results? 10%? Impossible to quantify, but still... And then we have people like, to take a random example, Count Fagnano. In 1718 he published a paper giving an integral formula somewhat like the double angle formula for the sine. Euler took it up in 1753 and extended it to the additional formula for elliptic integrals. That tributary flowed into work of Abel, Jacobi and Gauss on elliptic functions, Riemann's great paper on Riemann surfaces, and ultimately the broad and deep river of modern algebraic geometry. Reply 3. [e4772] jimhexis September 23, 2023 at 5:56 pm Happy to read your nod to the producers of textbooks. Come to think of it, I've edited quite a few math textbooks in my time, though I've yet to be lynched by a mob of zealots so I can't hold out much hope for lasting fame. Reply 4. [ab876] D.N. O'Donovan September 26, 2023 at 10:32 pm "she .. 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". How we rate her ability rather depends on what a person takes 'edit' to mean. If it's just word-checking, then a daddy's little helper, school-teacher image might apply. If 'edit' means to revise and correct astronomical data, then it implies rather more. Reply + [bb553] thonyc September 27, 2023 at 5:32 am Not the latter Reply o [ab876] D.N. O'Donovan September 27, 2023 at 6:48 am Thony, I don't mind, either way. Your mental image of Hypatia seems to regard her as a primary-school teacher and dad's secretary. Others see her a a female genius. I'm interested to see that those 'Handy Tables' derived from Ptolemy's work may be her doing, though. Very interesting. Also - speaking of a 'private school' makes me wonder what other kinds of school there were. Private tutors, temple-schools (also private).. can't think of any other kind. Would love to see a post about it. o [bb553] thonyc September 27, 2023 at 1:33 pm "Your mental image of Hypatia seems to regard her as a primary-school teacher and dad's secretary." I fail to see how what I wrote provokes in anyway that image. Theon ran a Neoplatonic school, teaching philosophy to adults! Hypatia, who he probably also educated, inherited the leadership of that school from him. The Neoplatonic philosophy entailed a certain level of astronomical and mathematical knowledge, which they both taught. Theon edited and provided commentaries to Euclid's Elements and Ptolemy's Almagest, both standard textbooks of the period, in order to elucidate sections that might prove difficult for students. He himself says that Hypatia was responsible for part of his edition of Ptolemy. According to a secondary source Hypatia did the same for Apollonius' Conic Sections and Diophantus' Arithemica two further standard textbooks. There is an indirect reference that is interpreted to refer to her doing the same for Ptolemy's Handy Tables. The Handy Tables, which is a collection of the astronomical tables from the Almagest were produced by Ptolemy for use by astronomers and astrologers. It can be assumed that her commentaries were on how to best use those tables. She did not in anyway produce them. She was obviously an intelligent woman, otherwise she would not have been the leader of a successful school for philosophy but there is no known evidence that she was a 'genius' whatever that might mean, and claims that she was are based on nothing more than wishful thinking. Leave a Reply Cancel reply [ ] [ ] [ ] [ ] [ ] [ ] [ ] D[ ] * Search for: [ ] [Search] * The Renaissance Mathematicus [bb553f8791a533302] * The Facts of Life If your philosophy of [scientific] history claims that the sequence should have been A-B-C, and it is C-A-B, then your philosophy of history is wrong. 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