A difficult period. All periods have their difficulties but in this case we are confronted with the basic problem of getting any concrete information at all. Jordanus was a closed book to me, and it was interesting and illuminating to look into the text as presented by Hughes, which is described rather oddly in the standard textbooks (but then, it's an odd text). Fibonacci is a bit more accessible, but the only really good book I know on his work is in German (I've neglected the Book of Squares, however, in favor of the Liber abbaci). The relative inaccessibility of primary sources and the paucity of secondary sources leaves one rather dependent on the sometimes casual opinions of writers whose primary interests may lie elsewhere ( in some cases outside of mathematics entirely. Yo u did an impressive job of locating usable relevant literature (more on that below), and the two figures together make an interesting pairing. The paucity of biographical data on Jordanus de Nemore is frustrating, and the unfounded conjectures that have b een tossed out in the past are certainly not helpful, but this all serves to illustrate very well the perils of historical research.
You seem to have been very rapidly convinced by the enthusiasm of some of your sources for the accomplishments of the Middle Ages, and I don't really see on what grounds. While this is a faithful reflection of the attitudes of some of the experts you cit e, given the limited information currently at our disposal, as exhibited in this essay, it would seem prudent to withhold judgement for the present. An excellent case can be made that European culture was extremely dismal, particularly on the technical si de, throughout most of the period, and they clearly were doing a fairly ineffective job of catching up with the more advanced civilizations of the east, until quite late in the period.
The conjecture that de Nemore may refer to Nemours is one that I have not seen elsewhere, and I do not know if it is linguistically viable, but it seems more appealing to me than the version in the Catholic Encyclopedia, which confidently associates Nemore with Nemi, near Rome, on unstated grounds. References
These all seem helpful. The De Datis is very nice. I still have not examined the Sigler, something that I'm going to need to get to one of these days. Menninger is very helpful in his particular area of concern, and certainly relevant to an understandin g of the medieveal period. As one goes back in time it starts to be more useful to have access to several European languages, because of the paucity of useful translations.
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