apart from destruction there are also things that are lost due to there being a lot of texts and not that many people looking at them. Eventually scholars in the west also got access to the Greek texts from the Byzantine empire and the attitudes towards censorship had changed (I guess it was less necessary for things that were not in the vernacular) and it was perhaps lucky that this happened before the fall of Constantinople. But it also may be that the culture around mathematics was somehow limited with no (evidence of anything like) algebra or calculus or coordinate systems which are pretty important to the developments in the last few hundred years of mathematics.Įarly western Christianity was pretty bad for preserving ancient texts (a silly and likely exaggerated way to phrase the attitude is something like ‘if it’s compatible with the bible it is unnecessary and if it disagrees with the bible it’s heresy and should be destroyed’ though it also seems the New Testament is somewhat Aristotelian) but the eastern empire kept many of them going (in their original Greek), and the Muslims ended up with Arabic translations and Western Europe then got copies or contemporary Arabic works through what is now Spain and translated them into Latin (this could be somewhat tricky for mathematics but worse for anything more philosophical which would have likely been changed first to be compatible with Islam and second to be compatible with Roman Catholicism). I do wonder what mathematics was done in that time but not recorded. There’s like 7-800 years between Apollonius and the construction of that church. Perhaps if you are copying books you’re more likely to be copying the important ancient foundational texts rather than more advanced narrower more recent things. If you look at the evidence that people were still capable of the kind of analysis required to build that structure it seems plausible that much mathematics or science was still happening (in the eastern Roman Empire) but not being recorded. Eg we don’t have much science or mathematics from anything like late antiquity but somehow the Hagia Sophia was built in 537. One thing to note is that there seems to be a compounding difficulty of preserving records. I mostly try to be amazed at what has survived (and the unlikely ways it did). We know that somewhere between Eudoxus and Galileo the idea of freely postulated axiom systems was lost, and it was not really fully rediscovered until the 19th century. Or perhaps it had to be recovered from the few manuscripts the Christians hadn't yet recycled into hymnals, like the Archimedes Palimpsest. Perhaps during the Roman rampages through Greece, the line of transmission of philosophy only survived in Alexandria, or less plausibly, somewhere in India, only to resurface in Arabia while Europe was sunken into its Dark Ages. It would be nice to be able to trace figures like al-Tusi back to Plato and Imhotep, to know if there really was an unbroken line of personal mentorship the way there is in the Buddhist lineages, or if at some point the oral line was severed. Thrun's page seems to have an error about Leibniz: "Gottfried Wilhelm Leibniz 1966, 1967, 1976" It turns out, for example, that you can also trace Leibniz back to Copernicus: I spent some time in 02016 digging through different sorts of academic lineages.
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