Was there any exact science or mathematics in the Eastern Roman Empire?

Question

I mean in the Byzantine empire, from the transfer of the capital to Constantinople till its conquest by the Turks, spanning about 12 centuries. Unlike the Western Roman Empire, this one was never conquered by "barbarians" (except for a brief period after the Fourth Crusade, and these were already not exactly barbarians :-). It was more Greek than Latin in its language and culture, and it was supposed to inherit the Hellenistic culture.

I am interested in any sources about the exact sciences and mathematics in this empire. Did they contribute anything at all during the 1200 years of their existence?

Their only well known invention, "Greek fire" is completely lost, and we cannot say what it really was (and it probably belongs to hydraulics or chemistry). And, like the Romans, they also had some magnificent architecture. In nearby Persia, and later in several Islamic countries, some mathematics and astronomy was cultivated. And we know about their achievements.

EDIT. In her answer, fdb writes that "the progress in the whole mediaeval period (in Western Europe, Byzantium and Islam) was slight", which is a well known fact. In my opinion, this is an understatement: there was an actual regress. Is there any convincing explanation why this did happen?

Answer 1

There is a chapter on Byzantine science in a recent Cambridge History of Science volume, see also this paper. As to why I'll articulate the non-controversial part that gets drowned in more detailed accounts. Byzantium was driven by two forces, imperial power and orthodox Christian culture, and neither one supported science.

Medieval orthodox Christianity was rather millenaristic, it was expected that kingdom come was not long at hand. Salvation of the soul was deemed far more important than trappings of mortal life, including study of nature. In education trivium was emphasized and quadrivium trivialized (pun intended), theorizing was dominated by theological studies. An exception that confirms the rule was John Philoponus, the founder of impetus theory, who rejected Aristotle's dynamics as erroneous remarking that "our view may be completely corroborated by actual observation more effectively than by any sort of verbal argument". He was shunned by colleagues, his empirical bent and critique of Aristotle gaining little influence, and forced to abandon philosophy for theology, where his views were declared heresy shortly after his death.

Why the emperors did not support science is also understandable. Throughout its history Byzantium was a castle under siege. First by barbarian hordes in the West during the Great Migration of Peoples, and no sooner that it subsided the rise of Islam brought Turks to the eastern borders of the empire, the force that haunted it since and eventually brought it down. The East-West schism of 1054 and subsequent papal crusades undermined its security further, at one point Constantinople was ransacked by the crusaders, even eastern Slavs that adopted orthodox Christianity warred with Byzantium. In such conditions people hunker down, collect and preserve rather than explore, and projects with immediate practical impact are favored over more contemplative and playful pursuits à la Euclid and Archimedes. And indeed architecture, engineering and medicine fared better in Byzantium than science.

In contrast, the rise of science in Hellenistic and post-Renaissence times was accompanied by the opposite conditions. As described in Lucio Russo's famous book at its zenith in Hellenistic Egypt the Alexandrian Library was funded and supported by Ptolemies, and Hellenistic cultural outlook was directed towards the world and its workings. Once support was replaced by repression under Euergetes II and then Romans with their "public duty is more important than heavens" attitude Alexandrian science floundered. Max Weber links reformed Christian culture in Europe to the enterprising spirit that drove science post-Renaissence, Russo describes traits of Hellenistic Egypt that can be seen as prototypes of capitalism too.

So it seems that science requires stable peace over large territories and an enterprising culture directed outward, the antithesis of Byzantium. Still, Byzantium fulfilled its role as a shield against Muslims, while Europe incubated its new order, and as preserver and transmitter, directly and through Arabs, of Greek and Latin works until the conditions were right for science to rise again.

Answer 2

The standard work on this subject is:

http://books.google.co.uk/books/about/Die_hochsprachliche_profane_Literatur_de.html?id=YC5wxKY_8wsC&redir_esc=y

To be honest, the amount of real scientific progress in the whole mediaeval period (in Western Europe, Byzantium and Islam) was slight, compared with what came before (classical antiquity) and after (Renaissance). This is not a specifically Byzantine issue.