136 A History ofMathematics
other than ‘revolution’. For mathematicians, it is likely to be the relatively early period when the
major translations of Greek and Arabic texts were made (from Arabic into Latin, the universal
language of culture in Western Europe), in the twelfth century. While this is commonly com-
pared to the Arabic ‘age of translations’ three centuries earlier, the differences are as striking as
the similarities.- In the first place, the Arabic translations were (on the whole) centrally organized around an
institution—the ‘House of Wisdom’—which was linked to the central political and religious power,
the khalif. The western Christian world in which the translations were made was less centralized,
and political and religious leaders, with a few exceptions, showed no particular interest. The
Islamic translations were also widely diffused through the use of paper; Western libraries were
smaller, literacy more restricted, and paper with all its cheapness and convenience only came into
general use at around the time of the invention of printing in the fifteenth century. - More importantly, the ‘caste of scholars’ who had done the work of translation were not
in a position to follow it up. We have, more than usually, a difficulty in identifying scholars
as ‘mathematicians’, and the term is hardly useful before the fifteenth century. Apart from a
scattered handful of specialists, most of those who studied mathematical questions (Albert of
Saxony, Bradwardine, Oresme) should be considered physicists, philosophers, even theologians first
with an auxiliary interest in mathematics—in some cases an intelligent one, but rarely interested
either in practical problems or in following up the studies of antiquity. The difference was, most
strikingly, in the lack of mathematicians interested in the more difficult work of Apollonius or
Archimedes, for example. So, while in Baghdad we find the translators of Archimedes immediately
taking up the problems which he failed to solve, or trying to understand his solution and work
out an alternative, there is no sign that anything of the same kind was attempted in western
Europe at all. Paul Lawrence Rose has pointed out the ‘failure’ (if one wants to pass judgment) of
the scholastics to do anything useful with the major translations of Archimedes, by William van
Moerbeke in the thirteenth century.
Why were Moerbeke’s mathematical translations neglected? [True,] there are indications that Moerbeke was not at
home with the mathematics of his subject. Yet the reason for the neglect lies not with the quality of the translation,
but with the failure of medieval scholars to take up the tradition. Those responsible included scholastic philosophers
who found a little Arabo-Latin Archimedes and a lot of Adelardian Euclid sufficient for their purposes. Equally to
blame were the mathematicians including those who had perhaps encouraged Moerbeke in his project in the first
place. (Rose 1975, pp. 80–1)At this point, the reader may be feeling in need of an explanation of the word ‘scholastic’.
It is overdue, but the meaning is a complex one. In the first place, it refers to the tradi-
tion of teaching and study centred on the universities (Bologna and Paris were founded in
the thirteenth century, then Oxford, Heidelberg, and others). A compromise between religious
orthodoxy and admiration for Aristotle, as interpreted by ibn Rushd (‘Averroes’ in European
translation) in particular led to an attachment to authority, both religious and ‘ancient’, and
to logical arguments. The teaching and reasoning style is called ‘scholastic’; its practitioners were
‘schoolmen’. The arguments were of a particular kind (what were calledquaestiones), in which
a question was posed (e.g. could the sun be still and the Earth move?); the arguments on both
sides were carefully set out and a series of objections had to be dealt with in a strictly defined
format before a conclusion could be reached; in its later development this was the scholastic