Th e logical Greek versus the imaginative Oriental 287
Indians. Of course, it was no longer possible, at the end of the nineteenth
century, to maintain the old myth of preservation. But this myth was
replaced by another version that was as economical as possible: Cantor
formulated it this way: ‘[Th e Arabs] have been capable not only to preserve,
but also to expand the treasures entrusted to them.’ 45 Th ese intellectual
treasures, however, were regarded by Cantor as fundamentally foreign ele-
ments, which could only live in the artifi cial milieu of the princely courts. 46
Symptomatically, Hankel, Cantor and Zeuthen found only few exam-
ples of original and independent contributions by the Arabs. Zeuthen,
indeed, introduced his chapter on Arabic mathematics by mentioning
that he ‘would have liked to emphasize the full extent and value of the
mathematical works of the Arabs, in order to avoid negative conclusions
from the relatively few positive results achieved beyond those known to
the Greeks’. 47 Th is fact, he says, provides the very reason for restricting his
presentation to a few selected examples of the kinds of works the Arabs
did. In this connection we should mention that, in 1888, Zeuthen had
off ered to the readers of Bibliotheca Mathematica a question that implicitly
sought to undermine Woepcke’s view of the originality of Islamic con-
tributions to algebra (especially the application of conic sections to the
resolution of algebraic equations). 48 Zeuthen suspected that the Greeks had
already applied these techniques to the same algebraic problems, thereby
raising serious doubts as to whether the Arabs had really been innovative
in this regard.
Th e obsessive search for infl uences
Otherwise, Hankel and especially Cantor were animated by a desire to iden-
tify in Islamic mathematics as many foreign infl uences they could, even on
the basis of tenuous similarities. Th us Hankel did not hesitate to assign to
the Indians a proof of a certain identity involving geometric series recorded
by al-Karajī, even though Woepcke had been unable to detect any Indian
infl uence on al-Karajī in general. 49 In the same manner, he saw nothing
in the indeterminate analysis of al-Karajī that went beyond Diophantus. 50
45 ‘[Die Araber] haben das Ihnen anvertraute Gut nicht nur zu bewahren, auch zu vermehren
gewusst.’ Cantor 1894 : 771.
46 Cantor 1894 : 741–2; 1907 : 786–7.
47 Zeuthen 1896 : 297.
48 Zeuthen 1888.
49 Woepcke 1853: 61–2; Hankel 1874 : 42.
50 Hankel 1874 : 270.