Th e logical Greek versus the imaginative Oriental 283
inherited from the Greeks they developed in this direction without being
burdened by the logical circumspection that characterizes the Greeks. In
this manner, they could appropriate new rules and methods without neces-
sarily understanding the underlying reason for their validity. Th e Indians
could also go beyond Diophantus especially ‘because of their less sensitive
( feinfühlig ) logic’,^27 which made the transfer of existing rules from rational
to irrational numbers easier than it would have been to a Greek.
Another example of Indian improvement over the Greeks is their use
of negative numbers. In contrast to the limitations a ‘cautious Greek’ had
to deal with, the ‘calculating Indian’ could take calculations ‘just as they
present themselves’, as Zeuthen writes, without caring as to whether or
not a quantity was positive or not; the Indians ‘arranged themselves’ with
such negative quantities, simply qualifying them as ‘debts’. 28 One sees here
a notable example of the Hellenocentrist tendency to systematically distort
the interpretation of non-Greek mathematical thought by reducing the
associated cognitive processes to irrational fortuities.
Excursus: Hero and Diophantus – two ‘orientalized’ Greeks?
Another problematic aspect encountered by historians of mathematics was
related to their interpretation of two ‘anomalous’ Greek mathematicians,
Hero and Diophantus, whose styles, methods and preoccupations pro-
foundly diverged from those of classical Greek mathematics.
Th e tone is set very clearly by Hankel when he writes about Diophantus
that ‘if his works were not written in Greek, it would occur to nobody to
think that he sprang from Greek culture; his mind and spirit is too far away
from that which revealed itself during the classical period of Greek math-
ematics.’ 29 Hankel sees Diophantus’ Arithmetica , from a historical point of
view, as counting among the most signifi cant mathematical works of Greek
antiquity; he even added the surprising (over)statement that, in terms of
originality and independence, his contributions stand perhaps higher than
those of any other Greek mathematician! 30 Hankel enthusiastically argued
for the dependence of Diophantus on Indian sources which would have
27 Zeuthen 1896 : 279.
28 Zeuthen 1896 : 180.
29 ‘Wären seine Schrift en nicht in griechischer Sprache geschrieben, niemand würde auf den
Gedanken kommen, dass sie aus griechischer Cultur entsprossen wären; so weit ist sein
Sinn und Geist von dem entfernt, der sich in der klassischen Zeit griechischer Mathematik
geoff enbart hatte.’ Hankel 1874 : 157.
30 Hankel 1874 : 170.