282 François charette
style as being intrinsically an impediment to mathematical progress, for he
went as far as declaring that a combination of Indian ideas (imagination!)
and Greek principles (logic!) would improve the contemporary teaching of
geometry, by giving students a sharper mathematical intuition. Such a com-
bination, he maintained, could also have helped to advance mathematical
progress, but logic , in the end, was wanting amongst the Indians.
A very pervasive dogma among nineteenth-century historians of mathe-
matics proclaimed the essentially geometrical character of the Greek mind,
in contrast to that of the Orientals (Indian and Chinese), more akin to com-
putational and algebraical operations. One consequence of this ideological
assumption led Cantor to assume rigidly that all geometrical notions attested
in India are necessarily infl uenced by the Greeks, because ‘we should not and
cannot expect a non-geometrical nation to have made essential progresses
[in geometry]’. 21 For the śulbasūtra s, Cantor had fi rst postulated an infl uence
through Hero of Alexandria, 22 but he had to retract his opinion in view of
the evidence, put forward by Indologists, for the chronological impossibil-
ity of such a transmission. 23 He later postulated a possible infl uence from
Mesopotamia.^24 Th e Greek infl uence on the geometry of Brahmagupta, for
example, he considered certain, and again he had less a ‘rigorous Euclid’
in mind than a ‘calculator’ like Hero. 25 Cantor’s mostly anti-Indian and
Hellenocentrist attitude is evident in a letter to Paul Tannery dated 6 June- Concerning an arithmetical method employed by Āryabhat. a, which,
although similar, diff ers from that of the Greek Th ymaridas, he wrote: ‘the
matter is that Āryabhat. a uses the method “epanthem of Th ymaridas”, which
proves indeed that those scientifi c bandits of India did not content them-
selves with Greek geometry, but also appropriated Greek algebra, to which,
it is true, they have added much’. 26
Zeuthen’s interpretation of Indian mathematical history stood closer
to Hankel’s views than those of Cantor. He agreed with both of them that
it was only through Greek infl uence that the Indian computing skills
(Rechenfertigkeit) could lead to real mathematical progress. What they
21 ‘Wesentliche Fortschritte dürfen und können wir von einem nicht geometrisch angelegten
Volksgeiste nicht erwarten.’ Cantor 1894 : 612.
22 Cantor 1894 : 603–4.
23 See Chapter 6 by Agathe Keller in this volume on the work of Th ibault.
24 ‘Erinnern wir uns, wie vieles an Babylon mahnt!’ Cantor 1907 : 645 [3rd edn of Cantor 1894 ].
25 Cantor 1894 : 615; 1907 : 657.
26 ‘ C ’ e s t q u ’ Ā r y a b h a t. a emploie la méthode dite «épanthème de Th ymaridas», ce qui prouve bien
que ces bandits scientifi ques de l’Inde ne se contentaient guère de la géométrie grecque, mais
qu’ils s’emparèrent encore de l’algèbre grecque, à laquelle, il est vrai, ils ajoutèrent beaucoup.’
Tannery 1950 : xiii 314; cf. Cantor 1894 : 583–4.