284 François charette
been circulating in Alexandria before his lifetime. 31 With the decline of
Hellenism, the rigidly systematical spirit of classical geometry was sup-
planted by a defi nitely orientalized form of mathematics exemplifi ed by
Diophantus’ Arithmetica.
Siegmund Günther, whom we mentioned above, saw in Diophantus a
‘double nature’. In his earlier works, such as the Porismata , it was possible
to detect purely Hellenistic demonstration practices which had obliged
him to employ laborious roundabouts. But by the time of composing the
Arithmetica , Diophantus had experienced a true emancipation from his
predecessors, notably in his use of symbolism and by his use of ‘clever
tricks’, his ‘boldness’ and his ‘skilfulness’. 32
Zeuthen implicitly followed Hankel by refusing to exclude an Indian
infl uence on Diophantus. Conversely, he wrote, later Indian authors may
also have been infl uenced by the Greek algebraist. For this statement
Zeuthen harvested the criticism of his friend Tannery:
Mr. Zeuthen shows a strong tendency to go back to Hankel’s thesis: the Greeks,
wonderfully gift ed in geometry, had no talent whatsoever for arithmetic. Th e com-
position of a work such as that of Diophantus can only be explained by supposing
the infl uence, in Hellenized Egypt, of a race particularly apt to numerical computa-
tions, such as that of the Hindus. 33
Tannery, in this case, shared the opinion of Cantor, to whom he wrote in
1885: ‘As for the sources I assume for Diophantus, I would not want you to
think that I am close to Hankel; I have always believed that Diophantus was
exclusively Greek.’ 34
Compare Cantor: ‘He belonged to his own time and to his own nation.’ 35
Note that Nesselmann in 1842 had expressed views similar to those of
Cantor and Tannery, and rejected Bombelli’s (1579) earlier assumption of an
Indian infl uence, to which he was led by mistaking a scholion of Maximus
Planudes in a Vatican manuscript for a part of Diophantus’ work. 36 It was31 Hankel 1874 : 204–5.
32 Günther 1908 : 163–8.
33 ‘M. Zeuthen accuse une propension assez marquée à revenir à la thèse de Hankel: les Grecs,
merveilleusement doués pour la Géométrie, ne l’étaient nullement pour l’Arithmétique;
la rédaction d’un ouvrage comme celui de Diophante ne peut s’expliquer qu’en supposant
l’infl uence, dans l’Egypte hellénisée, d’une race particulièrement apte aux calculs numériques,
comme celle des Hindous.’ Tannery 1950 : xii 219.
34 ‘Quant aux sources où je crois que puisait Diophante, je ne voudrais pas un seul instant
que vous pensiez que je me rapproche de Hankel; j’ai toujours cru que Diophante était
exclusivement grec.’ Tannery 1950 : xiii 328.
35 ‘Er stand... innerhalb seiner Zeit, innerhalb seines Volkes.’ Cantor 1894 : 450.
36 Nesselmann 1842 : 284–5.