Th e logical Greek versus the imaginative Oriental 279
death in 1873. It was published posthumously the next year by his father,
who was Professor of Physics in Leipzig. In spite of its being unfi nished,
this book can be rightly qualifi ed as the most original and refreshing view
on the topic to have been off ered in print up to its day. Hankel was notable
for including an up-to-date summary – the only one available to date, espe-
cially for Arabic mathematics – of the fi ndings of Colebrooke, Woepcke and
other orientalists on the mathematics of the Hindus and Muslims. With his
numerous thought-provoking interpretations, Hankel’s history represented
a compelling source of inspiration for the forthcoming generation of ‘pro-
fessional’ historians of mathematics, among whom we mention the names
of Cantor, Bretschneider, Zeuthen, Tannery, Heiberg, Eneström, Allman,
von Braunmühl, Günther, Loria, Hultsch, Curtze, Suter, etc. 9
Th e éminence grise among them was undoubtedly Moritz Cantor, who
enjoyed the privilege of studying mathematics in Göttingen with Carl Gauss
and others. But another Göttingen professor, Moritz Stern, instilled in him
the taste for historical studies. Arneth’s lectures on the history of mathemat-
ics in Heidelberg, which Cantor heard in 1848, are also said to have exerted
a strong infl uence on him. 10 Cantor’s ‘antiquarian’ style of scholarship – with
its erudite, detailed and comprehensive narrative of every single episode
of mathematical history within its own specifi c context – is evident in his
monumental Vorlesungen über Geschichte der Mathematik , whose fi rst
volume appeared in 1880. Th is style is oft en contrasted with the ‘presentist’
and Platonic approach of H. G. Zeuthen, who insisted on the necessity to
select the most signifi cant episodes of the history of mathematics in order
to illuminate our understanding of the development of mathematics from
a modern perspective, a vision embodied in his highly original and infl u-
ential historical essay on the theory of the conics in antiquity (published in
Copenhagen in 1885 and in German translation the next year). His intro-
ductory Geschichte der Mathematik im Altertum und Mittelalter ( 1896 ) of
didactic intent (the intended readership were the future teachers of math-
ematics in Denmark) had nevertheless a scope and depth similar to Hankel’s
history, and remained for several decades the best work of its genre.
India’s illogical lure
Playfair’s essay on Indian mathematics provided the inspiration for Arthur
Arneth’s ‘cultural’ history of mathematics, in which we fi nd the fi rst
9 On those historians of mathematics, see the biographical notices in Part ii of Dauben and
Scriba 2002.
10 See Hofmann 2008 ; Folkerts in Dauben and Scriba 2002 : 387–91, on 387.