278 François charette
Contexts and predecessors
In France, the geometer Michel Chasles (1793–1880) and the exiled Italian
mathematician Guglielmo Libri (1803–69) stirred interest in the history of
mathematics among fellow mathematicians. Th e fi rst published in 1837 a
remarkable book entitled Aperçu historique sur l’origine et le développement
des méthodes en Géométrie, particulièrement de celles qui se rapportent à
la Géométrie moderne , in which historical studies sought to inform and
inspire the renewal of modern geometry. Th e second, whose scientifi c con-
tributions are today completely forgotten, united patriotic feelings with a
liberal and enlightened historical erudition that found its expression in his
four-volume Histoire des sciences mathématiques en Italie. Th ese two works
certainly represent the fi nest pieces of scholarship in mathematical histori-
ography from the fi rst half of the nineteenth century.
In Germany, some men combined a command of science and of classical
and orientalist philology which helped them produce remarkable works
of historical erudition. We can mention Ludwig Ideler (1766–1846) in
Berlin (astronomy and mathematical chronology) or, more importantly for
us, Georg Heinrich Nesselmann in Königsberg (1811–81) who may have
been the fi rst to off er lectures on the history of mathematics on a regular
basis, which resulted in a much-praised history of Greek algebra ( 1842 ).
Another important fi gure for our present concerns is the Heidelberg pro-
fessor of mathematics Arthur Arneth (1802–58), author of a now forgotten
Geschichte der reinen Mathematik in ihrer Beziehung zur Entwicklung des
menschlichen Geistes (Stuttgart, 1852 ), in which he clearly enunciated the
fundamental opposition between the Greek and Indian styles of practising
mathematics. We shall return to his ideas below.
Th e works of Libri, Arneth, Nesselmann and Chasles impressed the three
most important writers on history of ancient and medieval mathematics
in the late nineteenth century mentioned above. Th e distinguished Danish
geometer and historian of mathematics Hieronymus Georg Zeuthen
(1839–1920) was a pupil of Chasles in Paris and he himself conceded
how Chasles’s infl uence had been decisive for his historical works. Moritz
Cantor (1829–1920) also went to Paris where he met Chasles, whose his-
torico-mathematical studies inspired an equally strong fascination in him.
But another mathematician produced a very infl uential book some years
before Cantor and Zeuthen would publish their major works. Hermann
Hankel was born in 1839, the same year as Cantor. His essay on ancient and
medieval mathematics originated from the lectures he gave at the University
of Tübingen from the year of his appointment in 1869 until his premature