98 A History ofMathematics
numbers as examples (cf. Høyrup 1994); then one can suppose that there is a common source,
though there is usually not enough evidence to deduce what the ultimate source was.9. The later period
TheMing dynasty, 1368–1644, a Chinese dynasty which overthrew the Mongol rulers, saw a
second period of ‘decline’, in that while mathematical work was still done, the emphasis was on
commenting the classics and the innovations of the eleventh to fourteenth centuries were gradually
forgotten (the works were lost, or found too difficult). Whether this was a result of the introduction
of the abacus, as some writers have suggested, or because of a renewed value given to the literary
as opposed to the practical arts, the description of the Song and Yuan as a ‘golden age’, and of
the Ming as a period of stagnation are a commonplace (and were even recognized at the time).
This was dramatically changed by the arrival of the Jesuit missionary Matteo Ricci at the end of
the sixteenth century. An able scientist himself, Ricci saw (as others have after him) the key to
conversion in the exploitation of Western science and technology, which were just entering the
period we call the ‘scientific revolution’ (see Chapter 6). Once again, the calendar was seen as a
way in:
We should change the Chinese calendar, this would enhance our reputation, the doors of China would be more open
to us, our position would be more stable and we would be freer. (Tacchi Venturi 1911–13, II, p. 285)Besides constructing the new calendar, Ricci with his Chinese assistants translated Euclid and other
Western works, simplifying as they went along. The Jesuits successfully predicted eclipses, which
the old calendar had been failing to do, and introduced logarithms not long after they had appeared
in Europe. The fall of the Ming and their replacement by new outsiders, the ManchuQing dynasty
(1644–1911), did not basically interrupt this programme.
Was the result a victory of the new European methods over the classical Chinese? Emphatically
not. The Jesuits hoped that the certainty of Euclid’s geometry could be related to that of their
religion—they were not the first nor the last to make the equation. Naturally, a reaction set in, and
there was a revaluation of traditional Chinese mathematics, helped by scholars who rediscovered
and edited many of the classics from the seventeenth to the nineteenth centuries. From this period
date such fascinating ‘hybrid’ figures as Mei Wending.Euclid’s geometry is completely transfigured in Mei Wending’s three-dimensional figures, which take no account of
perspective, and in his immersion in numerical computation^12 ...At the same time Mei Wending rehabilitated ancient
Chinese techniques such as thefangcheng[array] method for solving linear systems. (Martzloff 1995, p. 25)Again, there is much more work to be done on the history of Chinese mathematicsafterRicci,
precisely because it remained in tension between a vital, indeed increasingly strong tradition and
the Western mainstream. The final victory/assimilation to Western mathematics came, naturally,
with the fall of the Emperor in 1912.- It has to be said that many other writers in the Middle East and in Europe had ‘transfigured’ Euclid’s geometry in different
ways by this time.