The Ten Classics of
Ancient Chinese Mathematics:
Adversarial or
Authoritarian?
by
Joseph W. Dauben

[March
10, 2006]

In 1996 Sir
Geoffrey Lloyd
published a
comparative
study of ancient
science east and
west:
Adversaries and
Authorities.
Investigations
into Ancient
Greek and
Chinese
Science. In
this book he
argues that
Greek science
was successful
by virtue of its
adversarial
nature, whereas
Chinese science
was better
described as
authoritarian in
character. But
to what extent
does this
categorization
apply to Chinese
mathematics?

This lecture
will investigate
this question,
beginning with a
general overview
of ancient
Chinese
mathematics.
The earliest
yet-known
mathematical
work in China
was only
recently
discovered in a
tomb that can be
dated to the
early second
century BCE.
Previously
unknown, the
算數書
Suan Shu Shu (A
Book on Numbers
and
Computations) is
written on
nearly 200
bamboo slips and
is unique among
mathematical
works from
ancient China
because it
survives in a
durable form
from the time it
was written.

The other
classic texts of
ancient Chinese
mathematics like
the famous
九章算術Jiu
zhang suan shu
(Nine Chapters
on the Art of
Mathematics) are
known only from
an imperfect
copy printed in
the Southern
Song dynasty
(1213 CE), and
from other even
later collations
and editions.
Nevertheless,
from these it is
possible to
reconstruct the
state of
mathematics in
ancient China,
and in so doing,
counter many of
the myths and
untenable claims
about what was
actually the
case in ancient
China.

For example, it
is often said
that the Chinese
placed little
emphasis upon
mathematics, and
that lacking the
Greeks’ penchant
for axiomatic
treatments with
correspondingly
rigorous
standards of
proof, Chinese
mathematics was
comparatively
lacking.
Western
historians of
mathematics have
used such terms
as
“backwardness,”
“underdeveloped,”
“weak in
geometry,” and
even
“disorganized”
to criticize
Chinese
mathematics.
However, to
anyone familiar
with Chinese
texts, these
descriptions are
difficult to
justify.

The 3rd-century
CE commentator
Liu Hui devised
careful
arguments and
proofs to
justify his
commentary on
the Nine
Chapters, and
later
mathematicians
introduced
sophisticated
techniques that
in some cases
surpassed
western
mathematics,
especially
during the
“zenith” of
Chinese
accomplishments
in the Song and
Yuan dynasties
(960-1368 CE).

This lecture
will highlight
these
developments,
focusing in
particular on
the
十部算經
Shi bu suan jing
(Ten Books of
Mathematical
Classics) and
end with an
evaluation of
not only the
character of
ancient Chinese
mathematics, but
an assessment of
its major
innovations.