A monumental accomplishment in the history of non-Western
mathematics, "The Chinese Roots of Linear Algebra" explains the
fundamentally visual way Chinese mathematicians understood and
solved mathematical problems. It argues convincingly that what the
West "discovered" in the sixteenth and seventeenth centuries had
already been known to the Chinese for 1,000 years.
Accomplished historian and Chinese-language scholar Roger Hart
examines "Nine Chapters of Mathematical Arts"--the classic ancient
Chinese mathematics text--and the arcane art of "fangcheng," one of
the most significant branches of mathematics in Imperial China.
Practiced between the first and seventeenth centuries by anonymous
and most likely illiterate adepts, "fangcheng" involves
manipulating counting rods on a counting board. It is essentially
equivalent to the solution of systems of "N" equations in "N"
unknowns in modern algebra, and its practice, Hart reveals, was
visual and algorithmic. "Fangcheng" practitioners viewed problems
in two dimensions as an array of numbers across counting boards. By
"cross multiplying" these, they derived solutions of systems of
linear equations that are not found in ancient Greek or early
European mathematics. Doing so within a column equates to Gaussian
elimination, while the same operation among individual entries
produces determinantal-style solutions.
Mathematicians and historians of mathematics and science will
find in "The Chinese Roots of Linear Algebra" new ways to
conceptualize the intellectual development of linear algebra.
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