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,
involves manipulating counting rods on a counting board. It is essentially equivalent to the solution of systems of
N
equations in
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
new ways to conceptualize the intellectual development of linear algebra.