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The Chinese Roots of Linear Algebra

, 304 pages

5 halftones

November 2010



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The Chinese Roots of Linear Algebra

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.

Roger Hart is an assistant professor in the Department of History at the University of Texas, Austin.

"A beautifully written scholarly book in an area where books are scarce. Hart's scholarship is impeccable and his precision is a delight. The Chinese Roots of Linear Algebra will be essential reading for those interested in the history of Chinese mathematics."

"A pivotal work in the history of non-Western mathematics that will revolutionize people's understanding of the origins of techniques previously viewed as Western inventions."

"This study is an important contribution to making one field of the history of mathematical activity in China available to a non-Chinese audience."

"[A] challenging, inspiring book that is full of most valuable, new historial insights."

"Hart's provocative book deserves to be in every college and university collection."

"It seems likely that Hart's thoughtful, meticulous book will be the precursor to much fruitful study not only of pre-modern Chinese mathematics but also the roles of literacy and notation in its transmission."

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