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Why were algorithms especially important in traditional Chinese mathematics?

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East Asian mathematics Counting boards and markers, or counting rods, were used in China to solve systems of linear equations. This is an example from the 1st century ce.

In traditional Chinese mathematics, algorithms were of central importance because they served as the primary framework for organizing and solving mathematical problems. Rather than focusing on abstract proofs, canonical works like The Nine Chapters on the Mathematical Art presented mathematical knowledge as a collection of problems paired with general procedures for their solution.1

The significance of these algorithms was reinforced by several factors:

Practical Application: Algorithms were often developed to address the duties of civil administration, such as surveying land, calculating labor needs for earthworks, and determining tax levies based on grain ratios.1
Computational Tools: The use of counting rods on a counting board allowed for a decimal place-value system that enabled the manipulation of numbers within a computation. This physical method of calculation deeply influenced how mathematical procedures were conceptualized and recorded.2
Systematic Development: Commentators like Liu Hui played a crucial role by organizing these algorithms into systems, proving their correctness, and demonstrating how different procedures shared underlying formal operations. This allowed mathematicians to identify analogies between disparate problems, such as those involving fractions and linear equations, and to derive new algorithms from established ones.3