How did Liu Hui contribute to mathematical proof in China?

Liu Hui was a pivotal figure in Chinese mathematics whose 263 CE commentary on The Nine Chapters on the Mathematical Procedures provided the earliest-known Chinese proofs in the contemporary sense.1

Unlike ancient Greek mathematicians who focused on proving theorems, Liu sought to establish the logical correctness of algorithms. His contributions include:1

• Geometric Dissection: He rigorously validated algorithms for calculating the area of circles and the volume of pyramids by dissecting shapes into infinitely many pieces.1
• Algebraic Foundations: He proved algorithms for arithmetic operations and systems of linear equations, often using algebraic proofs to demonstrate that a few fundamental operations underpinned the diverse procedures in The Nine Chapters.1
• Methodological Innovation: His work is noted for its recurring use of algebraic proofs within an algorithmic context, which contributed to the development of mathematical proof as a discipline.1

Liu viewed mathematics through a philosophical lens, seeing algorithms as embodiments of the transformations occurring throughout the cosmos.1