Liu Hui

Liu Hui, (flourished c. 263 CE, China), Chinese mathematician.

All that is known about the life of Liu Hui is that he lived in the northern Wei kingdom (see Three Kingdoms) during the 3rd century CE. His fame rests on the commentary he completed in 263 on Jiuzhang suanshu (The Nine Chapters on the Mathematical Art)—a mathematical canon of the 1st century BCE or CE that played a similar role in the East to Euclid’s Elements in the West. Liu’s commentary on The Nine Chapters proved the correctness of its algorithms. These proofs are the earliest-known Chinese proofs in the contemporary sense. However, in contrast to authors of ancient Greek mathematical texts, Liu did not set out to prove theorems so much as to establish the correctness of algorithms. For example, he rigorously proved algorithms for determining the area of circles and the volume of pyramids by dissecting the regions into infinitely many pieces. He also proved algorithms for arithmetic and algebraic operations, such as adding fractions and solving systems of simultaneous linear equations.