Chinese Mathematics

3.1 The Nine Chapters

The Jiuzhang Suanshu (Nine Chapters on the Mathematical Art), compiled around the 1st century CE from earlier sources, is the most important Chinese mathematical classic. It contains 246 problems organized into nine chapters, covering field measurement, proportions, partnership, extraction of roots, volumes, taxation, excess and deficit, systems of linear equations, and right triangles.

The text presents methods equivalent to Gaussian elimination for solving systems of linear equations — nearly two millennia before Gauss. It also contains the earliest known use of negative numbers in a systematic mathematical context.

3.2 Liu Hui and Zu Chongzhi

Liu Hui (c. 225–295 CE) wrote a detailed commentary on the Nine Chapters and developed a method of successive polygon approximation to compute π. Starting with a hexagon and doubling sides repeatedly, he obtained π ≈ 3.1416.

Zu Chongzhi (429–500 CE) pushed this further, calculating π to seven decimal places: 3.1415926 < π < 3.1415927. He also found the remarkably accurate fraction 355/113 ≈ 3.1415929..., which remained the best rational approximation of π for nearly a thousand years.

3.3 The Chinese Remainder Theorem

The Chinese Remainder Theorem, first stated by Sun Zi (c. 3rd century CE), gives a method for solving systems of simultaneous congruences. The problem is posed practically: “Find a number which leaves remainder 2 when divided by 3, remainder 3 when divided by 5, and remainder 2 when divided by 7.”

This theorem became fundamental to modern number theory and has applications in cryptography, computer science, and abstract algebra. It was independently rediscovered in Europe by Euler and Gauss in the 18th and 19th centuries.

3.4 Key Contributions