Qin Jiushao - Biography

Biography

Qin was born in Ziyang, Sichuan, his ancestry was from Shandong, and he is now regarded as an outstanding mathematician of the 13th century CE. This is particularly remarkable, as Qin did not devote his life to mathematics. He was accomplished in many other fields, however, and held a series of bureaucratic positions in several Chinese provinces.

Qin’s reputation as a mathematician lies in his Shùshū Jiǔzhāng (“Mathematical Treatise in Nine Sections”), written in 1247 CE. The treatise covered matters that ranged from indeterminate equations, to military matters and surveying, to the numerical solution of certain polynomial equations up to 10th order. In the treatise, Qin included a general form of the Chinese remainder theorem, which used Da yan shu (大衍术) algorithms to solve it. In geometry, he discovered “Qin Jiushao's formula” for finding the area of a triangle from the given lengths of three sides. This formula is the same as Heron’s formula, proved by Heron of Alexandria about 60 BCE, though knowledge of the formula may go back to Archimedes.

Qin recorded the earliest explanation of how Chinese calendar experts calculated astronomical data according to the timing of the winter solstice. Among his accomplishments are introducing techniques for solving certain types of algebraic equations using a numerical algorithm equivalent to the 19th century Horner's method, and for finding sums of arithmetic series. He also introduced the use of the zero symbol into written Chinese mathematics.

After he completed his work on mathematics, he went into politics. He was boastful, corrupt, accused of bribery and of poisoning his enemies, so several times he was relieved of his duties. Even so, he managed to become very wealthy.