**Qin Jiushao** was a Chinese mathematician who wrote an important study *Shushu Jiuzang* on equations, including the Chinese Remainder Theorem.

- At this time Qin volunteered for the army, which was putting down a rebellion, and served for a while.
- Sadly, we do not know which recluse scholar taught Qin mathematics, but we do know that he studied the Nine Chapters on the Mathematical Art.
- By 1233 Qin was himself the sheriff of a subprefecture in Szechwan province and at this time he was instructed in writing poetry by an official from Chengdu, in central Szechwan province.
- It is worth noting at this point that as well as being a genius in mathematics and accomplished in poetry, Qin was expert at fencing, archery, riding, music and architecture.
- Their armies invaded Szechwan province in 1234 and Qin was forced to leave.
- We need not feel too sorry for Qin, however, for he was a dishonest rogue who was quite prepared to poison those whom he disliked.
- During his period of mourning in Hui-chou, Qin wrote his famous mathematical treatise Shushu Jiuzhang (Mathematical Treatise in Nine Sections) which appeared in 1247.
- Before we look at the contents of the Shushu Jiuzhang we continue our description of Qin's life.
- One might expect that by this time Qin would be unemployable, given his record of criminal dealings, but he next managed to gain an appointment as an assistant in the district of Yin (near Ningpo) in Zhekiang where his friend Wu Qian had been appointed as a naval officer.
- Perhaps Wu Qian was as corrupt as his friend Qin, for he was dismissed from Yin and, in 1260, Qin was also sent away to Meizhou (now Meixian), in Guangtong province where he died.
- We have seen that Qin was a highly unprincipled character but he was also a mathematical genius with few equals.
- It is recorded that Qin cheated his friend Wu Qian so that he became the owner of some of his land, and also that Qin punished a female member of his household by confining her without food.
- The Shushu Jiuzhang (Mathematical Treatise in Nine Sections) is to some extent modelled on the Nine Chapters on the Mathematical Art although Qin's treatise is far more sophisticated.
- Throughout the text, in addition to the tenth degree equation above, Qin also reduces the solution of certain problems to a cubic or quartic equation which he solves by the standard Chinese method (namely that which today is called the Ruffini-Horner method).
- However, Qin is happy to look at problems where the numbers concerned are rational.
- This is such a brilliant piece of work that we are left with asking how Qin could have achieved it.
- We certainly know that Qin was a rogue who was happy to steal, so could he have stolen his mathematics?
- Some historians have wondered whether Qin could have really solved such a deep problem, suggesting that perhaps he worked back from the answer.
- There seems little that is convincing in that suggestion since these problems are not readily worked in reverse and, anyway, Qin really does appear to know what he is doing.
- Although Qin's use of the symbol 0 suggests possible Indian knowledge, the Indian approach to such congruence problems is sufficiently different to make this highly unlikely.
- One is left with no conclusion other than accepting that Qin was one of the great mathematical geniuses of all time.
- Interestingly, despite Qin's character, he does not claim this brilliant method as his own.
- It would appear though that Qin must have taken these ideas much further and be showing a modesty in his mathematical work which was certainly lacking in other aspects of his life.

Born 1202, Puzhou (Anyue), Szechwan province, China. Died 1261, Meizhou (now Meixian), Guangtong province, China.

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Ancient Babylonian, Ancient Chinese, Chinese, Origin China, Puzzles And Problems, Special Numbers And Numerals

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**Oâ€™Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive