List of Chinese discoveries

Aside from many original inventions, the Chinese were also early original pioneers in the discovery of natural phenomena which can be found in the human body, the environment of the world, and the immediate Solar System. They also discovered many concepts in mathematics and music. The list below contains discoveries which found their origins in China.

Discoveries

Ancient and imperial era

Catalan numbers: Trigonometric identities and power-series calculations, written by Qing dynasty mathematician Minggatu around 1730, contain coefficients equal to the Catalan numbers. His manuscript was subsequently completed by his student Chen Jixin in 1774. Chinese remainder theorem: The Chinese remainder theorem, including simultaneous congruences in number theory, was first created in the 3rd century AD in the mathematical book Sunzi Suanjing posed the problem: "There is an unknown number of things, when divided by 3 it leaves 2, when divided by 5 it leaves 3, and when divided by 7 it leaves a remainder of 2. Find the number." This method of calculation was used in calendrical mathematics by Tang dynasty (618–907) mathematicians such as Li Chunfeng (602–670) and Yi Xing (683–727) in order to determine the length of the "Great Epoch", the lapse of time between the conjunctions of the moon, sun, and Five Planets (those discerned by the naked eye). Thus, it was strongly associated with the divination methods of the ancient Yijing. Its use was lost for centuries until Qin Jiushao (c. 1202–1261) revived it in his Mathematical Treatise in Nine Sections of 1247, providing constructive proof for it. Circadian rhythm in humans: The observation of a circadian or diurnal process in humans is mentioned in Chinese medical texts dated to around the 13th century, including the Noon and Midnight Manual and the Mnemonic Rhyme to Aid in the Selection of Acu-points According to the Diurnal Cycle, the Day of the Month and the Season of the Year. Decimal fractions: decimal fractions were used in Chinese mathematics by the 1st century AD, as evidenced by The Nine Chapters on the Mathematical Art, while they appear in the works of Arabic mathematics by the 11th century (most likely independently of Chinese influence) and in European mathematics by the 12th century, although the decimal point was not used until the work of Francesco Pellos in 1492 and not clarified until the 1585 publication of Flemish mathematician Simon Stevin (1548–1620). Diabetes, recognition and treatment of: The Huangdi Neijing compiled by the 2nd century BC during the Han dynasty identified diabetes as a disease suffered by those who had made an excessive habit of eating sweet and fatty foods, while the Old and New Tried and Tested Prescriptions written by the Tang dynasty physician Zhen Quan (died 643) was the first known book to mention an excess of sugar in the urine of diabetic patients.

Equal temperament: During the Han dynasty (202 BC–220 AD), the music theorist and mathematician Jing Fang (78–37 BC) extended the 12 tones found in the 2nd century BC Huainanzi to 60. While generating his 60-divisional tuning, he discovered that 53 just fifths is approximate to 31 octaves, calculating the difference at 177147 176776 {\displaystyle {\tfrac {177147}{176776}}} ; this was exactly the same value for 53 equal temperament calculated by the German mathematician Nicholas Mercator (c. 1620–1687) as 353/284, a value known as Mercator's Comma. The Ming dynasty (1368–1644) music theorist Zhu Zaiyu (1536–1611) elaborated in three separate works beginning in 1584 the tuning system of equal temperament. In an unusual event in music theory's history, the Flemish mathematician Simon Stevin (1548–1620) discovered the mathematical formula for equal temperament at roughly the same time, yet he did not publish his work and it remained unknown until 1884 (whereas the Harmonie Universelle written in 1636 by Marin Mersenne is considered the first publication in Europe outlining equal temperament); therefore, it is debatable who discovered equal temperament first, Zhu or Stevin. In order to obtain equal intervals, Zhu divided the octave (each octave with a ratio of 1:2, which can also be expressed as 1:212/12) into twelve equal semitones while each length was divided by the 12th root of 2. He did not simply divide the string into twelve equal parts (i.e. 11/12, 10/12, 9/12, etc.) since this would give unequal temperament; instead, he altered the ratio of each semitone by an equal amount (i.e. 1:2 11/12, 1:210/12, 1:29/12, etc.) and determined the exact length of the string by dividing it by 12√2 (same as 21/12). Gaussian elimination: First published in the West by Carl Friedrich Gauss (1777–1855) in 1826, the algorithm for solving linear equations known as Gaussian elimination is named after this Hanoverian mathematician, yet it was first expressed as the Array Rule in the Chinese Nine Chapters on the Mathematical Art, written at most by 179 AD during the Han dynasty (202 BC–220 AD) and commented on by the 3rd century mathematician Liu Hui.

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