List of Chinese discoveries

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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. The list below contains discoveries which found their origins in China.

Discoveries

Ancient and imperial era

• Yijing.^[1] 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.^[1]
• 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.^[2]
• 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).^[3]
• 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.^[4]

12-note scale, and how this scale differed from scales used by other Chinese states of the time; before this discovery in 1978, the oldest known surviving Chinese tuning set came from a 3rd-century BC text (which alleges was written by Guan Zhong, d. 645 BC) with five tones and additions or subtractions of ⅓ of successive tone values which produce the rising fourths and falling fifths of Pythagorean tuning.^[5]

• just fifths is approximate to 31 octaves
  , calculating the difference at ${\displaystyle {\tfrac {177147}{176776}}}$; 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.^[7][8] 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.^[9][10] In order to obtain equal intervals, Zhu divided the octave (each octave with a ratio of 1:2, which can also be expressed as 1:2^12/12) into twelve equal semitones while each length was divided by the 12th root of 2.^[11] 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, 1:2^10/12, 1:2^9/12, etc.) and determined the exact length of the string by dividing it by ¹²√2 (same as 2^1/12).^[11]
• 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.^[12][13][14]

climates naturally shifted geographically over time

.

• climate change occurred over time.^[15][16] Shen also advocated a hypothesis in line with geomorphology after he observed a stratum of marine fossils running in a horizontal span across a cliff of the Taihang Mountains, leading him to believe that it was once the location of an ancient shoreline that had shifted hundreds of km (mi) east over time (due to deposition of silt and other factors).^[17][18]
• Greatest Common Divisor: Rudolff gave in his text Kunstliche Rechnung, 1526 the rule for finding the greatest common divisor of two integers, which is to divide the larger by the smaller. If there is a remainder, divide the former divisor by this, and so on;. This is just the Mutual Subtraction Algorithm as found in the Rule for Reduction of Fractions, Chapter 1, of The Nine Chapters on the Mathematical Art ^[19]
• Grid reference: Although professional map-making and use of the grid had existed in China before, the Chinese cartographer and geographer Pei Xiu of the Three Kingdoms period was the first to mention a plotted geometrical grid reference and graduated scale displayed on the surface of maps to gain greater accuracy in the estimated distance between different locations.^[20][21][22] Historian Howard Nelson asserts that there is ample written evidence that Pei Xiu derived the idea of the grid reference from the map of Zhang Heng (78–139 CE), a polymath inventor and statesman of the Eastern Han dynasty.^[23]
• Irrational Numbers: Although irrational numbers were first discovered by the Pythagorean Hippasus, the ancient Chinese never had the philosophical difficulties that the ancient Greeks had with irrational numbers such as the square root of 2. Simon Stevin (1548–1620) considered irrational numbers are numbers that can be continuously approximated by rationals. Li Hui in his comments on the Nine Chapters of Mathematical Art show he had the same understanding of irrationals. As early as the third century Liu knew how to get an approximation to an irrational with any required precision when extracting a square root, based on his comment on 'the Rule for Extracting the Square Root', and his comment on 'the Rule for Extracting the Cube Root'. The ancient Chinese did not differentiate between rational and irrational numbers, and simply calculated irrational numbers to the required degree of precision.^[24]
• cubic roots. The original book by Jia Xian titled Shi Suo Suan Shu was lost; however, Jia's method was expounded in detail by Yang Hui, who explicitly acknowledged his source: "My method of finding square and cubic roots was based on the Jia Xian method in Shi Suo Suan Shu."^[25]
  A page from the Yongle Encyclopedia preserved this historic fact.

Mohandas Karamchand Gandhi tends to a leper; the Chinese were the first to describe the symptoms of leprosy

.

• Brāhmī script—is thought to have been created no earlier than the 3rd century BC.^[28]

• Li Shanlan identity: discovered by the mathematician Li Shanlan in 1867.^[29]
• Liu Hui's π algorithm: Liu Hui's π algorithm was invented by Liu Hui (fl. 3rd century), a mathematician of Wei Kingdom.
• Lo Shu square, dating to 4th century BCE China. The square was viewed as mystical, and according to Chinese mythology, "was first seen by Emperor Yu."^[30]
• carpenter's square's, plumb lines, compasses for drawing circles, and sighting tubes for measuring inclination. Reference frames postulating a nascent coordinate system for identifying locations were hinted by ancient Chinese astronomers that divided the sky into various sectors or lunar lodges.^[31] The Chinese cartographer and geographer Pei Xiu of the Three Kingdoms period created a set of large-area maps that were drawn to scale. He produced a set of principles that stressed the importance of consistent scaling, directional measurements, and adjustments in land measurements in the terrain that was being mapped.^[31]
• Girolamo Cardano (1501–1576).^[35]
• Pi calculated as ${\displaystyle {\tfrac {355}{113}}}$: The ancient
  Egyptians, Babylonians, Indians, and Greeks had long made approximations for π by the time the Chinese mathematician and astronomer Liu Xin (c. 46 BC–23 AD) improved the old Chinese approximation of simply 3 as π to 3.1547 as π (with evidence on vessels dating to the Wang Mang reign period, 9–23 AD, of other approximations of 3.1590, 3.1497, and 3.1679).^[36][37] Next, Zhang Heng
  (78–139 AD) made two approximations for π, by proportioning the celestial circle to the diameter of the earth as ${\displaystyle {\tfrac {736}{232}}}$ = 3.1724 and using (after a long algorithm) the square root of 10, or 3.162.^[37][38][39] In his commentary on the Han dynasty mathematical work The Nine Chapters on the Mathematical Art, Liu Hui (fl. 3rd century) used various algorithms to render multiple approximations for pi at 3.142704, 3.1428, and 3.14159.^[40] Finally, the mathematician and astronomer Zu Chongzhi (429–500) approximated pi to an even greater degree of accuracy, rendering it ${\displaystyle {\tfrac {355}{113}}}$, a value known in Chinese as
  denominator
  of up to four digits; the next rational number is ${\displaystyle {\tfrac {52163}{16604}}}$, which is the
  Jamshīd al-Kāshī^[45]
  in the early 15th century.

Emperor Zhenzong of Song (r. 997–1022), pictured here in this portrait, caught fire seemingly at random, a case which a 13th-century author related back to the spontaneous combustion described by Zhang Hua

(232–300) around 290 AD

• magnetic north pole instead of true north (indicated by the current pole star); this was a critical step in the history of accurate navigation with a compass.^[49][50][51]

Modern era

• Arteminisinin, anti-malarial treatment: The antimalarial drug of compound artemisinin found in Artemisia annua, the latter being a plant long used in traditional Chinese medicine, was discovered in 1972 by Chinese scientists in the People's Republic led by Tu Youyou and has been used to treat multi-drug resistant strains of Plasmodium falciparum malaria.^[52][53][54] Artemisinin remains the most effective treatment for malaria today and has saved millions of lives and is yielded one of the greatest drug discoveries in modern medicine.^[55]
• Chen's theorem: Chen's theorem states that every sufficiently large even number can be written as the sum of either two primes, or a prime and a semiprime, and was first proven by Chen Jingrun in 1966,^[56] with further details of the proof in 1973.^[57]
• even number 2p + 2 therefore satisfies Chen's theorem. The Chen primes are named after Chen Jingrun, who proved in 1966 that there are infinitely many such primes. This result would also follow from the truth of the twin prime conjecture.^[58]
• Cheng's eigenvalue comparison theorem: Cheng's theorem was introduced in 1975 by Hong Kong mathematician Shiu-Yuen Cheng.^[59] It states in general terms that when a domain is large, the first Dirichlet eigenvalue of its Laplace–Beltrami operator is small. This general characterization is not precise, in part because the notion of "size" of the domain must also account for its curvature.^[60]
• characteristic classes in mathematics first introduced by Shiing-Shen Chern in 1946.^[61][a]
• rationally equivalent to Z and Y and Z' intersect properly. The lemma is one of key ingredients in developing the intersection theory
  , as it is used to show the uniqueness of the theory.
• Culturing Chlamydia trachomatis bacteria: Chlamydia trachomatis agent was first cultured in the yolk sacs of eggs by Chinese scientists in 1957 ^[62]
• Feathered theropods: The first feathered dinosaur outside of Avialae, Sinosauropteryx, meaning "Chinese reptilian wing," was discovered in the Yixian Formation by Chinese paleontologists in 1996.^[63] The discovery is seen as evidence that dinosaurs originated from birds, a theory proposed and supported decades earlier by paleontologists like Gerhard Heilmann and John Ostrom, but "no true dinosaur had been found exhibiting down or feathers until the Chinese specimen came to light."^[64] The dinosaur was covered in what are dubbed 'protofeathers' and considered to be homologous with the more advanced feathers of birds,^[65] although some scientists disagree with this assessment.^[66]
• partial differential equations. The FEM was developed in the West by Alexander Hrennikoff and Richard Courant, and independently in China by Feng Kang
  .
• number field K is an nth power in K if it is an nth power in the completion
  ${\displaystyle K_{\mathfrak {p}}}$ for almost all (i.e. all but finitely many) primes ${\displaystyle {\mathfrak {p}}}$ of K. For example, a
  Shianghao Wang (1948
  ).
• Hua's identity: In algebra, Hua's identity^[67] states that for any elements a, b in a division ring, :${\displaystyle a-(a^{-1}+(b^{-1}-a)^{-1})^{-1}=aba}$ whenever ${\displaystyle ab\neq 0,1}$. Replacing ${\displaystyle b}$ with ${\displaystyle -b^{-1}}$ gives another equivalent form of the identity: :${\displaystyle (a+ab^{-1}a)^{-1}+(a+b)^{-1}=a^{-1}.}$
• Hua Loo-keng, is an estimate for exponential sums
  .
• Heterosis in rice, three-line hybrid rice system: A team of agricultural scientists headed by Yuan Longping applied heterosis to rice, developing the three-line hybrid rice system in 1973.^[69] The innovation allowed for roughly 12,000 kg (26,450 lbs) of rice to be grown per hectare (10,000 m²). Hybrid rice has proven to be greatly beneficial in areas where there is little arable land, and has been adopted by several Asian and African countries. Yuan won the 2004 Wolf Prize in agriculture for his work.^[70]
• carbonyl compound, potassium hydroxide, and hydrazine hydrate together in ethylene glycol in a one-pot reaction.^[73]
• Ky Fan norms: The sum of the k largest singular values of M is a matrix norm, the Ky Fan k-norm of M. The first of the Ky Fan norms, the Ky Fan 1-norm is the same as the operator norm
  of M as a linear operator with respect to the Euclidean norms of K^m and Kⁿ. In other words, the Ky Fan 1-norm is the operator norm induced by the standard l² Euclidean inner product.
• Chen Ning Yang in 1952. The theorem states that if partition functions of certain models in statistical field theory with ferromagnetic interactions are considered as functions of an external field, then all zeros are purely imaginary, or on the unit circle after a change of variable.^[74][b]
• Riemannian metric on the real projective plane
  RP².
• Siu (1973, 1974
  ).
• Zhi-Wei Sun
  in 2002:${\displaystyle (x+m+1)\sum _{i=0}^{m}(-1)^{i}{\dbinom {x+y+i}{m-i}}{\dbinom {y+2i}{i}}-\sum _{i=0}^{m}{\dbinom {x+i}{m-i}}(-4)^{i}=(x-m){\dbinom {x}{m}}.}$
• polynomial equations must have a solution in the field. It was introduced by mathematician Chiungtze C. Tsen in 1936.^[75]
• multivariate polynomial equations, based on the mathematical concept of characteristic set introduced in the late 1940s by J.F. Ritt.^[77]
• Yunnan Baiyao^[78]

See also

• Chinese exploration
• List of China-related topics
• List of Chinese inventions
• List of inventions and discoveries of Neolithic China
• History of Chinese archaeology
• History of science and technology in China
• History of typography in East Asia

Notes

1. ^ Chern later acquired American citizenship in 1961. He was born in Jiaxing, Zhejiang.
2. ^ Yang later acquired American citizenship in 1964, Lee in 1962. Both men were born in China.

References

Citations

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