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
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."[1] 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).[1] Thus, it was strongly associated with the
divination methods of the ancient 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]
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]
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.[6] While generating his 60-divisional tuning, he discovered that 53
just fifths is approximate to 31
octaves, calculating the difference at ; 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 1:212/12) 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, 1:210/12, 1:29/12, etc.) and determined the exact length of the string by dividing it by 12√2 (same as 21/12).[11]
Geomorphology: In his Dream Pool Essays of 1088,
Shen Kuo (1031–1095) wrote about a landslide (near modern
Yan'an) where petrified
bamboos were discovered in a preserved state underground, in the dry northern climate zone of
Shanbei,
Shaanxi; Shen reasoned that since bamboo was known only to grow in damp and humid conditions, the climate of this northern region must have been different in the very distant past, postulating that
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]
Jia Xian triangle: This triangle was the same as Pascal's Triangle, discovered by
Jia Xian in the first half of the 11th century, about six centuries before
Pascal. Jia Xian used it as a tool for extracting
square and
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.
Leprosy, first description of its symptoms: The
Feng zhen shi 封診式 (Models for sealing and investigating), written between 266 and 246 BC in the
State of Qin during the
Warring States period (403–221 BC), is the earliest known text which describes the symptoms of leprosy, termed under the generic word li 癘 (for skin disorders).[26] This text mentioned the destruction of the
nasal septum in those suffering from leprosy (an observation that would not be made outside of China until the writings of
Avicenna in the 11th century), and according to Katrina McLeod and Robin Yates it also stated lepers suffered from "swelling of the eyebrows, loss of hair, absorption of nasal cartilage, affliction of knees and elbows, difficult and hoarse respiration, as well as
anaesthesia."[26] Leprosy was not described
in the West until the writings of the
Roman authors
Aulus Cornelius Celsus (25 BC – 37 AD) and
Pliny the Elder (23–79 AD).[26] Although it is alleged that the Indian Sushruta Samhita, which describes leprosy,[27] is dated to the 6th century BC,
India's earliest written script (besides the then long extinct
Indus script)—the
Brāhmī script—is thought to have been created no earlier than the 3rd century BC.[28]
Magic squares: The earliest magic square is the
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]
Map scaling: The foundations for quantitative map scaling goes back to ancient China with textual evidence that the idea of map scaling was understood by the second century BC. Ancient Chinese surveyors and cartographers had ample technical resources used to produce maps such as
counting rods,
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]
Negative numbers, symbols for and use of: in the Nine Chapters on the Mathematical Art compiled during the
Han dynasty (202 BC–220 AD) by 179 AD and commented on by
Liu Hui (fl. 3rd century) in 263,[3] negative numbers appear as rod numerals in a slanted position.[32] Negative numbers represented as black rods and positive numbers as red rods in the Chinese
counting rods system perhaps existed as far back as the 2nd century BC during the
Western Han, while it was an established practice in Chinese algebra during the
Song dynasty (960–1279 AD).[33] Negative numbers denoted by a "+" sign also appear in the ancient
Bakhshali manuscript of
India, yet scholars disagree as to when it was compiled, giving a collective range of 200 to 600 AD.[34] Negative numbers were known in India certainly by about 630 AD, when the mathematician
Brahmagupta (598–668) used them.[35] Negative numbers were first used in Europe by the
Greek mathematician
Diophantus (fl. 3rd century) in about 275 AD, yet were considered an absurd concept in
Western mathematics until
The Great Art written in 1545 by the
Italian mathematician
Girolamo Cardano (1501–1576).[35]
Pi calculated as : 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 = 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 , a value known in Chinese as
Milü ("detailed ratio").[41] This was the best
rational approximation for pi with a
denominator of up to four digits; the next rational number is , which is the
best rational approximation. Zu ultimately determined the value for π to be between 3.1415926 and 3.1415927.[42] Zu's approximation was the most accurate in the world, and would not be achieved elsewhere for another millennium,[43] until
Madhava of Sangamagrama[44] and
Jamshīd al-Kāshī[45] in the early 15th century.
True north, concept of: The
Song dynasty (960–1279) official
Shen Kuo (1031–1095), alongside his colleague
Wei Pu, improved the orifice width of the sighting tube to make nightly accurate records of the paths of the moon, stars, and planets in the night sky, for a continuum of five years.[46] By doing so, Shen fixed the outdated position of the
pole star, which had shifted over the centuries since the time
Zu Geng (fl. 5th century) had plotted it; this was due to the
precession of the Earth's rotational axis.[47][48] When making the first known experiments with a magnetic
compass, Shen Kuo wrote that the needle always pointed slightly east rather than due south, an angle he measured which is now known as
magnetic declination, and wrote that the compass needle in fact pointed towards the
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]
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]
Chow's moving lemma: In algebraic geometry, Chow's moving lemma, named after
Wei-Liang Chow, states: given
algebraic cyclesY, Z on a nonsingular quasi-projective variety X, there is another algebraic cycle Z' on X such that Z' is
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]
Hua's identity: In algebra, Hua's identity[67] states that for any elements a, b in a
division ring, : whenever . Replacing with gives another equivalent form of the identity: :
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]
Ky Fan norms: The sum of the k largest singular values of M is a
matrix norm, the
Ky Fank-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 Km and Kn. In other words, the Ky Fan 1-norm is the operator norm induced by the standard l2 Euclidean inner product.
^Kangsheng Shen, John Crossley, Anthony W.-C. Lun (1999): "Nine Chapters of Mathematical Art", Oxford University Press, pp.33–37
^Thorpe, I. J.; James, Peter J.; Thorpe, Nick (1996). Ancient Inventions. Michael O'Mara Books Ltd (published March 8, 1996). p. 64.
ISBN978-1854796080.
^
abSelin, Helaine (2008). Encyclopaedia of the History of Science, Technology, and Medicine in Non-Western Cultures. Springer (published March 17, 2008). p. 567.
ISBN978-1402049606.
^Croft, S.L. (1997). "The current status of antiparasite chemotherapy". In G.H. Coombs; S.L. Croft; L.H. Chappell (eds.). Molecular Basis of Drug Design and Resistance. Cambridge: Cambridge University Press. pp. 5007–5008.
ISBN978-0-521-62669-9.
^Chen, J.R. (1966). "On the representation of a large even integer as the sum of a prime and the product of at most two primes". Kexue Tongbao. 17: 385–386.
^Chen, J.R. (1973). "On the representation of a larger even integer as the sum of a prime and the product of at most two primes". Sci. Sinica. 16: 157–176.
^Chen, J. R. (1966). "On the representation of a large even integer as the sum of a prime and the product of at most two primes". Kexue Tongbao 17: 385–386.
^Cheng, Shiu Yuen (1975a). "Eigenfunctions and eigenvalues of Laplacian". Differential geometry (Proc. Sympos. Pure Math., Vol. XXVII, Stanford Univ., Stanford, Calif., 1973), Part 2. Providence, R.I.:
American Mathematical Society. pp. 185–193.
MR0378003.
^Chavel, Isaac (1984). Eigenvalues in Riemannian geometry. Pure Appl. Math. Vol. 115.
Academic Press.
^S Darougar, B R Jones, J R Kimptin, J D Vaughan-Jackson, and E M Dunlop. Chlamydial infection. Advances in the diagnostic isolation of Chlamydia, including TRIC agent, from the eye, genital tract, and rectum. Br J Vener Dis. 1972 December; 48(6): 416–420; TANG FF, HUANG YT, CHANG HL, WONG KC. Further studies on the isolation of the trachoma virus. Acta Virol. 1958 Jul–Sep;2(3):164-70; TANG FF, CHANG HL, HUANG YT, WANG KC. Studies on the etiology of trachoma with special reference to isolation of the virus in chick embryo. Chin Med J. 1957 Jun;75(6):429-47; TANG FF, HUANG YT, CHANG HL, WONG KC. Isolation of trachoma virus in chick embryo. J Hyg Epidemiol Microbiol Immunol. 1957;1(2):109-20
^Sant S. Virmani, C. X. Mao, B. Hardy, (2003). Hybrid Rice for Food Security, Poverty Alleviation, and Environmental Protection. International Rice Research Institute.
ISBN971-22-0188-0, p. 248
Arndt, Jörg, and Christoph Haenel. (2001). Pi Unleashed. Translated by Catriona and David Lischka. Berlin: Springer.
ISBN3-540-66572-2.
Aufderheide, A. C.; Rodriguez-Martin, C. & Langsjoen, O. (1998). The Cambridge Encyclopedia of Human Paleopathology. Cambridge University Press.
ISBN0-521-55203-6.
Chan, Alan Kam-leung and Gregory K. Clancey, Hui-Chieh Loy (2002). Historical Perspectives on East Asian Science, Technology and Medicine. Singapore:
Singapore University Press.
ISBN9971-69-259-7
Medvei, Victor Cornelius. (1993). The History of Clinical Endocrinology: A Comprehensive Account of Endocrinology from Earliest Times to the Present Day. New York: Pantheon Publishing Group Inc.
ISBN1-85070-427-9.
Needham, Joseph. (1986). Science and Civilization in China: Volume 3, Mathematics and the Sciences of the Heavens and the Earth. Taipei: Caves Books, Ltd.
Needham, Joseph (1986). Science and Civilization in China: Volume 4, Physics and Physical Technology; Part 1, Physics. Taipei: Caves Books Ltd.
Salomon, Richard (1998), Indian Epigraphy: A Guide to the Study of Inscriptions in Sanskrit, Prakrit, and the Other Indo-Aryan Languages. Oxford: Oxford University Press.
ISBN0-19-509984-2.
Sivin, Nathan (1995). Science in Ancient China: Researches and Reflections. Brookfield, Vermont: VARIORUM, Ashgate Publishing.
Straffin Jr, Philip D. (1998). "Liu Hui and the First Golden Age of Chinese Mathematics". Mathematics Magazine. 71 (3): 163–181.
doi:
10.1080/0025570X.1998.11996627.
Teresi, Dick. (2002). Lost Discoveries: The Ancient Roots of Modern Science–from the Babylonians to the Mayas. New York: Simon and Schuster.
ISBN0-684-83718-8.
Wilson, Robin J. (2001). Stamping Through Mathematics. New York: Springer-Verlag New York, Inc.