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Historians and sociologists have remarked on the occurrence, in science, of "multiple independent discovery". Robert K. Merton defined such "multiples" as instances in which similar discoveries are made by scientists working independently of each other.^[1] "Sometimes the discoveries are simultaneous or almost so; sometimes a scientist will make a new discovery which, unknown to him, somebody else has made years before."^[2]

Commonly cited examples of multiple independent discovery are the 17th-century independent formulation of calculus by Isaac Newton, Gottfried Wilhelm Leibniz and others, described by A. Rupert Hall^[3]; the 18th-century discovery of oxygen by Carl Wilhelm Scheele, Joseph Priestley, Antoine Lavoisier and others; and the theory of evolution of species, independently advanced in the 19th century by Charles Darwin and Alfred Russel Wallace.

Multiple independent discovery, however, is not limited to only a few historic instances involving giants of scientific research. Merton believed that it is multiple discoveries, rather than unique ones, that represent the common pattern in science.^[4]

Merton contrasted a "multiple" with a "singleton"—a discovery that has been made uniquely by a single scientist or group of scientists working together.^[5]

Merton's hypothesis is also discussed extensively in Harriet Zuckerman's Scientific Elite.^[6]

List of multiple discoveries

Pre-thirteenth century

• Greenland was first discovered by early Palaeo-Eskimo cultures. In several immigration waves originating from the islands north of the North American mainland, they started settlement circa 2500 BCE. In the early tenth century CE, i.e. more than three millennia later, Greenland was rediscovered by Norse when Gunnbjörn Ulfsson accidentally sighted islands lying close off the coast of Greenland. Based on his report, there was an unsuccessful settlement led by Snaebjörn Galti around 978 and a successful settlement led by Erik the Red (first visit in 982). The Norse settlement disappeared in the fourteenth and fifteenth centuries.

Thirteenth century

• 1242 — first description of the function of pulmonary circulation, in Egypt, by Ibn al-Nafis. Later independently rediscovered by the Europeans, Michael Servetus (1553) and William Harvey (1616).

Fourteenth century

• Gresham's (Copernicus') law: Nicole Oresme (ca. 1370); Nicolaus Copernicus (1517); Thomas Gresham (16th century); Henry Dunning Macleod (1857).

Sixteenth century

• Galileo Galilei and Simon Stevin: heavy and light balls fall together (contra Aristotle).
• Galileo Galilei and Simon Stevin: Hydrostatic paradox (Stevin ca. 1585, Galileo ca. 1610).
• Scipione dal Ferro (1520) and Niccolò Tartaglia (1535) independently developed a method for solving cubic equations.

Seventeenth century

• Calculus — Isaac Newton, Gottfried Wilhelm Leibniz and others.
• Analytic geometry — René Descartes, Pierre de Fermat.
• Determinants — Gottfried Wilhelm Leibniz and Seki Kōwa.
• Boyle's law (sometimes referred to as the "Boyle-Mariotte law") is one of the gas laws and basis of derivation for the Ideal gas law, which describes the relationship between the product pressure and volume within a closed system as constant when temperature remains at a fixed measure. The law was named for chemist and physicist Robert Boyle who published the original law in 1662. The French physicist Edme Mariotte discovered the same law independently of Boyle in 1676.
• Logarithms — John Napier (Scotland, 1614) and Joost Bürgi (Switzerland, 1618)
• Sunspots — Thomas Harriot (England, 1610), Johannes and David Fabricius (Frisia, 1611), Galileo Galilei (Italy, 1612), Christoph Scheiner (Germany, 1612).
• Newton-Raphson method — Joseph Raphson (1690), Isaac Newton (Newton's work was written in 1671, but not published until 1736)

Eighteenth century

• Oxygen — Carl Wilhelm Scheele (Uppsala, 1773), Joseph Priestley (Wiltshire, 1774). The term was coined by Antoine Lavoisier (1777).
• Platinum — Antonio de Ulloa and Charles Wood.
• Complex plane, a geometric representation of the complex numbers — John Wallis (1685), Caspar Wessel (1797), Jean-Robert Argand (1806).

Nineteenth century

• In a treatise^[7] written in 1805 and published in 1866, Carl Friedrich Gauss describes an efficient algorithm to compute the discrete Fourier transform. James W. Cooley and John W. Tukey reinvented a similar algorithm in 1965. "GAUSS' algorithm is as general and powerful as the COOLEY–TUKEY algorithm and is, in fact, equivalent to an algorithm called decimation-in-frequency."^[8]
• Cadmium — Friedrich Strohmeyer, K.S.L Hermann (both in 1817).
• Beryllium — Friedrich Wöhler, A.A.B. Bussy (1828).
• Electromagnetic induction was discovered by Michael Faraday in England in 1831, and independently about the same time by Joseph Henry in the U.S.^[9]
• Chloroform — Samuel Guthrie in the U.S. (July 1831), and a few months later Eugène Soubeiran (France) and Justus von Liebig (Germany), all of them using variations of the haloform reaction.
• Non-Euclidian geometry hyperbolic geometry — Nikolai Ivanovich Lobachevsky (1830), János Bolyai (1832); preceded by Gauss (unpublished result) ca 1805.
• Dandelin–Gräffe method, aka Lobachevsky method — an algorithm for finding multiple roots of a polynomial, developed independently by Germinal Pierre Dandelin, Karl Heinrich Gräffe and Nikolai Ivanovich Lobachevsky.
• Electrical telegraph — Charles Wheatstone (England), Samuel F.B. Morse (United States), 1837.
• First law of thermodynamics - In the late 1800s, various scientists independently stated that energy and matter are persistent, although this was later to be disregarded under subatomic conditions. Hess's Law (Germain Hess), Julius Robert von Mayer, and James Joule were some of the first.
• In 1846, Urbain Le Verrier and John Couch Adams, studying Uranus' orbit, independently proved that another, farther planet must exist. Neptune was found at the predicted moment and position.
• The Möbius strip was discovered independently by the German astronomer–mathematician August Ferdinand Möbius and the German mathematician Johann Benedict Listing in 1858.
• Theory of evolution by natural selection — Charles Darwin (discovery about 1840), Alfred Russel Wallace (discovery about 1857-8) — joint publication, 1859.
• 109P/Swift-Tuttle, the comet generating the Perseid meteor shower, was independently discovered by Lewis Swift on July 16, 1862, and by Horace Parnell Tuttle on July 19, 1862. The comet made a return appearance in 1992, when it was rediscovered by Japanese astronomer Tsuruhiko Kiuchi.
• Helium — Pierre Jansen, Norman Lockyer (both in 1868).^[10]
• In 1876, Oskar Hertwig and Hermann Fol independently described the entry of sperm into the egg and the subsequent fusion of the egg and sperm nuclei to form a single new nucleus.
• Two proofs of the prime number theorem (the asymptotic law of the distribution of prime numbers) were obtained independently by Jacques Hadamard and Charles de la Vallée-Poussin and appeared in the same year (1896).
• Linguists Filip Fyodorovich Fortunatov and Ferdinand de Saussure independently formulated the sound law now known as the Saussure–Fortunatov law^[11].

Twentieth century

• In 1902 Walter Sutton and Theodor Boveri independently proposed that the hereditary information is carried in the chromosomes.
• In the same year (1902) Richard Assmann and Léon Teisserenc de Bort independently discovered the stratosphere.
• E = mc² — Henri Poincare, 1900; Olinto De Pretto, 1903; Albert Einstein, 1905; Paul Langevin, 1906.^[12]
• Lutetium — independently discovered in 1907 by French scientist Georges Urbain and Austrian mineralogist Baron Carl Auer von Welsbach.
• Hilbert space representation theorem, also known as Riesz representation theorem, the mathematical justification of the Bra-ket notation in the theory of quantum mechanics — 1907 independently proved by Frigyes Riesz and Maurice René Fréchet.
• Frequency hopping in radio work was described by Johannes Zenneck (1908), Leonard Danilewicz (1929), Willem Broertjes (1929), and Hedy Lamarr and George Antheil (1942 US patent).
• Bacteriophages (viruses that infect bacteria) — Frederick Twort (1915), Félix d'Hérelle (1917).
• Rotor cipher machines — Theo A. van Hengel and R.P.C. Spengler (1915); Edward Hebern (1917); Arthur Scherbius (Enigma machine, 1918); Hugo Koch (1919); Arvid Damm (1919).
• Sound film — Joseph Tykociński-Tykociner (1922), Lee De Forest (1923).
• "Primordial soup" theory of the evolution of life from carbon-based molecules — Alexander Oparin (1924), J.B.S. Haldane.
• Indefinability Theorem, an important limitative result in mathematical logic — Kurt Gödel, Alfred Tarski.
• Natural deduction, an approach to proof theory in philosophical logic — discovered independently by Gerhard Gentzen and Stanisław Jaśkowski in 1934.
• In mathematics, the Gelfond–Schneider theorem is a result which establishes the transcendence of a large class of numbers. It was originally proved in 1934 by Aleksandr Gelfond and again independently proved in 1935 by Theodor Schneider.
• The Penrose triangle, also known as the "tribar", is an impossible object. It was first created by the Swedish artist Oscar Reutersvärd in 1934. The mathematician Roger Penrose independently devised and popularised it in the 1950s.
• In computer science, the concept of the "universal computing machine" (now generally called the "Turing Machine") was proposed by Alan Turing, but also independently by Emil Post,^[13] both in 1936. Similar approaches, also aiming to cover the concept of universal computing, were introduced by S.C. Kleene and by Alonzo Church that same year. Also in 1936, Konrad Zuse tried to build a binary electrically-driven mechanical calculator with limited programmability; however, Zuse's machine was never fully functional.
• The jet engine, independently invented by them, was used in working aircraft by Hans von Ohain (1939), Secondo Campini (1940) and Frank Whittle (1941).
• Polio vaccine (1950–63): Hilary Koprowski, Jonas Salk, Albert Sabin.
• Quantum electrodynamics and renormalization (1930s–40s): Ernst Stueckelberg, Julian Schwinger, Richard Feynman, and Sin-Itiro Tomonaga, for which the latter 3 received the 1965 Nobel Prize in Physics.
• Kolmogorov Complexity, also known as "Kolmogorov-Chaitin complexity," descriptive complexity, etc., of an object such as a piece of text is a measure of the computational resources needed to specify the object. The concept was independently introduced by Ray Solomonoff, Andrey Kolmogorov and Gregory Chaitin in the 1960s.^[14]
• The concept of packet switching, a communications method in which discrete blocks of data (packets) are routed between nodes over data links, was first explored by Paul Baran in the early 1960s, and then independently a few years later by Donald Davies.
• The Cocke-Younger-Kasami algorithm was independently discovered three times: by T. Kasami (1965), by Daniel H. Younger (1967), and by John Cocke and Jacob T. Schwartz (1970).
• In 1970, Howard Temin and David Baltimore independently discovered reverse transcriptase enzymes.
• The Knuth-Morris-Pratt string searching algorithm was developed by Donald Knuth and Vaughan Pratt and independently by J. H. Morris.
• The Cook–Levin theorem (also known as "Cook's theorem"), a result in computational complexity theory, was proven independently by Stephen Cook (1971 in the U.S.) and by Leonid Levin (1973 in the USSR). Levin was not aware of Cook's achievement because of communication difficulties between East and West during the Cold War. The other way round, Levin's work was not widely known in the West until around 1978.^[15]
• The Bohlen-Pierce scale, a harmonic, non-octave musical scale, was independently discovered by Heinz Bohlen (1972), Kees van Prooijen (1978) and John R. Pierce (1984).
• RSA, an algorithm suitable for signing and encryption in public-key cryptography, was publicly described in 1977 by Ron Rivest, Adi Shamir and Leonard Adleman. An equivalent system had been described in 1973 in an internal document by Clifford Cocks, a British mathematician working for the UK intelligence agency GCHQ, but his work was not revealed until 1997 due to its top-secret classification.
• Asymptotic freedom, which states that the strong nuclear interaction between quarks decreases with distance, was discovered in 1973 by David Gross and Frank Wilczek, and by David Politzer, and was published in the same edition of the journal Physical Review Letters.^[16] For their work the three received the Nobel Prize in Physics in 1974.
• The J/ψ meson was independently discovered by a group at the Stanford Linear Accelerator Center, headed by Burton Richter, and by a group at Brookhaven National Laboratory, headed by Samuel Ting of MIT. Both announced their discoveries on November 11, 1974. For their shared discovery, Richter and Ting shared the 1976 Nobel Prize in Physics.
• Endorphins were discovered independently in Scotland and America in 1975.
• The Immerman-Szelepcsényi Theorem, another fundamental result in computational complexity theory, was proven independently by Neil Immerman and Róbert Szelepcsényi in 1987.^[17]
• In 1993, groups led by Donald S. Bethune at IBM and Sumio Iijima at NEC independently discovered single-wall carbon nanotubes and methods to produce them using transition-metal catalysts.

Quotations

"When the time is ripe for certain things, these things appear in different places in the manner of violets coming to light in early spring."

– Farkas Bolyai to his son János in urging him to claim the invention of non-Euclidean geometry without delay,
quoted in Li & Vitanyi, An introduction to Kolmogorov Complexity and Its Applications, 1st ed., p. 83.

See also

• Multiple discovery
• List of discoveries
• Convergent and divergent production
• Historic recurrence
• Matthew effect
• History of science
• History of technology

Notes

References

• N.E. Collinge (1985). The Laws of Indo-European. Amsterdam: John Benjamins. ISBN 0-915027-75-5 (U.S.), ISBN 90-272-2102-2 (Europe). 
• Michael R. Garey and David S. Johnson (1979). Computers and Intractability: A Guide to the Theory of NP-Completeness. W.H. Freeman. ISBN 0-7167-1045-5. 
• A. Rupert Hall, Philosophers at War, New York, Cambridge University Press, 1980.
• David Lamb, Multiple Discovery: The Pattern of Scientific Progress, Amersham, Avebury Press, 1984.
• Ming Li and Paul Vitanyi (1993). An Introduction to Kolmogorov Complexity and Its Applications. New York: Springer-Verlag. ISBN 0-387-94053-7 (U.S.), ISBN 3-540-94053-7 (Europe). 
• Robert K. Merton, The Sociology of Science: Theoretical and Empirical Investigations, University of Chicago Press, 1973.
• Robert K. Merton, On Social Structure and Science, edited and with an introduction by Piotr Sztompka, University of Chicago Press, 1996.
• Harriet Zuckerman, Scientific Elite: Nobel Laureates in the United States, Free Press, 1979.

External links

• A Survey of Russian Approaches to Perebor (Brute-Force Searches) Algorithms, by B.A. Trakhtenbrot, in the Annals of the History of Computing, 6(4):384-400, 1984.

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