Abstract
It is fairly well known that Darwin was inspired to formulate his theory of natural selection by reading Thomas Malthus’s Essay on the Principle of Population. In fact, by reading Darwin’s notebooks, we can even locate one particular sentence which started Darwin thinking about population and selection. What has not been done before is to explain exactly where this sentence – essentially Malthus’s ideas about geometric population growth – came from. In this essay we show that eighteenth century mathematician Leonhard Euler is responsible for this sentence, and in fact forms the beginning of the logical chain which leads to the creation of the theory of natural selection. We shall examine the fascinating path taken by a mathematical calculation, the many different lenses through which it was viewed, and the path through which it eventually influenced Darwin.
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References
Bacaër, Nicolas. 2011. A Short History of Mathematical Population Dynamics. New York: Springer. (English Translation of Histoires de mathématiques et de populations, Editions Cassini, Paris, 2009).
Bowler, Peter J. 2009. ‘Darwin’s Originality.’ Science 323: 223–226.
Chalub, Fabio A. C. C., and Rodrigues, José F. eds. 2011. The Mathematics of Darwin's Legacy. Birkhäuser.
Darwin, Charles. 1871. The Descent of Man. London:John Murray.
Darwin, Charles. 1875. The Variation of Animals and Plants Under Domestication, 2 vols, 2nd ed. London:John Murray.
Darwin, Charles. 1887. ‘Recollections of the Development of My Mind & Character.’ Francis Darwin (ed.), The Life and Letters of Charles Darwin, Including an Autobiographical Chapter, 1 vols. London:John Murray.
Elsner, Eckehardt. 1986. ‘Kurzer Überblick Über das Leben und Wirken des Johann Peter SÜßmilch (1707–1767).’ H Birg (ed.), UrsprÜnge der Demographie in Deutschland: Leben und Werk Johann Peter SÜssmilchs, 1707–1767. Frankfurt/Main:Campus Verlag, pp. 143–151.
Euler, Leonhard. 1748. Introductio in analysin infinitorum (E101), 2 vols. Lucerne: Bosquet. Reprinted in the Opera Omnia, Series I, vols. 8 and 9. English translation by John Blanton, Springer-Verlag, 1988 and 1990.
Euler, Leonhard. 1767. “Recherches générales sur la mortalité et la multiplication du genre humain.” (E334) First published in Mémoires de l’académie des sciences de Berlin 16, 144–164. Republished in Euler’s Opera Omnia: Series 1, Vol. 7, pp. 79–100. A scan of the original paper, and links to translations by Richard Pulskamp and Todd Doucet, are available at http://maa.eulerarchive.org.
Gumbel, EJ. 1917. ‘Eine Darstellung statischer Reihen durch Euler.’ Jahresbericht der Deutschen Mathematiker-Vereinigung 25: 251–264.
Hartwick, John M. 1988. ‘Robert Wallace and Malthus and the Ratios.’ History of Political Economy 203: 357–379.
Hecht, Jacqueline. 1980. ‘Johann Peter Süssmilch (1707–1767) aux origine de la démographie: L’ « Ordre Divine ».’ Population 3: 667–678.
Hecht, Jacqueline. 1987. ‘Johann Peter Süssmilch: A German Prophet in Foreign Countries.’ Population Studies 41(1): 31–58.
Herbert, Sandra. 1971. ‘Darwin, Malthus, and Selection.’ Journal of the History of Biology 4: 209–217.
Horvath, Robert. 1962. ‘L’ordre Divin de Süssmilch: Bicentaire du premier traité spécifique de démographie (1741–1761).’ Population: Revue trimestrielle 17: 267–288.
Ineichen, Robert. 2007. ‘The Contributions of Leonhard Euler to Actuarial Mathematics.’ Roger Baker (ed.), Euler Reconsidered: Tercentenary Essays. Heber City, UT:Kendrick Press.
Keyfitz, Nathan, Keyfitz, Beatrice. 1970. ‘A General Investigation into the Mortality and Multiplication of the Human Species.’ Theoretical Population Biology 1: 307–314.
Malthus, Thomas. 1826. An Essay on the Principle of Population; or, a View of Its Past and Present Effects on Human Happiness, 6th ed. London:John Murray.
Malthus, Thomas and Appleman, P. 1976. An Essay on the Principle of Population: Text, Sources and Background, Criticism, 1st and 2nd edn. New York: W. W. Norton & Company.
Ospovat, Dov. 1979. ‘Darwin After Malthus.’ Journal of the History of Biology 12: 211–230.
Petersen, William. 1998. Malthus, Founder of Modern Demography. New Brunswick, NJ:Transaction Publishers.
Prendergast, Renee. 1987. ‘James Anderson’s Political Economy – His Influence on Smith and Malthus.’ Scottish Journal of Political Economy 34(4): 388–409.
Price, Richard. 1772. Observations on Reversionary Payments: On Schemes for Providing Annuities for Widows and for Persons in Old Age; on the Methods of Calculating the Values of Assurances on Lives and on the National Debt. To Which are Added Four Essays on Different Subjects in the Doctrine of Life Annuities and Political Arithmetic. London: T. Cadell.
Pullen, J.M., and Perry, Trevor Hughes, eds. 1997. T. R. Malthus: The Unpublished Papers in the Collection of Kanto Gakuen University, Vol. 1. Cambridge: Cambridge University Press.
Romanes, John. 1908. The Life and Letters of George John Romanes, M.A., Ll.D., F.R.S. Late Honorary Fellow of Gonville and Caius Collage, Cambridge Written and Edited by his Wife. London: Sixth Impression Longmans, Green, and Co., p. 100.
Sandifer, Edward. 2007. The Early Mathematics of Leonhard Euler. Washington, DC:Mathematical Association of America.
Sandifer, Edward. 2008a. Life and Death – Part 1. How Euler Did It Column (July 2008), MAA Online.
Sandifer, Edward. 2008b. Life and Death – Part 2. How Euler Did It Column (July 2008), MAA Online
Schuster, P. 2011. ‘The Mathematics of Darwin's Theory of Evolution: 1859 and 150 years later.’ Chalub and Rodrigues (ed.) The Mathematics of Darwin's Legacy. Birkhäuser.
Simpkins, Diana A. 1974. Malthus, Thomas Robert. Entry in the Gillispie (ed.) Dictionary of Scientific Biography, Vol. IX, pp. 67–71.
Sokol, Barnett J. 1974. ‘Thomas Harriot – Sir Walter Raleigh’s Tutor – On Population.’ Annals of Science 31(3): 205–212.
Smith, David. 1977. ‘An Euler Contribution to Stable Theory from Süssmilch’s Göttliche Ordnung.’ Theoretical Population Biology 12: 246–251.
Süssmilch, Johann. 1761. Die Göttliche Ordnung in den Veränderungen des menschlichen Geschlechts, aus der Geburt, Tod und Fortpflanzung desselben erwiesen von Johann Peter Süssmilch, Königl. Preuss. Oberconsistorialrath, Probst in Cölln und Mitglied de Königl. Academie der Wissenschaften, worin die Regeln der Ordnung bewiesen werden welche Gottes Weischeit und Güte in dem Lauf der Natur zur Erhaltung, Vermehrung und Verdoppelung des menschlichen Geschlects festgesetzet hat, woraus dann die wahren Grundsätze einer vernüftigen Bevölkerung hergeleitet werden.
Vorzimmer, Peter. 1969. ‘Darwin, Malthus, and the Theory of Natural Selection.’ Journal of the History of Ideas 30: 527–542.
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Klyve, D. Darwin, Malthus, Süssmilch, and Euler: The Ultimate Origin of the Motivation for the Theory of Natural Selection. J Hist Biol 47, 189–212 (2014). https://doi.org/10.1007/s10739-013-9366-8
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DOI: https://doi.org/10.1007/s10739-013-9366-8