List of misnamed theorems

This is a list of misnamed theorems in mathematics. It includes theorems (and lemmas, corollaries, conjectures, laws, and perhaps even the odd object) that are well known in mathematics, but which are not named for the originator. That is, these items on this list illustrate Stigler's law of eponymy (which is not, of course, due to Stephen Stigler, who credits Robert K Merton).

Applied mathematics

Benford's law

Algebra

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Analysis

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Geometry and topology

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  • Ceva's theorem. The oldest extant proof can be found in Yusuf al-Mu'taman ibn Hud's 11th century Kitab al-Istikmal (Book of Perfection), about six centuries before Giovanni Ceva's 1678 De lineis rectis (On straight lines).[19]
  • Cramer's paradox. This was first noted by Colin Maclaurin in 1720, and then rediscovered by Leonhard Euler in 1748 (whose paper was not published for another two years, as Euler wrote his papers faster than his printers could print them). It was also discussed by Gabriel Cramer in 1750, who independently suggested the essential idea needed for the resolution, although providing a rigorous proof remained an outstanding open problem for much of the 19th century. Even though Cramer had cited Maclaurin, the paradox became known after Cramer rather than Maclaurin. Georges Halphen, Arthur Cayley, and several other mathematicians contributed to the earliest more or less correct proof. See [20] for an excellent review.
  • Heine–Borel theorem. This theorem was proved in 1872 by Émile Borel, not by Eduard Heine. Borel used techniques similar to those that Heine used to prove that continuous functions on closed intervals are uniformly continuous. Heine's name was attached because Schönflies noticed the similarity in Heine's and Borel's approaches. In fact, the theorem was first proved in 1852 by Peter Gustav Lejeune Dirichlet, but Lejeune Dirichlet's lecture notes were not published until 1904.[21]
  • Models of hyperbolic geometry. "By one of the injustices of nomenclature that are so common in mathematics, the three models – which could appropriately be called Riemann-Beltrami, Liouville-Beltrami, and Cayley-Beltrami models – are usually known as the Poincaré disk model, the Poincaré half-plane model and the Klein disk model."[22]
  • Morrie's law. The name is due to physicist Richard Feynman, who used to refer to the identity under that name. Feynman picked that name because he had learned the law during his childhood from a boy with the name Morrie Jacobs.[23]
  • Plimpton 322, a tablet that contained several Pythagorean triples
    Pythagoras' theorem. This was known to ancient Mesopotamian mathematicians over one thousand years before Pythagoras was born.[24]

Number theory

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  • Bézout's theorem. The statement may have been made first by Isaac Newton in 1665. The matter of a proof was taken up by Colin MacLaurin (c. 1720) and Leonhard Euler as well as Étienne Bézout (c. 1750). However, Bézout's "proof" was incorrect. The first correct proof seems to be due mostly to Georges-Henri Halphen in the 1870s.[25]
  • Cramer's rule. It is named after Gabriel Cramer (1704–1752), who published the rule in his 1750 Introduction à l'analyse des lignes courbes algébriques, although Colin Maclaurin also published the method in his 1748 Treatise of Algebra (and probably knew of the method as early as 1729).[26]
  • Pell's equation. The solution of the equation x2 − dy2 = 1, where x and y are unknown positive integers and where d is a known positive integer which is not a perfect square, is ascribed to John Pell. It seems to have been discovered by Fermat, who set it as a challenge problem in 1657. The first European solution is found in a joint work in 1658 by John Wallis and Lord Brouncker; in 1668, a shorter solution was given in an edition of a third mathematician's work by Pell; see ref.[27] The first rigorous proof may be due to Lagrange. The misnomer apparently came about when Euler confused Brouncker and Pell; see [28] for an extensive account of the history of this equation.

Set theory

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  • Zorn's lemma is named for Max Zorn. Much work on the theorem now known as Zorn's lemma, and on several closely related formulations such as the Hausdorff maximal principle, was done between 1907 and 1940 by Zorn, Brouwer, Hausdorff, Kuratowski, R. L. Moore, and others. But the particular theorem now known as "Zorn's lemma" was never proved by Zorn, and in any event Zorn's results were anticipated by Kuratowski. The theorem was discovered by Chevalley in 1936, and published and attributed to Zorn by him in Bourbaki's Théorie des Ensembles in 1939. A very similar result was anticipated by S. Bochner in 1928.[29]

See also

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References

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  1. ^ Newcomb, S. (1881). "Note on the frequency of use of the different digits in natural numbers". Amer. J. Math. 4 (1). The Johns Hopkins University Press: 39–40. Bibcode:1881AmJM....4...39N. doi:10.2307/2369148. JSTOR 2369148.
  2. ^ Benford, F. (1938). "The law of anomalous numbers". Proc. Am. Philos. Soc. 78: 551–572. Bibcode:1938PAPhS..78..551B.
  3. ^ Hill, Theodore P. (April 1995). "The Significant Digit Phenomenon". Amer. Math. Monthly. 102 (4). Mathematical Association of America: 322–327. doi:10.2307/2974952. JSTOR 2974952.
  4. ^ Diaconis, Persi (1977). "The distribution of leading digits and uniform distribution mod 1". Ann. Probab. 5 (1). The Institute of Mathematical Statistics: 72–81. doi:10.1214/aop/1176995891.
  5. ^ Feller, William (1968), An Introduction to Probability Theory and its Applications, Volume I (3rd ed.), Wiley, p. 69.
  6. ^ Burnside, William (1897). Theory of groups of finite order. Cambridge University Press.
  7. ^ Grattan-Guinness, Ivor (2002), Companion Encyclopaedia of the History and Philosophy of the Mathematical Sciences, Routledge, pp. 779–780, ISBN 9781134957507.
  8. ^ Kalman, Dan (2008), "An Elementary Proof of Marden's Theorem", The American Mathematical Monthly, 115 (4): 330–338, doi:10.1080/00029890.2008.11920532, ISSN 0002-9890, S2CID 13222698
  9. ^ Siebeck, Jörg (1864), "Über eine neue analytische Behandlungweise der Brennpunkte", Journal für die reine und angewandte Mathematik, 64: 175–182, ISSN 0075-4102
  10. ^ Redfield, J. H. (1927). "The theory of group related distributions". Amer. J. Math. 49 (3). The Johns Hopkins University Press: 433–445. doi:10.2307/2370675. JSTOR 2370675.
  11. ^ Pólya, G. (1936). "Algebraische Berechnung der Isomeren einiger organischer Verbindungen". Zeitschrift für Kristallographie. 93: 414. doi:10.1524/zkri.1936.93.1.415. S2CID 101816170.
  12. ^ Read, R. C. (December 1987). "Pólya's Theorem and its Progeny". Mathematics Magazine. 60 (5): 275–282. doi:10.2307/2690407. JSTOR 2690407.
  13. ^ Deahna, F. (1840). "Über die Bedingungen der Integrabilität". J. Reine Angew. Math. 20: 340–350. doi:10.1515/crll.1840.20.340. S2CID 120057555.
  14. ^ Frobenius, Georg (1895). "Ūber das Pfaffsche Problem". J. Reine Angew. Math.: 230–315.
  15. ^ a b Samelson, Hans (June–July 2001). "Differential Forms, the Early days; or the Stories of Deahna's Theorem and of Volterra's Theorem". Amer. Math. Monthly. 108 (6). Mathematical Association of America: 522–530. doi:10.2307/2695706. JSTOR 2695706.
  16. ^ Thomas & Finney (1996). Calculus and Analytic Geometry. Addison Wesley Publishing Company.
  17. ^ Poincaré, H. (1886–1887). "Sur les residus des intégrales doubles". Acta Math. 9: 321–380. doi:10.1007/BF02406742.
  18. ^ Victor J. Katz (May 1979). "The History of Stokes' Theorem". Mathematics Magazine. 52 (3): 146–156. doi:10.2307/2690275. JSTOR 2690275.
  19. ^ Hogendijk, Jan P (1995). "Al-Mu'taman ibn Hūd, 11th century king of Saragossa and brilliant mathematician". Historia Mathematica. 22 (1): 1–18. doi:10.1006/hmat.1995.1001.
  20. ^ Scott, Charlotte Agnas (March 1898). "On the Intersection of Plane Curves". Bull. Am. Math. Soc. 4 (6): 260–273. doi:10.1090/S0002-9904-1898-00489-5.
  21. ^ Sundström, Manya Raman (2010). "A pedagogical history of compactness". p. 7. arXiv:1006.4131v1 [math.HO].
  22. ^ John C. Stillwell (1996) Sources for Hyperbolic Geometry, page 35, American Mathematical Society and London Mathematical Society ISBN 0-8218-0529-0 Google preview
  23. ^ W.A. Beyer, J.D. Louck, and D. Zeilberger, A Generalization of a Curiosity that Feynman Remembered All His Life, Math. Mag. 69, 43–44, 1996.
  24. ^ Joran, Friberg. "Methods and traditions of Babylonian mathematics: Plimpton 322, Pythagorean Triples, and the Babylonian Triangle Parameter Equations". Historia Mathematica. doi:10.1016/0315-0860(81)90069-0.
  25. ^ Bix, Robert (1998). Conics and Cubics. Springer. ISBN 0-387-98401-1.
  26. ^ Carl B. Boyer (1968). A History of Mathematics, 2nd edition. Wiley. p. 431.
  27. ^ Cajori, Florian (1999). A History of Mathematics. New York: Chelsea. ISBN 0-8284-0203-5. (reprint of fifth edition, 1891).
  28. ^ Whitford, Edward Everett (1912). The Pell Equation. New York: E. E. Whitford. This is Whitford's 1912 Ph.D. dissertation, written at Columbia University and published at his own expense in 1912.
  29. ^ Campbell, Paul J. (1978). "The Origin of 'Zorn's Lemma'". Historia Mathematica. 5: 77–89. doi:10.1016/0315-0860(78)90136-2.