List of misnamed theorems

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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 Stigler, who credits Merton!).

• Benford's law. This was first stated in 1881 by Simon Newcomb,^[1] and rediscovered in 1938 by Frank Benford.^[2] The first rigorous formulation and proof seems to be due to Ted Hill in 1988.^[3]

• 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 Etienne 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.^[4]

• Burnside's lemma. This was stated and proven without attribution in Burnside's 1897 textbook,^[5] but it has previously been discussed by Augustin Cauchy, in 1845, and by Georg Frobenius in 1887.

• 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. Halphen, Arthur Cayley, and several other luminaries contributed to the earliest more or less correct proof. See ^[6] for an excellent review.

• 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).^[7]

• Fermat's last theorem. This was stated in 1637 in a marginal note in one of his books by Pierre de Fermat, who famously wrote that he had proven it but that the margin was too small to write out the proof there. After Fermat's death, this intriguing notation was mentioned c. 1670 by his son in a new edition of Fermat's collected works, and it became known by its present name. However, the "theorem" remained a conjecture until in 1995 it was finally proven by Andrew Wiles.

• Frobenius theorem. This fundamental theorem was stated and proven in 1840 by Feodor Deahna.^[8] Even though Frobenius cited Deahna's paper in his own 1875 paper,^[9] it became known after Frobenius, not Deahna. See ^[10] for a historical review.

• L'Hôpital's rule. The first appearance of this rule appear in L'Hôpital's book L'Analyse des Infiniment Petits pour l'Intelligence des Lignes Courbes in 1696. The rule is believed to be the work of Johann Bernoulli since l'Hôpital, a nobleman, paid Bernoulli a retainer of 300₣ per year to keep him updated on developments in calculus and to solve problems he had. See [1] and reference therein.

• Maclaurin series. The Maclaurin series was named after Colin Maclaurin, a professor in Edinburgh, who published the special case of the Brook Taylor's result in 1742, in which he never claimed to have discovered them. ^[11]

• Pell's equation. The solution of the equation where x,y are unknown positive integers and where d is a known positive integer which is not a perfect square, which is nominally ascribed to John Pell, was in fact known to Hindu mathematicians far earlier. In Europe, it seems to have been rediscovered 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 mathemathetician's work by Pell; see ^[12] The first rigorous proof may be due to Lagrange. The misnomer apparently came about when Euler confused Brouncker and Pell; see ^[13] for an extensive account of the history of this equation.

• Poincaré lemma. This was mentioned in 1886 by Henri Poincaré,^[14] but was first proven in a series of 1889 papers by the distinguished Italian mathematician Vito Volterra. Nonetheless it has become known after Poincaré. See ^[10] for the twisted history of this lemma.

• Pólya enumeration theorem. This was proven in 1927 in a difficult paper by J. H. Redfield.^[15] Despite the prominence of the venue (the American Journal of Mathematics), the paper was overlooked. Eventually, the theorem was independently rediscovered in 1936 by George Pólya.^[16] Not until 1960 did Frank Harary unearth the much earlier paper by Redfield. See ^[17] for historical and other information.

• Stokes' Theorem. It is named after Sir George Gabriel Stokes (1819–1903), although the first known statement of the theorem is by William Thomson (Lord Kelvin) and appears in a letter of his to Stokes. The theorem acquired its name from Stokes' habit of including it in the Cambridge prize examinations. In 1854, he asked his students to prove the theorem on an examination; it is unknown if anyone was able to do so. ^[18]

[edit] See also

• Stigler's law of eponymy
• Matthew effect
• List of theorems

[edit] References

1. ^ Newcomb, S. (1881). "Note on the frequency of use of the different digits in natural numbers". Amer. J. Math. 4: 39–40. doi:10.2307/2369148. 
2. ^ Benford, F. (1938). "The law of anomalous numbers". Proc. Amer. Phil. Soc. 78: 551–572. 
3. ^ Hill, Theodore P. (April 1995). "The Significant Digit Phenomenon". Am. Math. Monthly 102: 322–327. doi:10.2307/2974952. 
4. ^ Bix, Robert (1998). Conics and Cubics. Springer. ISBN 0-387-98401-1. 
5. ^ Burnside, William (1897). Theory of groups of finite order. Cambridge University Press. 
6. ^ Scott, Charlotte Agnas (March 1898). "On the Intersection of Plane Curves". Bull. Am. Math. Soc. 4: 260–273. doi:10.1090/S0002-9904-1898-00489-5. 
7. ^ Carl B. Boyer (1968). A History of Mathematics, 2nd edition. Wiley, 431. 
8. ^ Deahna, F. (1840). "Über die Bedingungen der Integrabilität". J. Reine Angew. Math. 20. 
9. ^ Frobenius, Georg (1895). "Ūber die Pfaffsche Problem". J. Reine Angew. Math.: 230–315. 
10. ^ ^{a b} Samelson, Hans (June-July 2001). "Differential Forms, the Early days; or the Stories of Deahna's Theorem and of Volterra's Theorem". Am. Math. Monthly 108: 552–530. doi:10.2307/2695706. 
11. ^ Thomas & Finney. Calculus and Analytic Geometry. 
12. ^ Cajori, Florian (1999). A History of Mathematics. New York: Chelsea. ISBN 0-8284-0203-5.  (reprint of fifth edition, 1891).
13. ^ 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.
14. ^ Poincaré, H. (1886-1887). "Sur les residus des intégrales doubles". Acta Math. 9: 321–380. doi:10.1007/BF02406742. 
15. ^ Redfield, J. H. (1927). "The theory of group related distributions". Amer. J. Math. 49: 433–445. doi:10.2307/2370675. 
16. ^ Pólya, G. (1936). "Algebraische Berechnung der Isomeren einiger organischer Verbindungen". Zeitschrift für Kristallographie A 93: 414. 
17. ^ Read, R. C. (December 1987). "Pólya's Theorem and its Progeny". Mathematics Magazine 60: 275–282. 
18. ^ Victor J. Katz (May 1979). "The History of Stokes' Theorem". Mathematics Magazine 52: 146–156.