# قائمة المبرهنات الرياضية

هذه هي قائمة المبرهنات. انظر أيضاً:

and, for proved results,

also

for problems not subject to conventional proof nor disproof.

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## Pure mathematics

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## Inequalities particular to physics

A list of articles with mathematical proofs:

## Articles devoted to theorems of which a (sketch of a) proof is given

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## Other related articles

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!).

• 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 McLaurin, the paradox became known after Cramer rather than McLaurin. Halphen, Arthur Cayley, and several other luminaries contributed to the earliest more or less correct proof. See [6] for an excellent review.
• 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.[7] Even though Frobenius cited Deahna's paper in his own 1875 paper,[8] it became known after Frobenius, not Deahna. See [9] for a historical review.
• Pell's equation. The solution of the equation ${\displaystyle x^{2}-d\,y^{2}=1}$  where ${\displaystyle x,y}$  are unknown positive integers and where ${\displaystyle d}$  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 mathemathecians work by Pell; see [10] The first rigorous proof may be due to Lagrange. The misnomer apparently came about when Euler confused Brouncker and Pell; see [11] for an extensive account of the history of this equation.

## انظر أيضاً

Most of the results below come from pure mathematics, but some are from theoretical physics, علم الاقتصاد, and other applied fields.

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## Z

1. ^ Newcomb, S. (1881). "Note on the frequency of use of the different digits in natural numbers". Amer. J. Math. 4: 39–40.
2. ^ Benford, F. (1938). "The law of anomalous numbers". Proc. Amer. Phil. Soc. 78: 551–572.
3. ^ Hill, Theodore P. (1995). "The Significant Digit Phenomenon". Am. Math. Monthly. 102 (4): 322–327. Unknown parameter `|month=` ignored (help)
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 (1898). "On the Intersection of Plane Curves". Bull. Am. Math. Soc. 4: 260–273. Unknown parameter `|month=` ignored (help)
7. ^ Deahna, F. (1840). "Über die Bedingungen der Integrabilität". J. Reine Angew. Math. 20. Text "pages-340-350" ignored (help)
8. ^ Frobenius, Georg (1895). "Ūber die Pfaffsche Problem". J. Reine Angew. Math.: 230–315.
9. ^ أ ب Samelson, Hans (2001). "Differential Forms, the Early days; or the Stories of Deahna's Theorem and of Volterra's Theorem". Am. Math. Monthly. 108 (6): 552–530. Unknown parameter `|month=` ignored (help)
10. ^ Cajori, Florian (1999). A History of Mathematics. New York: Chelsea. (reprint of fifth edition, 1891).
11. ^ 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.
12. ^ Poincaré, H. (1886–1887). "Sur les residus des intégrales doubles". Acta Math. 9: 321–380.CS1 maint: date format (link)
13. ^ Redfield, J. H. (1927). "The theory of group related distributions". Amer. J. Math. 49: 433–445.
14. ^ Pólya, G. (1936). "Algebraische Berechnung der Isomeren einiger organischer Verbindungen". Z. für Krystallogr. A. 93: 414.
15. ^ Read, R. C. (1987). "Pólya's Theorem and its Progeny". Mathematics Magazine. 60 (5): 275–282. Unknown parameter `|month=` ignored (help)
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