Δευτέρα 15 Οκτωβρίου 2012

▪ The Hundred Greatest Theorems

1The Irrationality of the Square Root of 2Pythagoras and his school500 B.C.
2Fundamental Theorem of AlgebraKarl Frederich Gauss1799
3The Denumerability of the Rational NumbersGeorg Cantor1867
4Pythagorean TheoremPythagoras and his school500 B.C.
5Prime Number TheoremJacques Hadamard and Charles-Jean de la Vallee Poussin (separately)1896
6Godel΄s Incompleteness TheoremKurt Godel1931
7Law of Quadratic ReciprocityKarl Frederich Gauss1801
8The Impossibility of Trisecting the Angle and Doubling the CubePierre Wantzel1837
9The Area of a CircleArchimedes
225 B.C.
10Euler΄s Generalization of Fermat΄s Little Theorem
(Fermat΄s Little Theorem)
Leonhard Euler
(Pierre de Fermat)
1760
(1640)
11The Infinitude of PrimesEuclid300 B.C.
12The Independence of the Parallel PostulateKarl Frederich GaussJanos BolyaiNikolai LobachevskyG.F. Bernhard Riemann collectively1870-1880
13Polyhedron FormulaLeonhard Euler1751
14Euler΄s Summation of 1 + (1/2)^2 + (1/3)^2 + .. (the Basel Problem).Leonhard Euler1734
15Fundamental Theorem of Integral CalculusGottfried Wilhelm von Leibniz1686
16Insolvability of General Higher Degree EquationsNiels Henrik Abel1824
17DeMoivre΄s TheoremAbraham DeMoivre1730
18Liouville΄s Theorem and the Construction of Trancendental NumbersJoseph Liouville1844
19Four Squares TheoremJoseph-Louis Lagrange1770
20Primes that Equal to the Sum of Two Squares (Genus theorem)??
21Green΄s TheoremGeorge Green1828
22The Non-Denumerability of the ContinuumGeorg Cantor1874
23Formula for Pythagorean TriplesEuclid300 B.C.
24The Undecidability of the Continuum HypothesisPaul Cohen1963
25Schroeder-Bernstein Theorem??
26Leibnitz΄s Series for PiGottfried Wilhelm von Leibniz1674
27Sum of the Angles of a TriangleEuclid300 B.C.
28Pascal΄s Hexagon TheoremBlaise Pascal1640
29Feuerbach΄s TheoremKarl Wilhelm Feuerbach1822
30The Ballot ProblemJ.L.F. Bertrand1887
31Ramsey΄s TheoremF.P. Ramsey1930
32The Four Color ProblemKenneth Appel and Wolfgang Haken1976
33Fermat΄s Last TheoremAndrew Wiles1993
34Divergence of the Harmonic SeriesNicole Oresme1350
35Taylor΄s TheoremBrook Taylor1715
36Brouwer Fixed Point TheoremL.E.J. Brouwer1910
37The Solution of a CubicScipione Del Ferro1500
38Arithmetic Mean/Geometric Mean (Proof by Backward Induction)
(Polya Proof)
Augustin-Louis Cauchy
George Polya
?
?
39Solutions to Pell΄s EquationLeonhard Euler1759
40Minkowski΄s Fundamental TheoremHermann Minkowski1896
41Puiseux΄s TheoremVictor Puiseux (based on a discovery of Isaac Newtonof 1671)1850
42Sum of the Reciprocals of the Triangular NumbersGottfried Wilhelm von Leibniz1672
43The Isoperimetric TheoremJacob Steiner1838
44The Binomial TheoremIsaac Newton1665
45The Partition TheoremLeonhard Euler1740
46The Solution of the General Quartic EquationLodovico Ferrari1545
47The Central Limit Theorem??
48Dirichlet΄s TheoremPeter Lejune Dirichlet1837
49The Cayley-Hamilton ThoeremArthur Cayley1858
50The Number of Platonic SolidsTheaetetus400 B.C.
51Wilson΄s TheoremJoseph-Louis Lagrange1773
52The Number of Subsets of a Set??
53Pi is TrancendentalFerdinand Lindemann1882
54Konigsberg Bridges ProblemLeonhard Euler1736
55Product of Segments of ChordsEuclid300 B.C.
56The Hermite-Lindemann Transcendence TheoremFerdinand Lindemann1882
57Heron΄s FormulaHeron of Alexandria75
58Formula for the Number of Combinations??
59The Laws of Large Numbers<many><many>
60Bezout΄s TheoremEtienne Bezout?
61Theorem of CevaGiovanni Ceva1678
62Fair Games Theorem??
63Cantor΄s TheoremGeorg Cantor1891
64L΄ Hopital΄s RuleJohn Bernoulli1696?
65Isosceles Triangle TheoremEuclid300 B.C.
66Sum of a Geometric SeriesArchimedes260 B.C.?
67e is TranscendentalCharles Hermite1873
68Sum of an arithmetic seriesBabylonians1700 B.C.
69Greatest Common Divisor AlgorithmEuclid300 B.C.
70The Perfect Number TheoremEuclid300 B.C.
71Order of a SubgroupJoseph-Louis Lagrange1802
72Sylow�s TheoremLudwig Sylow1870
73Ascending or Descending SequencesPaul Erdos and G. Szekeres1935
74The Principle of Mathematical InductionLevi ben Gerson1321
75The Mean Value TheoremAugustine-Louis Cauchy1823
76Fourier SeriesJoseph Fourier1811
77Sum of kth powersJakob Bernouilli1713
78The Cauchy-Schwarz InequalityAugustine-Louis Cauchy1814?
79The Intermediate Value TheoremAugustine-Louis Cauchy1821
80The Fundamental Theorem of ArithmeticEuclid300 B.C.
81Divergence of the Prime Reciprocal SeriesLeonhard Euler1734?
82Dissection of Cubes (J.E. Littlewood΄s (elegant proof)R.L. Brooks1940
83The Friendship TheoremPaul Erdos, Alfred Renyi, Vera Sos1966
84Morley΄s TheoremFrank Morley1899
85Divisibility by 3 Rule??
86Lebesgue Measure and IntegrationHenri Lebesgue1902
87Desargues΄s TheoremGerard Desargues1650
88Derangements Formula??
89The Factor and Remainder Theorems??
90Stirling΄s FormulaJames Stirling1730
91The Triangle Inequality??
92Pick΄s TheoremGeorge Pick1899
93The Birthday Problem??
94The Law of CosinesFrancois Viete1579
95Ptolemy΄s TheoremPtolemy120?
96Principle of Inclusion/Exclusion??
97Cramer΄s RuleGabriel Cramer1750
98Bertrand΄s PostulateJ.L.F. Bertrand1860?
99Buffon Needle ProblemComte de Buffon1733
100Descartes Rule of SignsRene Descartes1637

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