The dawn of the new millennium ushered in an era of intellectual retrospection, prompting enthusiasts across various disciplines to embark on a quest for identifying and enumerating the most significant achievements within their respective domains. Within the realm of mathematics, this penchant for recognition materialized into the compilation of a definitive list: the 100 Greatest Theorems. As a testament to the universal allure of rankings and lists, this undertaking mirrored similar endeavors in disparate fields, from the silver screen, where the American Film Institute meticulously cataloged the greatest movies, to the world of literature, with the Modern Library assembling a compendium of the most influential books.

### Navigating the Pantheon of Mathematical Brilliance

The compilation of the 100 Greatest Theorems is not merely an exercise in enumeration but a profound journey through the labyrinthine corridors of mathematical brilliance. Each theorem, a beacon illuminating the intellectual landscape, reflects the profound insights of the brilliant minds that conceived them. As one delves into the intricacies of these theorems, a tapestry of mathematical thought unfolds, weaving together disparate threads of logic, abstraction, and elegance. These theorems, like celestial bodies in a vast mathematical cosmos, not only stand as pillars of intellectual achievement but also serve as guiding lights for generations of mathematicians yet to traverse the uncharted territories of discovery.

### A Tapestry of Human Ingenuity and Insight

Beyond the mere abstraction of mathematical concepts, the compilation of the 100 Greatest Theorems is a celebration of human ingenuity and insight. It is a testament to the collective brilliance of minds across centuries, each contributing a stitch to the intricate tapestry of mathematical understanding. From the ancient Greeks who laid the foundations of geometry to the modern luminaries who unlocked the secrets of abstract algebra, this compilation transcends mere numerical rankings, serving as a testament to the enduring human spirit that seeks to unravel the mysteries of the universe through the language of mathematics.

### The Intersection of Art and Logic

Mathematics, often perceived as an austere and abstract discipline, reveals its profound beauty in the compilation of the 100 Greatest Theorems. Here, at the intersection of art and logic, elegance reigns supreme. Each theorem is not just a sterile statement of fact but a manifestation of aesthetic discernment, where the elegance of a proof is as revered as the profundity of its implications. In this curated collection, the mathematical landscape unfolds as a masterpiece, with each theorem contributing a brushstroke to the intricate canvas of human understanding, proving that in the world of mathematics, beauty is not just skin-deep but embedded in the very fabric of logical reasoning.

### A Global Intellectual Odyssey

The compilation of the 100 Greatest Theorems transcends geographic boundaries, reflecting a truly global intellectual odyssey. From the ancient civilizations along the Tigris and Euphrates to the modern research institutions scattered across the continents, the journey of mathematical discovery is a testament to the universal pursuit of knowledge. This compilation serves as a mosaic, piecing together the diverse contributions of mathematicians from different cultures and epochs, showcasing that the pursuit of truth and understanding is a collective endeavor that knows no borders. This article will give an overview of the 100 Greatest Theorems.

### A Living Document of Intellectual Progress

As a living document of intellectual progress, the compilation of the 100 Greatest Theorems is not a static inventory but a dynamic reflection of the evolving landscape of mathematical thought. It stands as an invitation for future generations to engage with the challenges and mysteries that lie ahead. The theorems, like sentinels standing at the frontier of knowledge, beckon mathematicians to push the boundaries further, to explore the uncharted territories of conjecture and proof. In this sense, the compilation becomes not just a testament to the past but a guiding compass for the perpetual journey of mathematical exploration.

### The Unveiling of Mathematical Greatness

In the riveting landscape of mathematical exploration, the stalwarts Paul and Jack Abad boldly unveiled their magnum opus, “The Hundred Greatest Theorem,” during the Mathematics Conference in the scorching July of 1999. This monumental list, akin to a sacred scripture for the mathematical community, emerged not as a deterrent but as a beacon of intellectual curiosity. The conference hall buzzed with anticipation as the Abad duo prepared to present a compendium of mathematical brilliance that would echo through the corridors of academia.

### The Art of Ranking

Embedded within the fabric of their compilation was a meticulous ranking, a labyrinthine web of criteria that determined the hierarchy of these mathematical gems. The Abad brothers, arbiters of this intellectual symphony, adjudicated the theorems based on a trifecta of considerations: the exalted place the subject matter occupied in the annals of mathematical literature, the irrefutable quality of the evidence underpinning each theorem, and the sheer audacity of outcomes, unexpected and profound. Their criteria were not mere metrics; they were the weaver’s loom, intricately threading together the narrative of mathematical significance. Phone/PC Surveillance Software for Your Kids and Teens

### Voluntary, Yet Invaluable

Unlike a rigid decree etched in stone, this list assumed a voluntary nature, akin to the fluidity of a movie or book compilation. The Abad brothers extended an invitation, a mathematical voyage, to partake in the exploration of these intellectual wonders. The allure lay not in compulsion but in the undeniable allure of the results that unfolded. Each theorem, a tantalizing subplot in the grand narrative of mathematical exploration, beckoned curious minds to delve into the nuances and intricacies of its proof.

### Beyond Lists: The Ineffable Worth of Mathematical Subtypes

While the comparison to a movie or book list may seem facile, the mathematical subtypes unveiled within this compendium transcended the mundane. They were not just entries on a checklist; they were intricate puzzles, intellectual treasures waiting to be unearthed. The Abad brothers, with an unwavering dedication to the pursuit of mathematical excellence, offered a promise — a promise that over time, a virtual library of proofs would accompany each theorem. A tantalizing prospect, indeed, as the mathematical enthusiasts could envision a future where the list was not a static entity but a living, breathing testament to the dynamism of mathematical thought. Earn high commissions, make easy transactions worldwide, and grow your business by promoting Payoneer

### Satisfying Curiosity, One Theorem at a Time

As we stand at the threshold of this intellectual banquet, the audience is left yearning for the intricate proofs, the mathematical alchemy that substantiates each theorem. The Abad brothers’ biography, a roadmap of their intellectual journey, serves as a tantalizing prelude to the feast of knowledge laid before us. The list, a mere starting point, beckons curious minds to traverse the labyrinthine corridors of mathematical reasoning, promising satisfaction not just in the grandeur of the theorems but in the exquisite details woven into the fabric of each proof. The quest for mathematical enlightenment unfolds, and the mathematicians of the world find themselves on a journey that transcends the boundaries of time and space.

## 100 Greatest Theorems

1 | The Irrationality of the Square Root of 2 | Pythagoras and his school | 500 B.C. |

2 | Fundamental Theorem of Algebra | Karl Frederich Gauss | 1799 |

3 | The Denumerability of the Rational Numbers | Georg Cantor | 1867 |

4 | Pythagorean Theorem | Pythagoras and his school | 500 B.C. |

5 | Prime Number Theorem | Jacques Hadamard and Charles-Jean de la Vallee Poussin (separately) | 1896 |

6 | Godel’s Incompleteness Theorem | Kurt Godel | 1931 |

7 | Law of Quadratic Reciprocity | Karl Frederich Gauss | 1801 |

8 | The Impossibility of Trisecting the Angle and Doubling the Cube | Pierre Wantzel | 1837 |

9 | The Area of a Circle | Archimedes | 225 B.C. |

10 | Euler’s Generalization of Fermat’s Little Theorem
(Fermat’s Little Theorem) |
Leonhard Euler
(Pierre de Fermat) |
1760
(1640) |

11 | The Infinitude of Primes | Euclid | 300 B.C. |

12 | The Independence of the Parallel Postulate | Karl Frederich Gauss, Janos Bolyai, Nikolai Lobachevsky, G.F. Bernhard Riemann collectively | 1870-1880 |

13 | Polyhedron Formula | Leonhard Euler | 1751 |

14 | Euler’s Summation of 1 + (1/2)^2 + (1/3)^2 + ‘ (the Basel Problem). | Leonhard Euler | 1734 |

15 | Fundamental Theorem of Integral Calculus | Gottfried Wilhelm von Leibniz | 1686 |

16 | Insolvability of General Higher Degree Equations | Niels Henrik Abel | 1824 |

17 | DeMoivre’s Theorem | Abraham DeMoivre | 1730 |

18 | Liouville’s Theorem and the Construction of Trancendental Numbers | Joseph Liouville | 1844 |

19 | Four Squares Theorem | Joseph-Louis Lagrange | 1770 |

20 | Primes that are Equal to the Sum of Two Squares (Genus theorem) | ? | ? |

21 | Green’s Theorem | George Green | 1828 |

22 | The Non-Denumerability of the Continuum | Georg Cantor | 1874 |

23 | Formula for Pythagorean Triples | Euclid | 300 B.C. |

24 | The Undecidability of the Continuum Hypothesis | Paul Cohen | 1963 |

25 | Schroeder-Bernstein Theorem | ? | ? |

26 | Leibnitz’s Series for Pi | Gottfried Wilhelm von Leibniz | 1674 |

27 | Sum of the Angles of a Triangle | Euclid | 300 B.C. |

28 | Pascal’s Hexagon Theorem | Blaise Pascal | 1640 |

29 | Feuerbach’s Theorem | Karl Wilhelm Feuerbach | 1822 |

30 | The Ballot Problem | J.L.F. Bertrand | 1887 |

31 | Ramsey’s Theorem | F.P. Ramsey | 1930 |

32 | The Four Color Problem | Kenneth Appel and Wolfgang Haken | 1976 |

33 | Fermat’s Last Theorem | Andrew Wiles | 1993 |

34 | Divergence of the Harmonic Series | Nicole Oresme | 1350 |

35 | Taylor’s Theorem | Brook Taylor | 1715 |

36 | Brouwer Fixed Point Theorem | L.E.J. Brouwer | 1910 |

37 | The Solution of a Cubic | Scipione Del Ferro | 1500 |

38 | Arithmetic Mean/Geometric Mean (Proof by Backward Induction)
(Polya Proof) |
Augustin-Louis Cauchy
George Polya |
?
? |

39 | Solutions to Pell’s Equation | Leonhard Euler | 1759 |

40 | Minkowski’s Fundamental Theorem | Hermann Minkowski | 1896 |

41 | Puiseux’s Theorem | Victor Puiseux (based on a discovery of Isaac Newton of 1671) | 1850 |

42 | Sum of the Reciprocals of the Triangular Numbers | Gottfried Wilhelm von Leibniz | 1672 |

43 | The Isoperimetric Theorem | Jacob Steiner | 1838 |

44 | The Binomial Theorem | Isaac Newton | 1665 |

45 | The Partition Theorem | Leonhard Euler | 1740 |

46 | The Solution of the General Quartic Equation | Lodovico Ferrari | 1545 |

47 | The Central Limit Theorem | ? | ? |

48 | Dirichlet’s Theorem | Peter Lejune Dirichlet | 1837 |

49 | The Cayley-Hamilton Thoerem | Arthur Cayley | 1858 |

50 | The Number of Platonic Solids | Theaetetus | 400 B.C. |

51 | Wilson’s Theorem | Joseph-Louis Lagrange | 1773 |

52 | The Number of Subsets of a Set | ? | ? |

53 | Pi is Trancendental | Ferdinand Lindemann | 1882 |

54 | Konigsberg Bridges Problem | Leonhard Euler | 1736 |

55 | Product of Segments of Chords | Euclid | 300 B.C. |

56 | The Hermite-Lindemann Transcendence Theorem | Ferdinand Lindemann | 1882 |

57 | Heron’s Formula | Heron of Alexandria | 75 |

58 | Formula for the Number of Combinations | ? | ? |

59 | The Laws of Large Numbers | <many> | <many> |

60 | Bezout�s Theorem | Etienne Bezout | ? |

61 | Theorem of Ceva | Giovanni Ceva | 1678 |

62 | Fair Games Theorem | ? | ? |

63 | Cantor’s Theorem | Georg Cantor | 1891 |

64 | L’Hopital’s Rule | John Bernoulli | 1696? |

65 | Isosceles Triangle Theorem | Euclid | 300 B.C. |

66 | Sum of a Geometric Series | Archimedes | 260 B.C.? |

67 | e is Transcendental | Charles Hermite | 1873 |

68 | Sum of an arithmetic series | Babylonians | 1700 B.C. |

69 | Greatest Common Divisor Algorithm | Euclid | 300 B.C. |

70 | The Perfect Number Theorem | Euclid | 300 B.C. |

71 | Order of a Subgroup | Joseph-Louis Lagrange | 1802 |

72 | Sylow’s Theorem | Ludwig Sylow | 1870 |

73 | Ascending or Descending Sequences | Paul Erdos and G. Szekeres | 1935 |

74 | The Principle of Mathematical Induction | Levi ben Gerson | 1321 |

75 | The Mean Value Theorem | Augustine-Louis Cauchy | 1823 |

76 | Fourier Series | Joseph Fourier | 1811 |

77 | Sum of kth powers | Jakob Bernouilli | 1713 |

78 | The Cauchy-Schwarz Inequality | Augustine-Louis Cauchy | 1814? |

79 | The Intermediate Value Theorem | Augustine-Louis Cauchy | 1821 |

80 | The Fundamental Theorem of Arithmetic | Euclid | 300 B.C. |

81 | Divergence of the Prime Reciprocal Series | Leonhard Euler | 1734? |

82 | Dissection of Cubes (J.E. Littlewood’s ‘elegant’ proof) | R.L. Brooks | 1940 |

83 | The Friendship Theorem | Paul Erdos, Alfred Renyi, Vera Sos | 1966 |

84 | Morley’s Theorem | Frank Morley | 1899 |

85 | Divisibility by 3 Rule | ? | ? |

86 | Lebesgue Measure and Integration | Henri Lebesgue | 1902 |

87 | Desargues’s Theorem | Gerard Desargues | 1650 |

88 | Derangements Formula | ? | ? |

89 | The Factor and Remainder Theorems | ? | ? |

90 | Stirling’s Formula | James Stirling | 1730 |

91 | The Triangle Inequality | ? | ? |

92 | Pick’s Theorem | George Pick | 1899 |

93 | The Birthday Problem | ? | ? |

94 | The Law of Cosines | Francois Viete | 1579 |

95 | Ptolemy’s Theorem | Ptolemy | 120? |

96 | Principle of Inclusion/Exclusion | ? | ? |

97 | Cramer’s Rule | Gabriel Cramer | 1750 |

98 | Bertrand’s Postulate | J.L.F. Bertrand | 1860? |

99 | Buffon Needle Problem | Comte de Buffon | 1733 |

100 | Descartes Rule of Signs | Rene Descartes | 1637 |

**Source**: http://pirate.shu.edu/~kahlnath/Top100.html

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