100 Greatest Theorems_

100 Greatest Theorems of All Time: Facts, Inventors, Years

Posted on
(Last Updated On: November 17, 2023)

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

More Interesting Articles

Post Views: 367

Leave a Reply

Your email address will not be published. Required fields are marked *