Sudah mulai ribuan tahun yang lalu manusia mencari hal-hal yang bisa dihimpun sesuai kategorinya untuk menjadi “100 hal ter-“ baik atau buruk dalam banyak bidang. Baik dalam dunia perfilman maupun ilmu pengetahuan. Mulai dari orang yang tertinggi, orang yang terkaya, dan banyak lagi lainnya.
Sudah kebiasaan manusia untuk membuat pola dan mendaftar segala sesuatu dengan maksud untuk memberikan penghargaan bagi mereka yang telah memberikan karya terbaik. Disegala bidang pasti ada yang terbaik di bidang masing-masing.
Tidak mau ketinggalan, para Matematikawan dunia, pada konferensi Matematika pada bulan Juli tahun 1999, Paul dan Jack Abad mempresentasikan daftar dari 100 teorema yang terkeren “The Hundred Greatest Theorems.” Mereka me-rankingnya berdasarkan kriteria-kriteria berikut ini : “Posisi teorema bergantung pada literature, kualitas dari pembuktiannya, dan hasil akhir yang tidak disangka-sangka”- “the place the theorem holds in the literature, the quality of the proof, and the unexpectedness of the result.” Waw, sungguh luar biasa. Bagi mereka, itulah sisi keindahan Matematika.
Daftar berikut ini pastinya bisa berubah-ubah layaknya penilaian pada dunia perfileman dan buku. Akan tetapi semua teorema yang berada di daftar berikut ini merupakan teorema-teorema yang benar-benar besar kegunaannya. Berikut ini teorema-teorema tersebut.
100 Teorema Terkeren untuk dibuktikan
| 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 | Kurl 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) | Leonhad 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 (The Basel Problem) | Leonhard Euler | 1734 |
| 15 | Fundamental Theorem of Integral Calculus | Gottfried Wilhel, 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 | |
| 20 | Primes that Equal to the Sum of Two Squares (Genus theorem) | ||
| 21 | Green’s Theorem | George Green | 1828 |
| 22 | The Non-Denumerability of the Continuum | George 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 Wilhel, 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 (Poof by Backward Induction)
(Polya Proof) |
Augustin-Louis Cauchy | |
| 39 | Solution 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 Newtown 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 General Quartic Equation | Lodovico Ferrari | 1545 |
| 47 | The Central Limit Theorem | ||
| 48 | Dirichlet’s Theorem | Peter Lejune Dirichlet | 1837 |
| 49 | The Cayley-Hamilton Theorem | 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 | Konigsbergs Bridges Problem | Leonhard Euler | 1736 |
| 55 | Product of Segments of Chords | Euclid | 300 B.C |
| 56 | The Hermite-Lindemann Transcendence Theorem | Ferdinan Lindemann | 1882 |
| 57 | Heron’s Formula | Heron of Alexandria | 75 |
| 58 | Formula for the Number of Combinations | ||
| 59 | The Laws of Large Number | ||
| 60 | Bezout’s Lemma | Etienne Bezout | |
| 61 | Theorem of Ceva | Giovanni Ceva | 1678 |
| 62 | Fair Games Theorem | ||
| 63 | Cantor’s Theorem | George Cantor | 1891 |
| 64 | L’Hopital’s Rule | John Bernouli | 1969 |
| 65 | Isosceles triangle Theorem | Euclid | 300 B.C |
| 66 | Sum of a Geometric Series | Archimedes | 260 B.C |
| 67 | 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 -th powers | Jakob Bernouilli | 1713 |
| 78 | The Cauchy –Szhwarz 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) | .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 | |
| 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 |
Mungkin jika kita menguasai semua pembuktian dari teorema-teorema di atas ini, kita akan lebih bisa mencintai Matematika. Karena keindahan mereka berada pada pembuktiannya. Kita semua tahu, keindahan identik dengan hal yang sulit. Sulit dicerna, sulit dibuat, sulit ditiru, sulit untuk dilakukan. Akan tetapi, ingat, sulit tidak berarti tidak mungkin. 🙂
MahinMuhammad 