Famous Mathematical Theorems
Theorem↕ | Proven By↕ | Year↕ | Field↕ | Known For↕ |
|---|---|---|---|---|
Pythagorean Theorem | Pythagoras (attributed) | ~500 BC | Geometry | a^2 + b^2 = c^2, most famous theorem in mathematics |
Fundamental Theorem of Arithmetic | Euclid | ~300 BC | Number theory | Every integer has unique prime factorization |
Fundamental Theorem of Calculus | Newton and Leibniz | 1670s | Calculus | Links differentiation and integration |
Euclid's Infinitude of Primes | Euclid | ~300 BC | Number theory | Proved there are infinitely many primes |
Fermat's Last Theorem | Andrew Wiles | 1994 | Number theory | No integer solutions to x^n + y^n = z^n for n>2, open for 358 years |
Godel's Incompleteness Theorems | Kurt Godel | 1931 | Logic | Any consistent system contains undecidable statements |
Prime Number Theorem | Hadamard and de la Vallee-Poussin | 1896 | Number theory | Density of primes approaches n/ln(n) |
Four Color Theorem | Appel and Haken | 1976 | Graph theory | Any planar map can be colored with 4 colors, first computer proof |
Poincare Conjecture | Grigori Perelman | 2003 | Topology | Only Millennium Prize problem solved, Perelman declined $1M and Fields |
Pythagorean Triples Theorem | Euclid | ~300 BC | Number theory | Parametrization of all integer right triangles |
Bayes' Theorem | Thomas Bayes | 1763 | Probability | Foundation of Bayesian inference, updates beliefs with evidence |
Central Limit Theorem | Laplace, Lyapunov | 1810-1901 | Statistics | Sums of random variables approach normal distribution |
Cantor's Diagonal Argument | Georg Cantor | 1891 | Set theory | Proved real numbers are uncountably infinite |
Banach-Tarski Paradox | Banach and Tarski | 1924 | Set theory | Sphere can be decomposed and reassembled into two identical copies |
Taylor's Theorem | Brook Taylor | 1715 | Analysis | Approximates functions by polynomial series |
Riemann Hypothesis (conjecture) | Bernhard Riemann (proposed) | 1859 | Number theory | Most famous unsolved problem, Clay Millennium Prize |
Euler's Identity | Leonhard Euler | 1748 | Analysis | e^(i*pi) + 1 = 0, called the most beautiful equation |
Bolzano-Weierstrass Theorem | Bolzano and Weierstrass | 1817-1865 | Analysis | Every bounded sequence has convergent subsequence |
Stokes' Theorem | George Stokes (generalized) | 1850s | Vector calculus | Generalizes fundamental theorem of calculus to manifolds |
Classification of Finite Simple Groups | Hundreds of mathematicians | 2004 | Group theory | Enormous theorem, ~15,000 pages, monstrous groups |
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