Skip to Main Content

Mathematics Atlas

How Proof Is Made

Sign In

Text size

100%

Theme

Switch Atlas

Interactive AtlasThe Family Home

The Inner World

The Civil World

The Natural World

Browse By

Inequality

Statement form sorts theorems by the shape of the claim they make, such as an equation, an inequality or an existence statement. Wikipedia states Fermat's Last Theorem as the claim "that there are no positive integers a, b, c, n with n greater than 2 such that a to the n plus b to the n equals c to the n," a negative existence claim rather than a formula to compute with. This dimension groups theorems that make the same kind of mathematical statement.

Inequality

164 entries

Branch

Topic Area

Proved

Proved By

Named After

Anderson's Theorem

Ankeny-Artin-Chowla Congruence

Approximate Max-Flow Min-Cut Theorem

Area Theorem (Conformal Mapping)

Art Gallery Problem

Artin-Rees Lemma

Azuma's Inequality

Baker's Theorem

Balinski's Theorem

Barban-Davenport-Halberstam Theorem

Bauer-Fike Theorem

Beck's Theorem (Geometry)

Behrend's Theorem

Berry-Esseen Theorem

Bertrand's Ballot Theorem

Bertrand's Postulate

Binet-Cauchy Identity

Blaschke-Santalo Inequality

Bombieri-Vinogradov Theorem

Bondy's Theorem

Bonnet-Myers Theorem

Borel-Caratheodory Theorem

Bourbaki-Witt Theorem

Bregman-Minc Inequality

Brooks' Theorem

Brouwer Fixed-Point Theorem

Brun-Titchmarsh Theorem

Budan's Theorem

Cantelli's Inequality

Cantor's Theorem

Carmichael's Theorem

Cartan-Dieudonne Theorem

Cauchy's Theorem (Group Theory)

Cauchy-Schwarz Inequality

Chebyshev's Inequality

Chernoff Bound

Chevalley-Warning Theorem

Cohn's Irreducibility Criterion

Condorcet Jury Theorem

Coupon Collector's Problem

Craig Interpolation Theorem

Cramer-Rao Bound

Cramer-Rao Inequality

Crossing Number Inequality

De Bruijn-Erdos Theorem (Incidence Geometry)

Descartes' Rule of Signs

Dirac's Theorem

Dirichlet's Approximation Theorem

Doob's Martingale Convergence Theorem

Double Bubble Theorem

Earnshaw's Theorem

Easton's Theorem

Egorov's Theorem

Elias Bassalygo Bound

Erdos-Ko-Rado Theorem

Erdos-Mordell Inequality

Erdos-Posa Theorem

Erdos-Stone Theorem

Erdos-Szekeres Theorem

Euclid's Lemma

Exterior Angle Theorem

Faltings's Theorem

Fatou's Lemma

Fermat's Last Theorem

Fermat's Polygonal Number Theorem

Fodor's Lemma

Folk Theorem (Game Theory)

Four Color Theorem

Freudenthal Suspension Theorem

Fundamental Theorem of Algebra

Gauss Congruence

Gershgorin Circle Theorem

Gibbard's Theorem

Gromov's Non-Squeezing Theorem

Gronwall's Inequality

Hadamard Three-Lines Theorem

Hales-Jewett Theorem

Hall's Marriage Theorem

Hasse's Theorem on Elliptic Curves

H-Cobordism Theorem

Helly's Theorem

Hilbert-Waring Theorem

Hinge Theorem

Hoeffding's Inequality

H-Theorem

Hurwitz's Theorem (Number Theory)

Immerman-Szelepcsenyi Theorem

Isoperimetric Inequality

Jurkat-Richert Theorem

Kepler Conjecture

Kneser's Theorem (Combinatorics)

Kolmogorov's Maximal Inequality

Kolmogorov's Three-Series Theorem

Konig's Theorem (Set Theory)

Kővári-Sos-Turán Theorem

Kronecker's Approximation Theorem

Krull-Akizuki Theorem

Krull's Principal Ideal Theorem

Landau Prime Ideal Theorem

Le Cam's Theorem

Leggett-Garg Inequality

Leray-Schauder Fixed-Point Theorem

Linnik's Theorem

Liouville's Approximation Theorem

Maier's Theorem

Mann's Theorem

Mantel's Theorem

Markov's Inequality

Mihailescu's Theorem

Minimax Theorem

Minkowski's Inequality

Minkowski's Theorem

Multiplicity-One Theorem

Nash Equilibrium

Nash-Williams Formula

Niven's Theorem

Noether Normalization Lemma

Ore's Theorem

Picard Theorem

Planar Separator Theorem

Poincare Lemma

Poppy-Seed Bagel Theorem

Prigogine's Theorem

Prime Number Theorem

Proof of Fermat's Last Theorem for Specific Exponents

Proof that 22/7 Exceeds Pi

Rauch Comparison Theorem

Rellich-Kondrachov Theorem

Riemann-Hurwitz Formula

Riesz-Thorin Interpolation Theorem

Rosser's Theorem

Roth's Theorem (Thue-Siegel-Roth)

Rouche's Theorem

Saint-Venant's Theorem

Sanov's Theorem

Savitch's Theorem

Schmidt Subspace Theorem

Schwarz Lemma

Sensitivity Theorem

Shapley-Folkman Theorem

Siegel's Theorem on Integral Points

Silver's Theorem

Six Exponentials Theorem

Sophie Germain's Theorem

Sperner's Theorem

Sphere Packing Theorems in Dimensions 8 and 24

Squeeze Theorem

Sunflower Lemma

Szemeredi Regularity Lemma

Three-Gap Theorem

Thue's Theorem

Tijdeman's Theorem

Titchmarsh Convolution Theorem

Transfinite Recursion Theorem

Turan-Kubilius Inequality

Turan's Theorem

Tutte's Theorem (Graph Theory)

Vinogradov's Mean-Value Theorem

Vizing's Theorem

Weinberg-Witten Theorem

Whitney Embedding Theorem

Whitney Immersion Theorem

Zorn's Lemma

Zsigmondy's Theorem

Connections

Showing the first 400 of 908 connections.

Sources

MacTutor History of Mathematics Archive

University of St Andrews, School of Mathematics and Statistics

Contains: Central Limit Theorem
Contains: Bayes' Theorem

View the Source

Wikipedia: Noether's Theorem

Wikimedia FoundationContains: Noether's TheoremView the Source

Wikipedia: Cayley's Theorem

Wikimedia FoundationContains: Cayley's TheoremView the Source

Comments (0)

No comments yet. Be the first to share a thought.

Reader Challenges (0)

No disputes yet. Spotted an error or a better source? Open the first one.