Mathematics

Definition

Mathematics is a field of study that discovers and organizes methods, theories, and theorems that are developed and proved either in response to the needs of empirical sciences or the needs of mathematics itself. There are many areas of mathematics, including number theory, algebra, geometry, analysis, and set theory.

Related concepts

A Mathematician's Apology Abel Prize Abstract algebra Abstraction (mathematics)Accountant Actually infinite Actuary Addison-Wesley Publishing Company Addition Adelard of Bath Adrien-Marie Legendre Advances in Mathematics Aesthetic Affine geometry Al-Jabr Al-Khwarizmi Alan Sokal Albert Einstein Alexander Marshack Alexandria Alfred Tarski Algebra Algebraic expression Algebraic geometry Algebraic number theory Algebraic structure Algebraic topology Algorithm American Mathematical Society Amir Alexander Amy Roth McDuffie Analysis (mathematics)Analytic geometry Analytic number theory Ancient China Ancient Egypt Ancient Egyptian mathematics Ancient Greek Ancient Greek mathematicians Ancient Greek mathematics Ancient Greeks Ancient Near East Andrew Wiles André Weil Angle Apery's theorem Apodictic Apollonius of Perga Applied mathematics Approximation Approximation theory Arabic Archimedes Architecture Archive.today Archive for History of Exact Sciences Area Areas of mathematics Aristotle Arithmetic Arithmetic geometry Armand Borel Astrology Astronomy Axiom Axiomatic method Babylonia Babylonian mathematics Bakhshali manuscript Beauty Benjamin Peirce Bertrand Russell Biology Boolean algebra Bulletin of the American Mathematical Society Butterfly Byju's C.R. Rao C. R. Rao Calculations Calculus Cambridge University Press Cantor's diagonal argument Carl B. Boyer Carl Benjamin Boyer Carl Friedrich Gauss Carl Gauss Carnegie Mellon University Cartesian coordinates Category theory Catherine Goldstein Cauchy sequence Celestial mechanics Central limit theorem Charles Hermite Charles Sanders Peirce Chern Medal Chess Christian Goldbach Christine Proust Cicero Circle Circular cylinder Claudia Zaslavsky Clause Clinical trial Cliodynamics Coding theory Columbia University Combinatorial optimization Combinatorics Commodity trader Communications on Pure and Applied Mathematics Commutative algebra Commutative ring Compiler Complex analysis Complex geometry Complex number Complex systems Computability theory Computational complexity Computational complexity theory Computational geometry Computational mathematics Computationally expensive Computer Computer-assisted proof Computer-based mathematics education Computer algebra Computer network Computer program Computer science Concept Concision Cone Conic section Conic sections Conjecture Consistent Constraint programming Continuous deformation Continuous functions Continuous game Continuum (set theory)Control theory Controversy over Cantor's theory Convex geometry Convex optimization Convex set Corollary Cosine Cost Countable Counterexample Counting Cryptography Curve Cyclic group Cylindrical algebraic decomposition Dark Age David Hilbert Decidability of the first-order theory of the real numbers Decimal point Decision science Decision theory Deductive reasoning Definitions of mathematics Dennis Elliot Shasha Design of experiments Differentiable function Differential calculus Differential equation Differential geometry Differential topology Diophantine analysis Diophantine geometry Diophantus Discrete geometry Discrete mathematics Discrete optimization Discrete probability distribution Discretization Division (mathematics)Dora Musielak Dover Publications Early modern period Economics Economist Einstein Eleanor Robson Elementary algebra Elementary arithmetic Elemente der Mathematik Ellipse Emmy Noether Empirical sciences Encyclopaedia of Islam Online Encyclopaedia of Mathematics Engineering Engineering mathematics Enumeration Epistemology Equals sign Equation Eric Temple Bell Error correcting code Euclid Euclid's Elements Euclidean geometry Euclidean plane Euclidean space Eugene Wigner Euler Evolutionary fitness Exclusive or Expected loss Experimentation Expression (mathematics)Faculty of Mathematics, University of Cambridge Falsifiable Fashionable Nonsense Fast Fourier transform Feit–Thompson theorem Fermat's Last Theorem Field (mathematics)Fields Medal Finance Financial analyst Finite geometry Flat module Florian Cajori Formal proof Formal system Formal verification Formalism (philosophy of mathematics)Formula Foundational crisis in mathematics Foundational crisis of mathematics Foundations of mathematics Four Color Theorem Four color theorem Fractal Fractals Frank Kelly (mathematician)François Viète Fred S. Roberts Free module Frequencies Function (mathematics)Functional analysis Future of mathematics G. H. Hardy Game theory Gaussian distribution General relativity General topology Generating series Geomathematics Geometric shape Geometric topology Geometric transformation Geometry Geometry of numbers Geopolitics Georg Cantor George E. Collins George Saliba Gerhard Heinzmann Giant pufferfish Girard Desargues Glossary of mathematical symbols Glossary of mathematics Glyph Goldbach's conjecture Golden Age of Islam Gottfried Leibniz Gottfried Wilhelm Leibniz Graph of a function Graph theory Greco-Roman world Greek alphabet Greek mathematics Grigori Perelman Group theory Gödel's incompleteness theorems Gödel's theorems Günter M. Ziegler Harmonic analysis Henri Poincaré Herbert M. Sauro Herbert Robbins Hermann Weyl Higher arithmetic Hilbert's problems Hindu–Arabic numeral system Hipparchus of Nicaea Historical dynamics History of logarithms History of mathematics Homeomorphism Homo economicus Homological algebra Homotopy theory Howard Eves Human activity Hypercomplex analysis Hypergraph Hypothesis testing Ian Stewart (mathematician)Illuminated manuscript Imperial China Imperial examination Implementation Implementation (computer science)Implicit equation Imre Leader Independence (probability theory)Indian mathematics Inference rule Infinite series Infinite set Infinitesimal calculus Infinity Informal mathematics Information technology consulting Information theory Integer Integer factorization Integer programming Integral calculus Integral sign Integration (mathematics)International Association for the Evaluation of Educational Achievement Internet Intuition Intuitionistic logic Invariant (mathematics)Isaac Newton Ishango bone Islamic mathematics Israel Kleiner (mathematician)Jackie Stedall James Franklin (philosopher)Jan Gullberg Jean Bricmont Jeremy Avigad Jesuit Jo-Anne LeFevre Joachim Schwermer Joan Moschovakis Johannes Kepler John Charles Fields John Napier John Wiley & Sons Johns Hopkins University Press Josef Mitterer Joseph Halpern June Barrow-Green Karen Hunger Parshall Karl Popper Karl Weierstrass Kepler conjecture Klaus Hulek Kluwer Academic Publishers Knot theory Kondratiev cycle Kurt Gödel L'Enseignement Mathématique L. E. J. Brouwer Language of mathematics Large numbers Late Middle English Latin alphabet Laurent Schwartz Law (mathematics)Law of excluded middle Leibniz Lemma (mathematics)Leo Corry Leonhard Euler Leroy P. Steele Prize Less-than sign Liberal arts Lie algebra Lie group Line (geometry)Line segments Linear algebra Linear equation Linguistics List of films about mathematicians List of mathematical jargon List of mathematicians List of mathematics awards List of mathematics books List of mathematics journals Lists of mathematicians Lists of mathematics topics Lloyd N. Trefethen Logic Logical disjunction Lotka–Volterra equations Lynch School of Education and Human Development Manifold Manifold theory Marine navigation Mario Bunge Markov chain Martianus Capella Massimo Pigliucci Math (disambiguation)Mathematical Association of America Mathematical Platonism Mathematical Reviews Mathematical abstraction Mathematical analysis Mathematical and theoretical biology Mathematical anxiety Mathematical chemistry Mathematical constant Mathematical economics Mathematical finance Mathematical formulas Mathematical geology Mathematical linguistics Mathematical logic Mathematical model Mathematical notation Mathematical object Mathematical optimization Mathematical physics Mathematical problem Mathematical proof Mathematical psychology Mathematical rigor Mathematical rigour Mathematical sciences Mathematical sociology Mathematical statistics Mathematical structure Mathematical theory Mathematician Mathematicians Mathematics, form and function Mathematics (disambiguation)Mathematics Subject Classification Mathematics and art Mathematics education Matrix (mathematics)Matrix theory Matroid Mean Measure (mathematics)Measure theory Measurement Medicine Mesopotamia Metaphysics Meteorology Method of exhaustion Methodist University Michael Atiyah Michael Sipser Michiel Hazewinkel Millennium Prize Problems Model theory Moderne Algebra Modular arithmetic Morris Kline Moscow Mathematical Papyrus Moshe Vardi Multilinear algebra Multiplication Multiplication sign Multivariable calculus NASA Nabta Playa Natalie Wolchover National Research Council (United States)Natural number Natural science Neil Immerman Neologism Neurobiology Neuter (grammar)Newton's law of gravitation Niccolò Guicciardini Nicolas Bouleau Nikolai Kondratiev Nobel Prize Non-Euclidean geometries Nonlinear system Norbert Schappacher Norwood Russell Hanson Noun phrase Nubians Number Number line Number theory Numerical analysis Numerical calculation Numerical linear algebra Numerology Objective function Oceanography Omar Khayyam Omega baryon Open Court Publishing Company Open access Open problem Operation (mathematics)Operations research Optimization Oral tradition Order theory Ordinary differential equation Oxford English Dictionary Oxford University Press PIRLS P versus NP problem Parabola Paradigm shift Parallel (geometry)Parallel lines Parallel postulate Parameter estimation Partial differential equation Particle Paul Erdős Peano arithmetic Pedagogy Penelope Maddy Perfect fifth Perfect information Perihelion precession of Mercury Perspectives on Science Peter Turchin Peter Whittle (mathematician)PhilArchive Philip J. Davis Philip Jourdain Philosophy Philosophy Now Philosophy of Science (journal)Philosophy of mathematics Phokion Kolaitis Physics Pi Mu Epsilon Journal Pierre de Fermat Plane (geometry)Plane geometry Planet Planetology Plato Pleonasm Plimpton 322 Plural Plus sign Poincaré conjecture Points at infinity Poker Polymath Polynomial Polynomial equation Popular mathematics Population dynamics Positron Postulate Potential theory Prehistoric Prime factorization Prime number Prime numbers Princeton University Press Probability Probability distribution Probability theory Program analysis Projective geometry Proof (mathematics)Proof assistant Proof theory Proofs from THE BOOK Property (philosophy)Pseudoscience Psychology Pure mathematics Pure mathematics in Ancient Greece Puzzle Pythagoras Pythagorean theorem Pythagorean triple Pythagoreanism Pythagoreans Quadratic equation Quadratic formula Quadrivium Quanta Magazine Quantum mechanics Quasi-empiricism in mathematics RSA cryptosystem Ralph P. Boas Jr.Random sampling Rational choice theory Rational number Raymond Clare Archibald Raymond L. Wilder Reaction–diffusion system Real algebraic geometry Real analysis Real number Reason Recreational mathematics Relation (mathematics)Relationship between mathematics and physics Renaissance Renate Tobies René Descartes Reuben Hersh Rhind papyrus Richard Courant Richard Dedekind Riemann hypothesis Riemannian geometry Ring (mathematics)Ring theory Risk Robert Harper (computer scientist)Roberta Millstein Robin Hartshorne Rod Downey Roger Apery Roman Frigg Ronald Brown (mathematician)Rorschach test Rounding error Rubik's Cube group Russell's paradox STEM Saint Augustine Sal Restivo Saunders Mac Lane Scheme theory Science Science, technology, engineering, and mathematics Selection algorithm Self-similarity Series (mathematics)Set (mathematics)Set theory Sexagesimal Sharaf al-Dīn al-Ṭūsī Sigma Xi Simplicity Sine Sirius Social sciences Sociology Solid mechanics Solids of revolution Solomon Feferman Sonja Brentjes South China Morning Post Space (mathematics)Spacetime Special relativity Sphere packing Spherical trigonometry Springer International Publishing Springer New York Springer Science & Business Media Stanford Encyclopedia of Philosophy Statistical decision theory Statistical hypothesis testing Statistical method Statistical theory Statistician Statistics Stephan Hartmann Stephen Wolfram Straightedge and compass construction Structural geology Subscript Subset Subtraction Summation Sundials Supply and demand Surveying Symbolic computation Symmetry Symmetry group Synthetic geometry Syracuse, Italy Systems science TIMSS Tang dynasty Technical definition The Compendious Book on Calculation by Completion and Balancing The Mathematical Experience The Mathematical Intelligencer The Oxford Dictionary of English Etymology The University of Georgia Theoni Pappas Theorem Theoretical computer science Theory of computation Theory of distributions Theory of relativity Thomas Callister Hales Thomas Heath (classicist)Thomas Kuhn Timeline of mathematics Timeline of scientific discoveries Timothy Gowers Topological space Topology Trajectories Transcendence theory Trigonometry Turing pattern Type theory Ulam spiral Universal algebra University University of California Merced University of Cambridge University of Kentucky University of St. Andrews University of St Andrews Unknown (algebra)Unreasonable effectiveness of mathematics Van der Waerden Variable (mathematics)Variance Vector space Vedic period Venn diagram Victor Vianu Weierstrass function Western Europe Western world Wiles's proof of Fermat's Last Theorem Wiley (publisher)William J. LeVeque Wolf Prize in Mathematics Wolfgang Sartorius von Waltershausen World Scientific World War II World War II in Yugoslavia Yadolah Dodge Zermelo–Fraenkel set theory Øystein Ore

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