Home›Mathematics›Discipline›MathematicsDisciplineMathematicsAlso Known As MathFormal SciencesReference and ClassificationVerifiedMathematics is the study of numbers, quantities, shapes, and the logical relationships between them, built up from definitions and proof rather than observation alone. It has been developed independently in many civilizations, from Babylonian and Egyptian arithmetic through Greek geometry and Indian and Islamic algebra to modern analysis, and it supplies the language in which every other science states and tests its theories. This description is adapted from Wikipedia contributors under CC BY-SA 4.0; changes were made. https://creativecommons.org/licenses/by-sa/4.0/FactsMathematicsConnectionsSourcesOpen Questions (1 open question)Comments (0)Reader Challenges (0)FactsFounded YearWell-attested300 BCE 1Euclid's Elements (c. 300 BCE) systematized geometry and number theory into the axiomatic, proof-based form that defines mathematics as a discipline rather than a scattered set of practical techniques; the same landmark-publication convention this atlas already uses for physics (Newton's Principia, 1687) and chemistry (Lavoisier's Traite, 1789). The exact year is not recorded; MacTutor and the wider historiography place it circa 300 BCE.Central QuestionWell-attestedWhat can be proven true from a given set of axioms, and which of the field's enduring unsolved problems, such as whether P equals NP, will yield to that method? 2ScopeWell-attestedMathematics studies abstract concepts such as numbers, geometric shapes, sets, functions and probabilities, using logical reasoning and proof to establish their properties as theorems, formulas and equations. 2SignificanceWell-attestedAround 300 BC Euclid organized the mathematical knowledge of his day by way of postulates and first principles, originating the axiomatic method that still defines mathematical proof today. The more than sixty first level branches recognized now, from number theory and geometry to discrete mathematics and mathematical logic, all still build proof on that same foundation. 2MathematicsFilter Results42 entriesField (legacy)AllAbstract algebra and theoretical physics (1)Analysis, number theory and mathematical notation (1)Calculus and its notation (1)Computability theory and cryptanalysis (1)Foundations of geometry, formalism and functional analysis (1)Geometry and the axiomatic method (1)Mathematical logic and philosophy (1)Mathematics (12)Mathematics (algebraic geometry) (1)Mathematics (geometry) (1)Mathematics (probability theory) (1)Mathematics (set theory and mathematical logic) (1)Mathematics and astronomy (2)Mathematics and computing (1)Mathematics and law (1)Mathematics and philosophy (1)Mathematics, nuclear physics, and computer science (1)Mathematics, Physics (2)Mathematics, physics and astronomy (1)Mathematics, specifically probability theory and statistics (1)Natural philosophy, mathematics and astronomy (1)Number Theory (1)Number theory, geodesy, differential geometry and astronomy (1)Number theory, infinite series and partition functions (1)Set theory and mathematics (1)EraAll626 BCE (1)287 BCE (1)780 (1)1596 (1)1601 (1)1646 (1)1707 (1)1736 (1)1749 (1)1752 (1)1777 (1)1789 (1)1802 (1)1811 (1)1815 (1)1821 (1)1826 (1)1845 (1)1850 (1)1854 (1)1856 (1)1862 (1)1868 (1)1882 (1)1887 (1)1892 (1)1903 (1)1906 (1)1909 (1)1912 (1)1913 (1)1916 (1)1928 (2)1934 (1)1949 (1)1953 (1)1955 (1)1966 (1)1975 (1)1977 (1)InstitutionAllBell Labs (1)In GroupAllAlgebra And Number Theory (13)Analysis (4)Applied Mathematics (1)Geometry And Topology (16)Logic And Foundations (3)Other Mathematicians (3)Probability And Statistics (2)NationalityAllAustria (1)France (7)Germany (2)Greece (2)Hungary (1)Iran (1)Norway (1)Poland (1)Russia (4)United Kingdom (1)United States (2)BrowseCompareSelect all 42Ada LovelaceMathematicsAdrien-Marie LegendreMathematicsAlan TuringMathematicsAlexander GrothendieckMathematicsAl-KhwarizmiMathematicsAndrew WilesMathematicsAndrey KolmogorovMathematicsAndrey MarkovMathematicsArchimedesMathematicsAugustin-Louis CauchyMathematicsBernhard RiemannMathematicsCarl Friedrich GaussMathematicsClaude ShannonMathematicsDavid HilbertMathematicsEmmy NoetherMathematicsEuclidMathematicsEvariste GaloisMathematicsFelix HausdorffMathematicsGeorg CantorMathematicsGottfried Wilhelm LeibnizMathematicsGrigori PerelmanMathematicsHenri PoincareMathematicsJohn NashMathematicsJoseph-Louis LagrangeMathematicsKurt GodelMathematicsLeonhard EulerMathematicsMaryam MirzakhaniMathematicsNiels Henrik AbelMathematicsPafnuty ChebyshevMathematicsPaul CohenMathematicsPaul ErdosMathematicsPierre de FermatMathematicsPierre-Simon LaplaceMathematicsRene DescartesMathematicsShing-Tung YauMathematicsSofia KovalevskayaMathematicsSrinivasa RamanujanMathematicsStanislaw UlamMathematicsStefan BanachMathematicsTerence TaoMathematicsThales of MiletusMathematicsYitang ZhangMathematicsConnectionsAssociated WithFields Medal, Institutions Well-attested ConnectedThe Fields Medal is awarded to mathematicians at the International Congress of Mathematicians.Source Fields Medal (Wikipedia)tier 3London Mathematical Society, Institutions Well-attested Source London Mathematical Society (Wikipedia)tier 2Founded ByEuclid, Scientists Well-attested Source Wikipedia: Mathematicstier 2Has ScientistAda Lovelace, Scientists Well-attested Adrien-Marie Legendre, Scientists Well-attested Source Adrien-Marie Legendre (Wikipedia)tier 3Alan Turing, Scientists Well-attested Al-Biruni, Scientists Well-attested Alexander Grothendieck, Scientists Well-attested Al-Khwarizmi, Scientists Well-attested Andrew Wiles, Scientists Well-attested Andrey Kolmogorov, Scientists Well-attested Andrey Markov, Scientists Well-attested Archimedes, Scientists Well-attested Aryabhata, Scientists Well-attested Augustin-Louis Cauchy, Scientists Well-attested Bernhard Riemann, Scientists Well-attested Carl Friedrich Gauss, Scientists Well-attested Source Carl Friedrich Gauss (MacTutor)tier 2Claude Shannon, Scientists Well-attested David Hilbert, Scientists Well-attested Source David Hilbert (MacTutor)tier 2Emmy Noether, Scientists Well-attested Source Emmy Noether (MacTutor)tier 2Euclid, Scientists Well-attested Evangelista Torricelli, Scientists Well-attested Source Evangelista Torricelli (Wikipedia)tier 2Evariste Galois, Scientists Well-attested Felix Hausdorff, Scientists Well-attested Georg Cantor, Scientists Well-attested Gottfried Wilhelm Leibniz, Scientists Well-attested Source Gottfried Wilhelm Leibniz (MacTutor)tier 2Grigori Perelman, Scientists Well-attested Henri Poincare, Scientists Well-attested Hypatia, Scientists Well-attested Isaac Newton, Scientists Well-attested Source Isaac Newton (Britannica)tier 1John Nash, Scientists Well-attested Joseph-Louis Lagrange, Scientists Well-attested Kurt Godel, Scientists Well-attested Leonhard Euler, Scientists Well-attested Source Leonhard Euler (MacTutor)tier 2Maryam Mirzakhani, Scientists Well-attested Niels Henrik Abel, Scientists Well-attested Pafnuty Chebyshev, Scientists Well-attested Paul Cohen, Scientists Well-attested Paul Erdos, Scientists Well-attested Pierre de Fermat, Scientists Well-attested Pierre-Simon Laplace, Scientists Well-attested Rene Descartes, Scientists Well-attested Shing-Tung Yau, Scientists Well-attested Sofia Kovalevskaya, Scientists Well-attested Srinivasa Ramanujan, Scientists Well-attested Source Srinivasa Ramanujan (MacTutor)tier 2Stanislaw Ulam, Scientists Well-attested Stefan Banach, Scientists Well-attested Terence Tao, Scientists Well-attested Thales of Miletus, Scientists Well-attested Source Thales of Miletus (Wikipedia)tier 3Yitang Zhang, Scientists Well-attested Has TheoryCalculus, Theories Well-attested Source The Rise of Calculus (MacTutor)tier 2Central Limit Theorem, Theories Well-attested Fermat's Last Theorem, Theories Well-attested Fundamental Theorem of Algebra, Theories Well-attested Game Theory, Theories Well-attested Information Theory, Theories Well-attested Non-Euclidean Geometry, Theories Well-attested Source Non-Euclidean Geometry (MacTutor)tier 2Prime Number Theorem, Theories Well-attested Pythagorean Theorem, Theories Well-attested Ramsey Theory, Theories Well-attested Set Theory, Theories Well-attested Source Set Theory (Stanford Encyclopedia of Philosophy)tier 1Long-Form ArticlesThe Postulate Euclid Could Not Prove, Articles Well-attested Open QuestionsDoes P equal NP?, Open Questions Well-attested Source Wikipedia: Mathematicstier 2When did mathematics become a discipline rather than a scattered set of practical and philosophical techniques?, Open Questions Well-attested StudiesAxiom, Concepts Well-attested Source Euclid (MacTutor)tier 2Number Theory, Concepts Well-attested Source Disquisitiones Arithmeticae (1801)Carl Friedrich Gausstier 1Proof, Concepts Well-attested Source Euclid (MacTutor)tier 2Theorem, Concepts Well-attested Source Euclid (MacTutor)tier 2Sources1. Euclid (MacTutor)MacTutor History of Mathematics, University of St Andrews2. Wikipedia: Mathematicstier 2WikipediaLead sectionMathematics is a field of knowledge concerned with abstract concepts such as numbers, geometric shapes, sets, functions, and probabilities. It uses logical reasoning and proof to study and establish their properties, often expressed as theorems, formulas, and equations.Founded By: EuclidView the SourceEvangelista Torricelli (Wikipedia)tier 2WikipediaHas Scientist: Evangelista TorricelliView the SourceStatistics (Wikipedia)tier 3WikipediaEncompasses: StatisticsView the SourceFields Medal (Wikipedia)tier 3WikipediaAssociated With: Fields MedalView the SourceLondon Mathematical Society (Wikipedia)tier 2WikipediaAssociated With: London Mathematical SocietyView the SourceThales of Miletus (Wikipedia)tier 3WikipediaHas Scientist: Thales of Miletus, Lead section, second paragraphQuote, Has Scientist: Thales of Miletus, Lead section, second paragraphHe is thus otherwise referred to as the first to have engaged in mathematics, science, and deductive reasoning.View the SourceAdrien-Marie Legendre (Wikipedia)tier 3WikipediaHas Scientist: Adrien-Marie Legendre, Lead section, second sentenceQuote, Has Scientist: Adrien-Marie Legendre, Lead section, second sentenceWell-known and important concepts such as the Legendre polynomials and Legendre transformation are named after him.View the SourceOpen Questions (1 open question)Does P equal NP?The P versus NP problem asks whether every problem whose solution can be quickly checked can also be quickly solved. It has resisted proof or disproof since it was formalized in the early 1970s and is one of the seven Millennium Prize Problems; a solution in either direction would reshape cryptography, optimization and much of theoretical computer science.What would resolve this A rigorous proof that P equals NP, exhibiting a general fast algorithm for an NP-complete problem, or a proof that P does not equal NP, most likely by establishing a genuine computational barrier no such algorithm can cross.Theoretical computer science and mathematical logicWikipedia: MathematicsComments (0)No comments yet. Be the first to share a thought.Sign in to join the discussion.Reader Challenges (0)No disputes yet. Spotted an error or a better source? Open the first one.Sign in to dispute this or suggest a correction.