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The Mathematics Portal
Mathematics, from Greek μαθηματικά mathēmatiká, is the study of patterns. Such patterns include quantities resp. numbers and their operations, interrelations, combinations and abstractions; and of space configurations and their structure, measurement, transformations, and generalizations. Mathematics evolved through the use of abstraction and logical reasoning, from counting, calculation, measurement, and the systematic study of positions, shapes and motions of abstract objects. Mathematicians explore such concepts, aiming to formulate new conjectures and establish their truth by rigorous deduction from appropriately chosen axioms and definitions.
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Categories | WikiProjects | Things you can do | Index | Related portalsThere are approximately 26757 mathematics articles in Wikipedia.
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A dodecahedron, one of the five Platonic solids
Image credit: User:DTRA regular polytope is a geometric figure with a high degree of symmetry. Examples in two dimensions include the square, the regular pentagon and hexagon, and so on. In three dimensions the regular polytopes include the cube, the dodecahedron, and all other Platonic solids. Other Platonic solids include the tetrahedron, the octahedron, the icosahedron. Examples exist in higher dimensions also, such as the 5-dimensional hendecatope. Circles and spheres, although highly symmetric, are not considered polytopes because they do not have flat faces. The strong symmetry of the regular polytopes gives them an aesthetic quality that interests both non-mathematicians and mathematicians.
Many regular polytopes, at least in two and three dimensions, exist in nature and have been known since prehistory. The earliest surviving mathematical treatment of these objects comes to us from ancient Greek mathematicians such as Euclid. Indeed, Euclid wrote a systematic study of mathematics, publishing it under the title Elements, which built up a logical theory of geometry and number theory. His work concluded with mathematical descriptions of the five Platonic solids.
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Credit: KieffAn animation of a coffee mug morphing into a torus, a popular example of a homeomorphism in topology.
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Algebra | Arithmetic | Analysis | Complex analysis | Applied mathematics | Calculus | Category theory | Chaos theory | Combinatorics | Dynamic systems | Fractals | Game theory | Geometry | Algebraic geometry | Graph theory | Group theory | Linear algebra | Mathematical logic | Model Theory | Multi-dimensional geometry | Number theory | Numerical analysis | Optimization | Order theory | Probability and statistics | Set theory | Statistics | Topology | Algebraic topology | Trigonometry |
Mathematics (books) | History of mathematics | Mathematicians | Awards | Education | Institutes and societies | Literature | Notation | Theorems | Proofs | Unsolved problemsDid you know...
- ...that Euler found 59 more amicable numbers while for 2000 years, only 3 pairs had been found before him?
- ...that you cannot knot strings in 4-dimensions? You can, however, knot 2-dimensional surfaces like spheres.
- ...that there are 6 unsolved mathematics problems whose solutions will earn you one million US dollars each?
- ...that there are different sizes of infinite sets in set theory? More precisely, not all infinite cardinal numbers are equal?
- ...that every natural number can be written as the sum of four squares?
- ...that the largest known prime number is over 12 million digits long?
- ...that the set of rational numbers is equal in size to the subset of integers; that is, they can be put in one-to-one correspondence?
- ...that there are precisely six convex regular polytopes in four dimensions? These are analogs of the five Platonic solids known to the ancient Greeks.
- ...that it is unknown whether π and e are algebraically independent?
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The Mathematics WikiProject is the center for mathematics-related editing on Wikipedia. Join the discussion on the project's talk page.
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Topics in mathematics
General Foundations Number theory Discrete mathematics 
- Set theory (portal)
- Naive set theory
- Axiomatic set theory
- Category theory (portal)
- Topos theory
- Discrete mathematics (portal)
- Combinatorics
- Combinatorial geometry
- Coding theory
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- Enumerative combinatorics
- Combinatorial optimization
- Graph theory
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Analysis Algebra Geometry and topology Applied mathematics 
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- Mathematical modeling
- Mathematical physics
- Differential equations
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- Dynamical systems
- Optimization
- Mathematical economics
- Statistics (portal)
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- Numerical analysis
- Theoretical computer science
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Index of mathematics articles
ARTICLE INDEX: A B C D E F G H I J K L M N O P Q R S T U V W X Y Z 0-9 MATHEMATICIANS: A B C D E F G H I J K L M N O P Q R S T U V W X Y Z Related portals
Algebra Analysis Category
theoryComputer
scienceCryptography Discrete
mathematicsGeometry 
Logic Mathematics Number
theoryPhysics Science Set theory Statistics Topology
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