Portal:Mathematics
The Mathematics Portal
Mathematics is the study of numbers, quantity, space, structure, and change. Mathematics is used throughout the world as an essential tool in many fields, including natural science, engineering, medicine, and the social sciences. Applied mathematics, the branch of mathematics concerned with application of mathematical knowledge to other fields, inspires and makes use of new mathematical discoveries and sometimes leads to the development of entirely new mathematical disciplines, such as statistics and game theory. Mathematicians also engage in pure mathematics, or mathematics for its own sake, without having any application in mind. There is no clear line separating pure and applied mathematics, and practical applications for what began as pure mathematics are often discovered.
Selected article  Selected picture  Did you know...  Topics in mathematics
Categories  WikiProjects  Things you can do  Index  Related portals
There are approximately 31,444 mathematics articles in Wikipedia.
Selected article
Dodecahedron Image credit: 
Due to their aesthetic beauty and symmetry, the Platonic solids have been a favorite subject of geometers for thousands of years. They are named after the ancient Greek philosopher Plato who claimed the classical elements were constructed from the regular solids.
The Platonic solids have been known since antiquity. The five solids were certainly known to the ancient Greeks and there is evidence that these figures were known long before then. The neolithic people of Scotland constructed stone models of all five solids at least 1000 years before Plato.
View all selected articles  Read More... 
Selected image
A line integral is an integral where the function to be integrated, be it a scalar field as here or a vector field, is evaluated along a curve. The value of the line integral is the sum of values of the field at all points on the curve, weighted by some scalar function on the curve (commonly arc length or, for a vector field, the scalar product of the vector field with a differential vector in the curve). A detailed explanation of the animation is available. The key insight is that line integrals may be reduced to simpler definite integrals. (See also a similar animation illustrating a line integral of a vector field.) Many formulas in elementary physics (for example, W = F · s to find the work done by a constant force F in moving an object through a displacement s) have line integral versions that work for nonconstant quantities (for example, W = ∫_{C} F · ds to find the work done in moving an object along a curve C within a continuously varying gravitational or electric field F). A higherdimensional analog of a line integral is a surface integral, where the (double) integral is taken over a twodimensional surface instead of along a onedimensional curve. Surface integrals can also be thought of as generalizations of multiple integrals. All of these can be seen as special cases of integrating a differential form, a viewpoint which allows multivariable calculus to be done independently of the choice of coordinate system. While the elementary notions upon which integration is based date back centuries before Newton and Leibniz independently invented calculus, line and surface integrals were formalized in the 18th and 19th centuries as the subject was placed on a rigorous mathematical foundation. The modern notion of differential forms, used extensively in differential geometry and quantum physics, was pioneered by Élie Cartan in the late 19th century.
Did you know…
 ...that a nonconvex polygon with three convex vertices is called a pseudotriangle?
 ...that the axiom of choice is logically independent of the other axioms of Zermelo–Fraenkel set theory?
 ...that the Pythagorean Theorem generalizes to any three similar shapes on the three sides of a rightangled triangle?
 ...that the orthocenter, circumcenter, centroid and the centre of the ninepoint circle all lie on one line, the Euler line?
 ...that an arbitrary quadrilateral will tessellate?
 ...that it has not been proven whether or not every even integer greater than two can be expressed as the sum of two primes?
 ...that the sum of the first n odd numbers divided by the sum of the next n odd numbers is always equal to one third?
WikiProjects
The Mathematics WikiProject is the center for mathematicsrelated editing on Wikipedia. Join the discussion on the project's talk page.
Project pages
Essays
Subprojects
Related projects
Things you can do
Categories
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  Multidimensional geometry  Number theory  Numerical analysis  Optimization  Order theory  Probability and statistics  Set theory  Statistics  Topology  Algebraic topology  Trigonometry  Linear programming
Mathematics (books)  History of mathematics  Mathematicians  Awards  Education  Literature  Notation  Organizations  Theorems  Proofs  Unsolved problems
Topics in mathematics
General  Foundations  Number theory  Discrete mathematics 



Algebra  Analysis  Geometry and topology  Applied mathematics 
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 theory 
Computer science 
Cryptography 
Discrete mathematics 
Logic  Mathematics 
Number theory 
Physics  Science  Set theory  Statistics 
In other Wikimedia projects