Portal:Mathematics
The Mathematics Portal
Mathematics is the study of representing and reasoning about abstract objects (such as numbers, points, spaces, sets, structures, and games). 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. (Full article...)
Featured articles –
![](http://upload.wikimedia.org/wikipedia/commons/thumb/c/cf/Cscr-featured.png/23px-Cscr-featured.png)
Selected image –
![diagram of a unit circle and several associated triangles whose side lengths are the values of the various trigonometric functions](http://upload.wikimedia.org/wikipedia/commons/thumb/9/9d/Circle-trig6.svg/500px-Circle-trig6.svg.png)
Good articles –
Did you know (auto-generated) –
![](http://upload.wikimedia.org/wikipedia/commons/thumb/4/44/Nuvola_apps_filetypes.svg/47px-Nuvola_apps_filetypes.svg.png)
- ... that ten-sided gaming dice have kite-shaped faces?
- ... that Fairleigh Dickinson's upset victory over Purdue was the biggest upset in terms of point spread in NCAA tournament history, with Purdue being a 23+1⁄2-point favorite?
- ... that two members of the French parliament were killed when a delayed-action German bomb exploded in the town hall at Bapaume on 25 March 1917?
- ... that a folded paper lantern shows that certain mathematical definitions of surface area are incorrect?
- ... that Ukrainian baritone Danylo Matviienko, who holds a master's degree in mathematics, appeared as Demetrius in Britten's opera A Midsummer Night's Dream at the Oper Frankfurt?
- ... that mathematician Daniel Larsen was the youngest contributor to the New York Times crossword puzzle?
- ... that circle packings in the form of a Doyle spiral were used to model plant growth long before their mathematical investigation by Doyle?
- ... that owner Matthew Benham influenced both Brentford FC in the UK and FC Midtjylland in Denmark to use mathematical modelling to recruit undervalued football players?
More did you know –
![Did you know...](http://upload.wikimedia.org/wikipedia/commons/thumb/4/44/Nuvola_apps_filetypes.svg/50px-Nuvola_apps_filetypes.svg.png)
- ...that the Catalan numbers solve a number of problems in combinatorics such as the number of ways to completely parenthesize an algebraic expression with n+1 factors?
- ...that a ball can be cut up and reassembled into two balls, each the same size as the original (Banach-Tarski paradox)?
- ...that it is impossible to devise a single formula involving only polynomials and radicals for solving an arbitrary quintic equation?
- ...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, but you can knot 2-dimensional surfaces, such as 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?
Selected article –
![]() |
A homotopy from a circle around a sphere down to a single point. Image credit: Richard Morris |
The homotopy groups of spheres describe the different ways spheres of various dimensions can be wrapped around each other. They are studied as part of algebraic topology. The topic can be hard to understand because the most interesting and surprising results involve spheres in higher dimensions. These are defined as follows: an n-dimensional sphere, n-sphere, consists of all the points in a space of n+1 dimensions that are a fixed distance from a center point. This definition is a generalization of the familiar circle (1-sphere) and sphere (2-sphere).
The goal of algebraic topology is to categorize or classify topological spaces. Homotopy groups were invented in the late 19th century as a tool for such classification, in effect using the set of mappings from a c-sphere into a space as a way to probe the structure of that space. An obvious question was how this new tool would work on n-spheres themselves. No general solution to this question has been found to date, but many homotopy groups of spheres have been computed and the results are surprisingly rich and complicated. The study of the homotopy groups of spheres has led to the development of many powerful tools used in algebraic topology. (Full article...)
View all selected articles |
Subcategories
![](http://upload.wikimedia.org/wikipedia/commons/thumb/d/da/C_Puzzle.png/42px-C_Puzzle.png)
Algebra | Arithmetic | Analysis | Complex analysis | Applied mathematics | Calculus | Category theory | Chaos theory | Combinatorics | Dynamical 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 | Linear programming
Mathematics | 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: | |
MATHEMATICIANS: |
Related portals
WikiProjects
The Mathematics WikiProject is the center for mathematics-related editing on Wikipedia. Join the discussion on the project's talk page.
In other Wikimedia projects
The following Wikimedia Foundation sister projects provide more on this subject:
-
Commons
Free media repository -
Wikibooks
Free textbooks and manuals -
Wikidata
Free knowledge base -
Wikinews
Free-content news -
Wikiquote
Collection of quotations -
Wikisource
Free-content library -
Wikiversity
Free learning tools -
Wiktionary
Dictionary and thesaurus