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 –
![low-resolution ASCII-art depiction of the Mandelbrot set](http://upload.wikimedia.org/wikipedia/commons/thumb/d/d7/Mandel.png/300px-Mandel.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 subgroup distortion theory, introduced by Misha Gromov in 1993, can help encode text?
- ... that ten-sided gaming dice have kite-shaped faces?
- ... that Catechumen, a Christian first-person shooter, was funded only in the aftermath of the Columbine High School massacre?
- ... that after Archimedes first defined convex curves, mathematicians lost interest in their analysis until the 19th century, more than two millennia later?
- ... that mathematics professor Ari Nagel has fathered more than a hundred children?
- ... that more than 60 scientific papers authored by mathematician Paul Erdős were published posthumously?
- ... that a folded paper lantern shows that certain mathematical definitions of surface area are incorrect?
- ... that mathematician Daniel Larsen was the youngest contributor to the New York Times crossword puzzle?
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, in the Rule 90 cellular automaton, any finite pattern eventually fills the whole array of cells with copies of itself?
- ... that, while the criss-cross algorithm visits all eight corners of the Klee–Minty cube when started at a worst corner, it visits only three more corners on average when started at a random corner?
- ...that in senary, all prime numbers other than 2 and 3 end in 1 or a 5?
- ...that, for all prime numbers p, the pth Perrin number is divisible by p?
- ...that it is impossible to trisect a general angle using only a ruler and a compass?
- ...that in a group of 23 people, there is a more than 50% chance that two people share a birthday?
- ...that the 1966 publication disproving Euler's sum of powers conjecture, proposed nearly 200 years earlier, consisted of only two sentences?
Selected article –
![]() |
The region between two loxodromes on a geometric sphere. Image credit: Karthik Narayanaswami |
The Riemann sphere is a way of extending the plane of complex numbers with one additional point at infinity, in a way that makes expressions such as
well-behaved and useful, at least in certain contexts. It is named after 19th century mathematician Bernhard Riemann. It is also called the complex projective line, denoted CP1.
On a purely algebraic level, the complex numbers with an extra infinity element constitute a number system known as the extended complex numbers. Arithmetic with infinity does not obey all of the usual rules of algebra, and so the extended complex numbers do not form a field. However, the Riemann sphere is geometrically and analytically well-behaved, even near infinity; it is a one-dimensional complex manifold, also called a Riemann surface.
In complex analysis, the Riemann sphere facilitates an elegant theory of meromorphic functions. The Riemann sphere is ubiquitous in projective geometry and algebraic geometry as a fundamental example of a complex manifold, projective space, and algebraic variety. It also finds utility in other disciplines that depend on analysis and geometry, such as quantum mechanics and other branches of physics. (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