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.

There are approximately 31,444 mathematics articles in Wikipedia.

Selected article


Leonhard Euler.jpg
Leonhard Euler
Image credit: Emanuel Handmann

Leonhard Euler (pronounced oiler; IPA /ˈɔɪlər/) (April 15, 1707 Basel, Switzerland - September 18, 1783 St Petersburg, Russia) was a Swiss mathematician and physicist. He is considered to be the dominant mathematician of the 18th century and one of the greatest mathematicians of all time; he is certainly among the most prolific, with collected works filling over 70 volumes.

Euler developed many important concepts and proved numerous lasting theorems in diverse areas of mathematics, from calculus to number theory to topology. In the course of this work, he introduced many of modern mathematical terminologies, defining the concept of a function, and its notation, such as sin, cos, and tan for the trigonometric functions.

View all selected articlesRead More...

Selected picture

three-dimensional rendering of a pink, translucent Klein bottle
Credit: Wridgers

A Klein bottle is an example of a closed surface (a two-dimensional manifold) that is non-orientable (no distinction between the "inside" and "outside"). This image is a representation of the object in everyday three-dimensional space, but a true Klein bottle is an object in four-dimensional space. When it is constructed in three-dimensions, the "inner neck" of the bottle curves outward and intersects the side; in four dimensions, there is no such self-intersection (the effect is similar to a two-dimensional representation of a cube, in which the edges seem to intersect each other between the corners, whereas no such intersection occurs in a true three-dimensional cube). Also, while any real, physical object would have a thickness to it, the surface of a true Klein bottle has no thickness. Thus in three dimensions there is an inside and outside in a colloquial sense: liquid forced through the opening on the right side of the object would collect at the bottom and be contained on the inside of the object. However, on the four-dimensional object there is no inside and outside in the way that a sphere has an inside and outside: an unbroken curve can be drawn from a point on the "outer" surface (say, the object's lowest point) to the right, past the "lip" to the "inside" of the narrow "neck", around to the "inner" surface of the "body" of the bottle, then around on the "outer" surface of the narrow "neck", up past the "seam" separating the inside and outside (which, as mentioned before, does not exist on the true 4-D object), then around on the "outer" surface of the body back to the starting point (see the light gray curve on this simplified diagram). In this regard, the Klein bottle is a higher-dimensional analog of the Möbius strip, a two-dimensional manifold that is non-orientable in ordinary 3-dimensional space. In fact, a Klein bottle can be constructed (conceptually) by "gluing" the edges of two Möbius strips together.

Did you know...

Did you know...

                         

Showing 7 items out of 73

WikiProjects

Things you can do

Categories


Topics in mathematics

GeneralFoundationsNumber theoryDiscrete mathematics
Nuvola apps bookcase.svg
Set theory icon.svg
Nuvola apps kwin4.png
Nuvola apps atlantik.png


AlgebraAnalysisGeometry and topologyApplied mathematics
Arithmetic symbols.svg
Source
Nuvola apps kpovmodeler.svg
Gcalctool.svg

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

In other Wikimedia projects

The following Wikimedia Foundation sister projects provide more on this subject:

Commons
Media

Wikinews 
News

Wikiquote 
Quotations

Wikisource 
Texts

Wikiversity
Learning resources

Wiktionary 
Definitions

Wikidata 
Database

Other Languages
አማርኛ: በር:ሒሳብ
Bân-lâm-gú: Portal:Sò͘-ha̍k
беларуская (тарашкевіца)‎: Партал:Матэматыка
한국어: 포털:수학
Bahasa Indonesia: Portal:Matematika
interlingua: Portal:Mathematica
Kiswahili: Lango:Hisabati
Kreyòl ayisyen: Pòtay:matematik
македонски: Портал:Математика
Bahasa Melayu: Portal:Matematik
မြန်မာဘာသာ: Portal:သင်္ချာ
Nederlands: Portaal:Wiskunde
日本語: Portal:数学
oʻzbekcha/ўзбекча: Portal:Matematika
português: Portal:Matemática
slovenčina: Portál:Matematika
Soomaaliga: Portal:Xisaab
српски / srpski: Портал:Математика
Taqbaylit: Awwur:Tusnakt
татарча/tatarça: Портал:Математика
українська: Портал:Математика
Tiếng Việt: Chủ đề:Toán học
文言: 門:數學