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


P1S2all.jpg
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.

View all selected articles Read More...

Selected picture

graph of an increasing curve showing cumulative share of income earned versus cumulative share of people from lowest to highest income

A Lorenz curve shows the distribution of income in a population by plotting the percentage y of total income that is earned by the bottom x percent of households (or individuals). Developed by economist Max O. Lorenz in 1905 to describe income inequality, the curve is typically plotted with a diagonal line (reflecting a hypothetical "equal" distribution of incomes) for comparison. This leads naturally to a derived quantity called the Gini coefficient, first published in 1912 by Corrado Gini, which is the ratio of the area between the diagonal line and the curve (area A in this graph) to the area under the diagonal line (the sum of A and B); higher Gini coefficients reflect more income inequality. Lorenz's curve is a special kind of cumulative distribution function used to characterize quantities that follow a Pareto distribution, a type of power law. More specifically, it can be used to illustrate the Pareto principle, a rule of thumb stating that roughly 80% of the identified "effects" in a given phenomenon under study will come from 20% of the "causes" (in the first decade of the 20th century Vilfredo Pareto showed that 80% of the land in Italy was owned by 20% of the population). As this so-called "80–20 rule" implies a specific level of inequality (i.e., a specific power law), more or less extreme cases are possible. For example, in the United States in the first half of the 2010s, 95% of the financial wealth was held by the top 20% of wealthiest households (in 2010), the top 1% of individuals held approximately 40% of the wealth (2012), and the top 1% of income earners received approximately 20% of the pre-tax income (2013). Observations such as these have brought income and wealth inequality into popular consciousness and have given rise to various slogans about "the 1%" versus "the 99%".

Did you know...

Did you know...

                         

Showing 7 items out of 71

WikiProjects

The Mathematics WikiProject is the center for mathematics-related editing on Wikipedia. Join the discussion on the project's talk page.

WikiProjects

Project pages

Essays

Subprojects

Related projects

Things you can do

Categories


Topics in mathematics

General Foundations Number theory Discrete mathematics
Nuvola apps bookcase.svg
Set theory icon.svg
Nuvola apps kwin4.png
Nuvola apps atlantik.png


Algebra Analysis Geometry and topology Applied 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:

Wikibooks
Books

Commons
Media

Wikinews 
News

Wikiquote 
Quotations

Wikisource 
Texts

Wikiversity
Learning resources

Wiktionary 
Definitions

Wikidata 
Database

Other Languages
አማርኛ: በር:ሒሳብ
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