# 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...)

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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%".

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## Selected article – Alan Turing memorial statue in Sackville ParkImage credit: User:Lmno

Alan Mathison Turing, OBE (June 23, 1912 – June 7, 1954), was an English mathematician, logician, and cryptographer.

Turing is often considered to be the father of modern computer science. Turing provided an influential formalisation of the concept of the algorithm and computation with the Turing machine, formulating the now widely accepted "Turing" version of the Church–Turing thesis, namely that any practical computing model has either the equivalent or a subset of the capabilities of a Turing machine. With the Turing test, he made a significant and characteristically provocative contribution to the debate regarding artificial intelligence: whether it will ever be possible to say that a machine is conscious and can think. He later worked at the National Physical Laboratory, creating one of the first designs for a stored-program computer, although it was never actually built. In 1947 he moved to the University of Manchester to work, largely on software, on the Manchester Mark I then emerging as one of the world's earliest true computers.

During World War II, Turing worked at Bletchley Park, Britain's codebreaking centre, and was for a time head of Hut 8, the section responsible for German Naval cryptanalysis. He devised a number of techniques for breaking German ciphers, including the method of the bombe, an electromechanical machine which could find settings for the Enigma machine. (Full article...)

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## Index of mathematics articles

 ARTICLE INDEX: 0–9ABCDEFGHIJKLMNOPQRSTUVWXYZ MATHEMATICIANS: ABCDEFGHIJKLMNOPQRSTUVWXYZ

## 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

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## Media files used on this page

Nuvola apps bookcase.svg
Author/Creator: SVG by Peter Kemp based on original work by Virginie Quesnay, Licence: LGPL
Svg of File:Nuvola apps bookcase.png
999 Perspective.svg
Author/Creator: , Licence: CC BY-SA 3.0
A view of 0.999… in rectangular perspective. Each character has a small but finite depth so that the image blends to solid black at infinity.
The Earth seen from Apollo 17 with transparent background.png
"The Blue Marble" is a famous photograph of the Earth taken on December 7, 1972 by the crew of the Apollo 17 spacecraft en route to the Moon at a distance of about 29,000 kilometers (18,000 statute miles). It shows Africa, Antarctica, and the Arabian Peninsula.
MolyneuxCelestialGlobe-MiddleTemple-1889.jpg
A celestial globe made by Emery Molyneux in 1592. Such globes were the first to be made in England and the first to be made by an Englishman. The globe, and a terrestrial globe also manufactured by Molyneux, belong to Middle Temple and are displayed in its library. The caption of the image is: "The Molyneux Celestial Globe. One of a pair at Middle Temple Library. (After a photograph.)"
Pythagorean.svg
Author/Creator: en:User:Wapcaplet, Licence: CC-BY-SA-3.0
Illustration of the Pythagorean theorem. The sum of two squares whose sides are the two legs (blue and red) is equal to the area of the square whose side is the hypotenuse (purple).
De-Euler.ogg
Author/Creator: Jeuwre, Licence: CC BY-SA 4.0
Pronunciation recording of German noun "Euler". Male voice, recorded by native German speaker from Berlin, Germany.
Kawasaki's theorem.jpg
Author/Creator: David Eppstein, Licence: CC BY-SA 3.0
Kawasaki's theorem: a single-vertex crease pattern can be flat-folded if and only if the two alternating sets of angles around the crease have the same total angle.
Cassini-science-br.jpg
إختبار عالي الدقة للنسبية العامة بواسطة مسبار الفضاء كاسيني (تصور فني) يظهر تأخير إشارات الراديو المرسلة بين الأرض والمسبار (الموجة الخضراء) بانحناء الزمكان (الخطوط الزرقاء) بسبب كتلة الشمس.
Title page of Edward Wright (1599) Certaine Errors in Navigation, arising either of the Ordinarie Erroneous Making or Vsing of the Sea Chart, Compasse, Crosse Staffe, and Tables of Declination of the Sunne, and Fixed Starres Detected and Corrected. (The Voyage of the Right Ho. George Earle of Cumberl. to the Azores, &c.), London: Printed ... [by Valentine Simmes and W. White] for Ed. Agas
Complex adaptive system : A way of modelling a Complex Adaptive System. A system with high adaptive capacity exerts complex adaptive behavior in a changing environment.
De-Johannes Kepler.ogg
Author/Creator: Jeuwre, Licence: CC BY-SA 4.0
Pronunciation recording of German noun inflection "Johannes Kepler", IPA: /jo.ˈha.nəs ˈkɛplɐ/. Male voice, recorded by native German speaker from Berlin, Germany.
Dirac distribution PDF.svg
Author/Creator:
• Original SVG by Omegatron
• Original PNG version by PAR
• This version adapted by Qef
, Licence: CC BY-SA 3.0
Schematic diagram of the Dirac delta function by a line surmounted by an arrow. The height of the arrow is usually used to specify the value of any multiplicative constant, which will give the area under the function. The other convention is to write the area next to the arrowhead.
Economics Gini coefficient2.svg
Gini coefficient diagram, based on the version by Bluemoose/BenFrantzDale. You can think of the horizontal axis as percent of people and the vertical axis as the percent of income those people receive. Therefore the Lorenz curves always start and end at the same places, where 0% of people make 0% of the country's income and 100% of people make 100% of the total income.

Inequality is implied when the curve is below the 45-degree line: At the left, the percentage of people is higher than the percent of income they receive (i.e. 10% of the people getting 5% of the total income); at the right, the percent of income received rises more than the percent of people receiving it.

The area above the Lorenz curve -- marked "A" -- is shaded differently from the area below the curve -- marked "B". This simplifies the mathematical explanation of the gini coefficient, which is A/(A+B)
Shifted square tiling.svg
Author/Creator: David Eppstein, Licence: CC0
A tiling of the plane by squares, shifted so that each square meets only two others edge-to-edge. Keller's cube-tiling conjecture (true in the plane but now known to be false in dimensions greater than eight) states that in any tiling of space by squares, cubes, or higher-dimensional hypercubes, some of the tiles must meet face-to-face.
Scale of justice 2.svg
A conversion of Image:Scale of justice.png to an SVG. The previous version was an automatic trace, whereas this version is a manual trace and of a higher quality.