Page semi-protected
From Wikipedia, the free encyclopedia

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 – load new batch

  Featured articles are displayed here, which represent some of the best content on English Wikipedia.

Selected image – show another

animation showing a torus (a doughnut shape) being cut diagonally by a plane, causing the appearance of two interlocking circles on the cut surface
animation showing a torus (a doughnut shape) being cut diagonally by a plane, causing the appearance of two interlocking circles on the cut surface
An animation showing how an obliquely cut torus reveals a pair of intersecting circles known as Villarceau circles, named after the French astronomer and mathematician Yvon Villarceau. These are two of the four circles that can be drawn through any given point on the torus. (The other two are oriented horizontally and vertically, and are the analogs of lines of latitude and longitude drawn through the given point.) The circles have no known practical application and seem to be merely a curious characteristic of the torus. However, Villarceau circles appear as the fibers in the Hopf fibration of the 3-sphere over the ordinary 2-sphere, and the Hopf fibration itself has interesting connections to fluid dynamics, particle physics, and quantum theory.

Good articles – load new batch

  These are Good articles, which meet a core set of high editorial standards.

Did you know (auto-generated) load new batch

More did you know – view different entries

Did you know...
Did you know...
Showing 7 items out of 75

Selected article – show another

In search of a new car, the player picks door 1. The game host then opens door 3 to reveal a goat and offers to let the player pick door 2 instead of door 1.
Image credit: Cepheus

The Monty Hall problem is a puzzle involving probability similar to the American game show Let's Make a Deal. The name comes from the show's host, Monty Hall. A widely known, but problematic (see below) statement of the problem is from Craig F. Whitaker of Columbia, Maryland in a letter to Marilyn vos Savant's September 9, 1990, column in Parade Magazine (as quoted by Bohl, Liberatore, and Nydick).

Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, "Do you want to pick door No. 2?" Is it to your advantage to switch your choice?

The problem is also called the Monty Hall paradox; it is a veridical paradox in the sense that the solution is counterintuitive, although the problem does not yield a logical contradiction. ( Full article...)

View all selected articles


Full category tree. Select [►] to view subcategories.

Topics in mathematics

General Foundations Number theory Discrete mathematics

Algebra Analysis Geometry and topology Applied mathematics

Index of mathematics articles


Related portals


In other Wikimedia projects

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

More portals

Discover Wikipedia using portals