Portal:Mathematics
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.
| More about Mathematics... |
Selected article | Selected picture | Did you know... | Topics in mathematics
Categories | WikiProjects | Things you can do | Index | Related portals
There are approximately 31,444 mathematics articles in Wikipedia.
Selected article
 |
| Johannes Kepler Image credit: User:ArtMechanic |
Johannes Kepler (1571 – 1630) was an Austrian Lutheran mathematician, astronomer and astrologer, and a key figure in the 17th century astronomical revolution. He is best known for his laws of planetary motion, based on his works Astronomia nova and Harmonice Mundi; Kepler's laws provided one of the foundations of Isaac Newton's theory of universal gravitation. Before Kepler, planets' paths were computed by combinations of the circular motions of the celestial orbs; after Kepler astronomers shifted their attention from orbs to orbits—paths that could be represented mathematically as an ellipse.
During his career Kepler was a mathematics teacher at a Graz seminary school (later the University of Graz, Austria), an assistant to Tycho Brahe, court mathematician to Emperor Rudolf II, mathematics teacher in Linz, Austria, and adviser to General Wallenstein. He also did fundamental work in the field of optics and helped to legitimize the telescopic discoveries of his contemporary Galileo Galilei.
Kepler lived in an era when there was no clear distinction between astronomy and astrology, while there was a strong division between astronomy (a branch of mathematics within the liberal arts) and physics (a branch of the more prestigious discipline of philosophy).
| View all selected articles | Read More... |
Selected picture
 |
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.
Did you know...
- ...that the six permutations of the vector (1,2,3) form a regular hexagon in 3d space, the 24 permutations of (1,2,3,4) form a truncated octahedron in four dimensions, and both are examples of permutohedra?
- ...that Ostomachion is a mathematical treatise attributed to Archimedes on a 14-piece tiling puzzle similar to tangram?
- ...that some functions can be written as an infinite sum of trigonometric polynomials and that this sum is called the Fourier series of that function?
- ...that the identity elements for arithmetic operations make use of the only two whole numbers that are neither composites nor prime numbers, 0 and 1?
- ...that as of April 2010 only 35 even numbers have been found that are not the sum of two primes which are each in a Twin Primes pair? ref
- ...the Piphilology record (memorizing digits of Pi) is in excess of 67000 as of Apr 2010?
- ...with a Perrin number denoted P(i), i=1,2,3..., when i is prime then P(i) is composite, being divisible by i?
| Showing 7 items out of 72 | More did you know |
WikiProjects
The Mathematics WikiProject is the center for mathematics-related editing on Wikipedia. Join the discussion on the project's talk page.
Project pages
Essays
Subprojects
Related projects
Things you can do
Categories
Algebra | Arithmetic | Analysis | Complex analysis | Applied mathematics | Calculus | Category theory | Chaos theory | Combinatorics | Dynamic 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 (books) | History of mathematics | Mathematicians | Awards | Education | Institutes and societies | Literature | Notation | 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: | 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
 |
 |
 |
 |
 |
 |
 |
| Algebra | Analysis | Category theory |
Computer science |
Cryptography | Discrete mathematics |
Geometry |
 |
 |
 |
 |
 |
 |
 |
 |
| Logic | Mathematics | Number theory |
Physics | Science | Set theory | Statistics | Topology |
Mathematics
- What are portals?
- List of portals
- Featured portals
