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...)
Featured articles –
Selected image –
Good articles –
Did you know (auto-generated) –
- ... that circle packings in the form of a Doyle spiral were used to model plant growth long before their mathematical investigation by Doyle?
- ... that more than 60 scientific papers authored by mathematician Paul Erdős were published posthumously?
- ... that the British National Hospital Service Reserve trained volunteers to carry out first aid in the aftermath of a nuclear or chemical attack?
- ... that after Archimedes first defined convex curves, mathematicians lost interest in their analysis until the 19th century, more than two millennia later?
- ... that Fathimath Dheema Ali is the first Olympic qualifier from the Maldives?
- ... that owner Matthew Benham influenced both Brentford FC in the UK and FC Midtjylland in Denmark to use mathematical modelling to recruit undervalued football players?
- ... that the prologue to The Polymath was written by Martin Kemp, a leading expert on Leonardo da Vinci?
- ... that subgroup distortion theory, introduced by Misha Gromov in 1993, can help encode text?
More did you know –
- ... that the Life without Death cellular automaton, a mathematical model of pattern formation, is a variant of Conway's Game of Life in which cells, once brought to life, never die?
- ... that one can list every positive rational number without repetition by breadth-first traversal of the Calkin–Wilf tree?
- ... that the Hadwiger conjecture implies that the external surface of any three-dimensional convex body can be illuminated by only eight light sources, but the best proven bound is that 16 lights are sufficient?
- ... that an equitable coloring of a graph, in which the numbers of vertices of each color are as nearly equal as possible, may require far more colors than a graph coloring without this constraint?
- ... that no matter how biased a coin one uses, flipping a coin to determine whether each edge is present or absent in a countably infinite graph will always produce the same graph, the Rado graph?
- ...that it is possible to stack identical dominoes off the edge of a table to create an arbitrarily large overhang?
- ...that in Floyd's algorithm for cycle detection, the tortoise and hare move at very different speeds, but always finish at the same spot?
Selected article –
Image credit: User:Fropuff |
Knot theory is the branch of topology that studies mathematical knots, which are defined as embeddings of a circle S1 in 3-dimensional Euclidean space, R3. This is basically equivalent to a conventional knotted string with the ends of the string joined together to prevent it from becoming undone. Two mathematical knots are considered equivalent if one can be transformed into the other via continuous deformations (known as ambient isotopies); these transformations correspond to manipulations of a knotted string that do not involve cutting the string or passing the string through itself.
Knots can be described in various ways, but the most common method is by planar diagrams (known as knot projections or knot diagrams). Given a method of description, a knot will have many descriptions, e.g., many diagrams, representing it. A fundamental problem in knot theory is determining when two descriptions represent the same knot. One way of distinguishing knots is by using a knot invariant, a "quantity" which remains the same even with different descriptions of a knot.
Research in knot theory began with the creation of knot tables and the systematic tabulation of knots. While tabulation remains an important task, today's researchers have a wide variety of backgrounds and goals. Classical knot theory, as initiated by Max Dehn, J. W. Alexander, and others, is primarily concerned with the knot group and invariants from homology theory such as the Alexander polynomial.
The discovery of the Jones polynomial by Vaughan Jones in 1984, and subsequent contributions from Edward Witten, Maxim Kontsevich, and others, revealed deep connections between knot theory and mathematical methods in statistical mechanics and quantum field theory. A plethora of knot invariants have been invented since then, utilizing sophisticated tools as quantum groups and Floer homology. (Full article...)
View all selected articles |
Subcategories
Algebra | Arithmetic | Analysis | Complex analysis | Applied mathematics | Calculus | Category theory | Chaos theory | Combinatorics | Dynamical 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 | History of mathematics | Mathematicians | Awards | Education | Literature | Notation | Organizations | 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: | |
MATHEMATICIANS: |
Related portals
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
|
In other Wikimedia projects
The following Wikimedia Foundation sister projects provide more on this subject:
-
Commons
Free media repository -
Wikibooks
Free textbooks and manuals -
Wikidata
Free knowledge base -
Wikinews
Free-content news -
Wikiquote
Collection of quotations -
Wikisource
Free-content library -
Wikiversity
Free learning tools -
Wiktionary
Dictionary and thesaurus