Portal:Mathematics

From Wikipedia, the free encyclopedia
Jump to: navigation, search

The Mathematics Portal


Mathematics is the study of numbers, quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity. The research required to solve mathematical problems can take years or even centuries of sustained inquiry. However, mathematical proofs are less formal and painstaking than proofs in mathematical logic. Since the pioneering work of Giuseppe Peano (1858–1932), David Hilbert (1862–1943), and others on axiomatic systems in the late 19th century, it has become customary to view mathematical research as establishing truth by rigorous deduction from appropriately chosen axioms and definitions. When those mathematical structures are good models of real phenomena, then mathematical reasoning often provides insight or predictions.

Through the use of abstraction and logical reasoning, mathematics developed from counting, calculation, measurement, and the systematic study of the shapes and motions of physical objects. Practical mathematics has been a human activity for as far back as written records exist. Rigorous arguments first appeared in Greek mathematics, most notably in Euclid's Elements. Mathematics developed at a relatively slow pace until the Renaissance, when mathematical innovations interacting with new scientific discoveries led to a rapid increase in the rate of mathematical discovery that continues to the present day.

Galileo Galilei (1564–1642) said, "The universe cannot be read until we have learned the language and become familiar with the characters in which it is written. It is written in mathematical language, and the letters are triangles, circles and other geometrical figures, without which means it is humanly impossible to comprehend a single word. Without these, one is wandering about in a dark labyrinth". Carl Friedrich Gauss (1777–1855) referred to mathematics as "the queen of sciences". The mathematician Benjamin Peirce (1809–1880) called the discipline, "the science that draws necessary conclusions". David Hilbert said of it: "We are not speaking here of arbitrariness in any sense. Mathematics is not like a game whose tasks are determined by arbitrarily stipulated rules. Rather, it is a conceptual system possessing internal necessity that can only be so and by no means otherwise." Albert Einstein (1879–1955) stated that "as far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality".

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...

There are approximately 30,455 mathematics articles in Wikipedia.

View new selections below (purge)

Selected article


Wallpaper group-p6m-1.jpg
Example of a Persian design with wallpaper group type "p6m"
Image credit: Owen Jones

A wallpaper group is a mathematical concept used to classify repetitive designs on two-dimensional surfaces, such as floors and walls, based on the symmetries in the pattern. Such patterns occur frequently in architecture and decorative art. The mathematical study of such patterns reveals that exactly 17 different types of pattern can occur.

Wallpaper groups are examples of an abstract algebraic structure known as a group. Groups are frequently used in mathematics to study the notion of symmetry. Wallpaper groups are related to the simpler frieze groups, and to the more complex three-dimensional crystallographic groups.

View all selected articles Read More...

Selected picture

animation of the act of "unrolling" a circle's circumference, illustrating the ratio pi (π)
Credit: John Reid

Pi (represented by the Greek letter π) is a mathematical constant whose value is the ratio of any circle's circumference to its diameter in Euclidean space; it is also the ratio of a circle's area to the square of its radius. In this animation, the circle has a diameter of 1 unit, giving it a circumference of π. The rolling shows that the distance a point on the circle moves linearly in one complete revolution is equal to pi. Pi is an irrational number and so can not be expressed as the ratio of two integers; as a result, the decimal expansion of pi is nonterminating and nonrepeating. To 50 decimal places, pi is approximately equal to 3.14159 26535 89793 23846 26433 83279 50288 41971 69399 37510. In addition to geometry and trigonometry, pi appears in many other areas of mathematics, including number theory, probability, and statistics.

More selected pictures... Read more...

Did you know...

Did you know...

                           

Showing 6 items out of 70 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.

WikiProjects

Project pages

Essays

Subprojects

Related projects

Things you can do

Nuvola apps korganizer.svg

Categories

C Puzzle.png

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
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

Portal:Algebra
Portal:Analysis
Portal:Category theory
Portal:Computer science
Portal:Cryptography
Portal:Discrete mathematics
Portal:Geometry
Algebra Analysis Category
theory
Computer
science
Cryptography Discrete
mathematics
Geometry
Portal:Logic
Portal:Mathematics
Portal:Number theory
Portal:Physics
Portal:Science
Portal:Set theory
Portal:Statistics
Portal:Topology
Logic Mathematics Number
theory
Physics Science Set theory Statistics Topology


In other Wikimedia projects

The following Wikimedia sister projects provide more on this subject:
Wikibooks  Wikimedia Commons Wikinews  Wikiquote  Wikisource  Wikiversity  Wiktionary  Wikidata 
Books Media News Quotations Texts Learning resources Definitions Database