Portal:Mathematics

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 29044 mathematics articles in Wikipedia.

View new selections below (purge)

Selected article

e is the unique number such that the slope of y=e^x (blue curve) is exactly 1 when x=0 (illustrated by the red tangent line). For comparison, the curves y=2^x (dotted curve) and y=4^x (dashed curve) are shown.
Image credit: Dick Lyon

The mathematical constant e is occasionally called Euler's number after the Swiss mathematician Leonhard Euler, or Napier's constant in honor of the Scottish mathematician John Napier who introduced logarithms. It is one of the most important numbers in mathematics, alongside the additive and multiplicative identities 0 and 1, the imaginary unit i, and π, the circumference to diameter ratio for any circle. It has a number of equivalent definitions. One is given in the caption of the image to the right, and three more are:

The sum of the infinite series

$\begin{align} e & = \sum_{n = 0}^\infty \frac{1}{n!} \\ & = \frac{1}{0!} + \frac{1}{1!} + \frac{1}{2!} + \frac{1}{3!} + \cdots \\ \end{align}$

where n! is the factorial of n.
The global maximum of the function

$f(x) = x^{1 \over x}.$
The limit:

$e = \lim_{n\to\infty} \left( 1 + \frac{1}{n} \right)^n$

The number e is also the base of the natural logarithm. Since e is transcendental, and therefore irrational, its value can not be given exactly. The numerical value of e truncated to 20 decimal places is 2.71828 18284 59045 23536.

View all selected articles

Read More...

Picture of a previous month

Credit: User:Ixnay

In compass and straightedge constructions an angle can be bisected, divided evenly in to two, using only an unmarked ruler and a compass as seen above. Many tried and failed to trisect a general angle; Gauss proved it impossible.

...Archive

Read more...

You are seeing a previous month's picture as no-one has created this month's yet. Add a picture for this month here.

Did you know...

...that the axiom of choice is logically independent of the other axioms of Zermelo–Fraenkel set theory?
...that the Pythagorean Theorem generalizes to any three similar shapes on the three sides of a right-angled triangle?
...that the orthocenter, circumcenter, centroid and the centre of the nine-point circle all line on one line, the Euler line?
...that an arbitrary quadrilateral will tessellate?
...that it has not been proven whether or not every even integer greater than two can be expressed as the sum of two primes?
...that outstanding mathematician Grigori Perelman was offered a Fields Medal in 2006, in part for his proof of the Poincaré conjecture, which he declined?
...that a regular heptagon is the regular polygon with the fewest number of sides which is not constructible with a compass and straightedge?
...that the Gudermannian function relates the regular trigonometric functions and the hyperbolic trigonometric functions without the use of complex numbers?
...that the Catalan numbers solve a number of problems in combinatorics such as the number of ways to completely parenthesize an algebraic expression with n+1 factors?

Showing 9 items out of 66

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

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

Science:

History of science Philosophy of science Systems science Mathematics Biology Chemistry Physics Earth sciences Technology

What are portals?
List of portals
Featured portals

	HPTS - Area Progetti - Edu-Soft - JavaEdu - N.Saperi - Ass.Scuola.. - TS BCTV - TSODP - TRTWE

	TSE-Wiki - Blog Lavoro - InterAzioni- NormaScuola - Editoriali - Job Search - DownFree !