The Mathematics Portal
Mathematics is the study of numbers, quantity, space, pattern, 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.
Selected article
Euclidean geometry is a mathematical system attributed to the Greek mathematician Euclid of Alexandria. Euclid's text Elements was the first systematic discussion of geometry. It has been one of the most influential books in history, as much for its method as for its mathematical content. The method consists of assuming a small set of intuitively appealing axioms, and then proving many other propositions (theorems) from those axioms. Although many of Euclid's results had been stated by earlier Greek mathematicians, Euclid was the first to show how these propositions could fit together into a comprehensive deductive and logical system.
The Elements begin with plane geometry, still often taught in secondary school as the first axiomatic system and the first examples of formal proof. The Elements goes on to the solid geometry of three dimensions, and Euclidean geometry was subsequently extended to any finite number of dimensions. Much of the Elements states results of what is now called number theory, proved using geometrical methods.
For over two thousand years, the adjective "Euclidean" was unnecessary because no other sort of geometry had been conceived. Euclid's axioms seemed so intuitively obvious that any theorem proved from them was deemed true in an absolute sense. Today, however, many other self-consistent geometries are known, the first ones having been discovered in the early 19th century. It also is no longer taken for granted that Euclidean geometry describes physical space. An implication of Einstein's theory of general relativity is that Euclidean geometry is only a good approximation to the properties of physical space if the gravitational field is not too strong.
View all selected articles | Read More... |
Selected image
This is a hand-drawn graph of the absolute value (or modulus) of the gamma function on the complex plane, as published in the 1909 book Tables of Higher Functions, by Eugene Jahnke and Fritz Emde. Such three-dimensional graphs of complicated functions were rare before the advent of high-resolution computer graphics (even today, tables of values are used in many contexts to look up function values instead of consulting graphs directly). Published even before applications for the complex gamma function were discovered in theoretical physics in the 1930s, Jahnke and Emde's graph "acquired an almost iconic status", according to physicist Michael Berry. See a similar computer-generated image for comparison. When restricted to positive integers, the gamma function generates the factorials through the relation Γ(n) = (n − 1)!, which is the product of all positive integers from n − 1 down to 1 (0! is defined to be equal to 1). For real and complex numbers, the function is defined by the improper integral . This integral diverges when t is a negative integer, which is causing the spikes in the left half of the graph (these are simple poles of the function, where its values increase to infinity, analogous to asymptotes in two-dimensional graphs). The gamma function has applications in quantum physics, astrophysics, and fluid dynamics, as well as in number theory and probability.
In the news
- 19 March 2019 –
- The Norwegian Academy of Science and Letters awards this year's Abel Prize to Karen Uhlenbeck for "her pioneering achievements in geometric partial differential equations, gauge theory and integrable systems." Uhlenbeck is the first woman to win this prize. (The New York Times via MSN.com)
Did you know…
- ... that as the dimension of a hypersphere tends to infinity, its "volume" (content) tends to 0?
- ...that the line separating the numerator and denominator of a fraction is called a solidus if written as a diagonal line or a vinculum if written as a horizontal line?
- ...that a monkey hitting keys at random on a typewriter keyboard for an infinite amount of time will almost surely type the complete works of William Shakespeare?
- ... that there are 115,200 solutions to the ménage problem of permuting six female-male couples at a twelve-person table so that men and women alternate and are seated away from their partners?
- ... that mathematician Paul Erdős called the Hadwiger conjecture, a still-open generalization of the four-color problem, "one of the deepest unsolved problems in graph theory"?
- ...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?
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
Subcategories
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 | 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: | 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 |
Logic | Mathematics | Number theory |
Physics | Science | Set theory | Statistics |
In other Wikimedia projects