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.


Mathematik Göttingen.jpg
Mathematics department in Göttingen where Hilbert worked from 1895 until his retirement in 1930
Image credit: Daniel Schwen

David Hilbert (January 23, 1862, Wehlau, Prussia–February 14, 1943, Göttingen, Germany) was a German mathematician, recognized as one of the most influential mathematicians of the 19th and early 20th centuries. He established his reputation as a great mathematician and scientist by inventing or developing a broad range of ideas, such as invariant theory, the axiomization of geometry, and the notion of Hilbert space, one of the foundations of functional analysis. Hilbert and his students supplied significant portions of the mathematic infrastructure required for quantum mechanics and general relativity. He is one of the founders of proof theory, mathematical logic, and the distinction between mathematics and metamathematics, and warmly defended Cantor's set theory and transfinite numbers. A famous example of his world leadership in mathematics is his 1900 presentation of a set of problems that set the course for much of the mathematical research of the 20th century.

View all selected articlesRead More...
animation of the classic "butterfly-shaped" Lorenz attractor seen from three different perspectives
Credit: Wikimol

The Lorenz attractor is an iconic example of a strange attractor in chaos theory. This three-dimensional fractal structure, resembling a butterfly or figure eight, reflects the long-term behavior of solutions to the Lorenz system, a set of three differential equations used by mathematician and meteorologist Edward N. Lorenz as a simple description of fluid circulation in a shallow layer (of liquid or gas) uniformly heated from below and cooled from above. To be more specific, the figure is set in a three-dimensional coordinate system whose axes measure the rate of convection in the layer (x), the horizontal temperature variation (y), and the vertical temperature variation (z). As these quantities change over time, a path is traced out within the coordinate system reflecting a particular solution to the differential equations. Lorenz's analysis revealed that while all solutions are completely deterministic, some choices of input parameters and initial conditions result in solutions showing complex, non-repeating patterns that are highly dependent on the exact values chosen. As stated by Lorenz in his 1963 paper Deterministic Nonperiodic Flow: "Two states differing by imperceptible amounts may eventually evolve into two considerably different states". He later coined the term "butterfly effect" to describe the phenomenon. One implication is that computing such chaotic solutions to the Lorenz system (i.e., with a computer program) to arbitrary precision is not possible, as any real-world computer will have a limitation on the precision with which it can represent numerical values. The particular solution plotted in this animation is based on the parameter values used by Lorenz (σ = 10, ρ = 28, and β = 8/3, constants reflecting certain physical attributes of the fluid). Note that the animation repeatedly shows one solution plotted over a specific period of time; as previously mentioned, the true solution never exactly retraces itself. Not all solutions are chaotic, however. Some choices of parameter values result in solutions that tend toward equilibrium at a fixed point (as seen, for example, in this image). Initially developed to describe atmospheric convection, the Lorenz equations also arise in simplified models for lasers, electrical generators and motors, and chemical reactions.

Did you know...

             

Showing 7 items out of 75

WikiProjects

Things you can do

Subcategories


Select [►] to view subcategories

Topics in mathematics

GeneralFoundationsNumber theoryDiscrete mathematics
Nuvola apps bookcase.svg
Set theory icon.svg
Nuvola apps kwin4.png
Nuvola apps atlantik.png


AlgebraAnalysisGeometry and topologyApplied 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

In other Wikimedia projects

The following Wikimedia Foundation sister projects provide more on this subject:

Commons
Media

Wikinews 
News

Wikiquote 
Quotations

Wikisource 
Texts

Wikiversity
Learning resources

Wiktionary 
Definitions

Wikidata 
Database

Other Languages
አማርኛ: በር:ሒሳብ
Bân-lâm-gú: Portal:Sò͘-ha̍k
беларуская (тарашкевіца)‎: Партал:Матэматыка
한국어: 포털:수학
Bahasa Indonesia: Portal:Matematika
interlingua: Portal:Mathematica
Kiswahili: Lango:Hisabati
Kreyòl ayisyen: Pòtay:matematik
македонски: Портал:Математика
Bahasa Melayu: Portal:Matematik
မြန်မာဘာသာ: Portal:သင်္ချာ
Nederlands: Portaal:Wiskunde
日本語: Portal:数学
oʻzbekcha/ўзбекча: Portal:Matematika
português: Portal:Matemática
slovenčina: Portál:Matematika
Soomaaliga: Portal:Xisaab
српски / srpski: Портал:Математика
ၽႃႇသႃႇတႆး : ၵိူၼ်ႇတူ:Mathematics
татарча/tatarça: Портал:Математика
українська: Портал:Математика
Tiếng Việt: Chủ đề:Toán học
文言: 門:數學