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...)
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In the news
 22 March 2023 –
 Argentine mathematician Luis Caffarelli wins this year's Abel Prize "for his seminal contributions to regularity theory for nonlinear partial differential equations including freeboundary problems and the Monge–Ampère equation". He becomes the first Latin American to win this prize. (The Guardian)
Did you know (autogenerated) 
 ... that after Archimedes first defined convex curves, mathematicians lost interest in their analysis until the 19th century, more than two millennia later?
 ... that Donn Piatt threw his mathematics teacher out of the window?
 ... that A Passage North, which is shortlisted for the 2021 Booker Prize, is set in the aftermath of the Sri Lankan Civil War?
 ... that Coastal Carolina football coach Chad Staggs has degrees in math education and tourism management?
 ... that Piper Harron's 2016 mathematics doctoral thesis has been described as "feminist", "unique", "honest", "generous", and "refreshing"?
 ... 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 a mathematical conjecture about tiling space by cubes was transformed into a problem in graph theory that became a benchmark for cliquefinding algorithms?
 ... that mathematician Daniel Larsen was the youngest contributor to the New York Times crossword puzzle?
More did you know –
 ...that it is possible for a threedimensional figure to have a finite volume but infinite surface area, such as Gabriel's Horn?
 ... that as the dimension of a hypersphere tends to infinity, its "volume" (content) tends to 0?
 ...that the primality of a number can be determined using only a single division using Wilson's Theorem?
 ...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 femalemale couples at a twelveperson table so that men and women alternate and are seated away from their partners?
 ... that mathematician Paul Erdős called the Hadwiger conjecture, a stillopen generalization of the fourcolor problem, "one of the deepest unsolved problems in graph theory"?
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A Hilbert space is a real or complex vector space with a positivedefinite Hermitian form, that is complete under its norm. Thus it is an inner product space, which means that it has notions of distance and of angle (especially the notion of orthogonality or perpendicularity). The completeness requirement ensures that for infinite dimensional Hilbert spaces the limits exist when expected, which facilitates various definitions from calculus. A typical example of a Hilbert space is the space of square summable sequences.
Hilbert spaces allow simple geometric concepts, like projection and change of basis to be applied to infinite dimensional spaces, such as function spaces. They provide a context with which to formalize and generalize the concepts of the Fourier series in terms of arbitrary orthogonal polynomials and of the Fourier transform, which are central concepts from functional analysis. Hilbert spaces are of crucial importance in the mathematical formulation of quantum mechanics. (Full article...)
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