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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- ... that circle packings in the form of a Doyle spiral were used to model plant growth long before their mathematical investigation by Doyle?
- ... that although the problem of squaring the circle with compass and straightedge goes back to Greek mathematics, it was not proven impossible until 1882?
- ... that after Archimedes first defined convex curves, mathematicians lost interest in their analysis until the 19th century, more than two millennia later?
- ... that ten-sided gaming dice have kite-shaped faces?
- ... 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 in the aftermath of the American Civil War, the only Black-led organization providing teachers to formerly enslaved people was the African Civilization Society?
- ... that the music of math rock band Jyocho has been alternatively described as akin to "madness" or "contemplative and melancholy"?
- ... that a folded paper lantern shows that certain mathematical definitions of surface area are incorrect?
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- ...that it is not possible to configure two mutually inscribed quadrilaterals in the Euclidean plane, but the Möbius–Kantor graph describes a solution in the complex projective plane?
- ...that the six permutations of the vector (1,2,3) form a 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?
- ...that the Rule 184 cellular automaton can simultaneously model the behavior of cars moving in traffic, the accumulation of particles on a surface, and particle-antiparticle annihilation reactions?
- ...that a cyclic cellular automaton is a system of simple mathematical rules that can generate complex patterns mixing random chaos, blocks of color, and spirals?
- ...that a nonconvex polygon with three convex vertices is called a pseudotriangle?
- ...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?
Selected article –
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. (Full article...)
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