Portal:Mathematics
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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 the word algebra is derived from an Arabic term for the surgical treatment of bonesetting?
- ... that the prologue to The Polymath was written by Martin Kemp, a leading expert on Leonardo da Vinci?
- ... that mathematics professor Ari Nagel has fathered more than a hundred children?
- ... that despite published scholarship to the contrary, Andrew Planta neither received a doctorate nor taught mathematics at Erlangen?
- ... that two members of the French parliament were killed when a delayed-action German bomb exploded in the town hall at Bapaume on 25 March 1917?
- ... that in 1940 Xu Ruiyun became the first Chinese woman to receive a PhD in mathematics?
- ... that ten-sided gaming dice have kite-shaped faces?
- ... that subgroup distortion theory, introduced by Misha Gromov in 1993, can help encode text?
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- ...that the set of rational numbers is equal in size to the set of integers; that is, they can be put in one-to-one correspondence?
- ...that there are precisely six convex regular polytopes in four dimensions? These are analogs of the five Platonic solids known to the ancient Greeks.
- ...that it is unknown whether π and e are algebraically independent?
- ...that a nonconvex polygon with three convex vertices is called a pseudotriangle?
- ...that it is possible for a three-dimensional 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?
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The continuum hypothesis is a hypothesis, advanced by Georg Cantor, about the possible sizes of infinite sets. Cantor introduced the concept of cardinality to compare the sizes of infinite sets, and he showed that the set of integers is strictly smaller than the set of real numbers. The continuum hypothesis states the following:
- There is no set whose size is strictly between that of the integers and that of the real numbers.
Or mathematically speaking, noting that the cardinality for the integers is ("aleph-null") and the cardinality of the real numbers is , the continuum hypothesis says
This is equivalent to:
The real numbers have also been called the continuum, hence the name. (Full article...)
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