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 ten-sided gaming dice have kite-shaped faces?
- ... that in 1940 Xu Ruiyun became the first Chinese woman to receive a PhD in mathematics?
- ... that the prologue to The Polymath was written by Martin Kemp, a leading expert on Leonardo da Vinci?
- ... 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 more than 60 scientific papers authored by mathematician Paul Erdős were published posthumously?
- ... that Fathimath Dheema Ali is the first Olympic qualifier from the Maldives?
- ... that people in Madagascar perform algebra on tree seeds in order to tell the future?
- ... 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?
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- ...that a ball can be cut up and reassembled into two balls, each the same size as the original (Banach-Tarski paradox)?
- ...that it is impossible to devise a single formula involving only polynomials and radicals for solving an arbitrary quintic equation?
- ...that Euler found 59 more amicable numbers while for 2000 years, only 3 pairs had been found before him?
- ...that you cannot knot strings in 4 dimensions, but you can knot 2-dimensional surfaces, such as spheres?
- ...that there are 6 unsolved mathematics problems whose solutions will earn you one million US dollars each?
- ...that there are different sizes of infinite sets in set theory? More precisely, not all infinite cardinal numbers are equal?
- ...that every natural number can be written as the sum of four squares?
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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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