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 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 Catechumen, a Christian first-person shooter, was funded only in the aftermath of the Columbine High School massacre?
- ... that circle packings in the form of a Doyle spiral were used to model plant growth long before their mathematical investigation by Doyle?
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- ... that despite published scholarship to the contrary, Andrew Planta neither received a doctorate nor taught mathematics at Erlangen?
- ... that ten-sided gaming dice have kite-shaped faces?
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- ...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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Problem II.8 in the Arithmetica by Diophantus, annotated with Fermat's comment, which became Fermat's Last Theorem Image credit: |
Fermat's Last Theorem is one of the most famous theorems in the history of mathematics. It states that:
- has no solutions in non-zero integers , , and when is an integer greater than 2.
Despite how closely the problem is related to the Pythagorean theorem, which has infinite solutions and hundreds of proofs, Fermat's subtle variation is much more difficult to prove. Still, the problem itself is easily understood even by schoolchildren, making it all the more frustrating and generating perhaps more incorrect proofs than any other problem in the history of mathematics.
The 17th-century mathematician Pierre de Fermat wrote in 1637 in his copy of Bachet's translation of the famous Arithmetica of Diophantus: "I have a truly marvelous proof of this proposition which this margin is too narrow to contain." However, no correct proof was found for 357 years, until it was finally proven using very deep methods by Andrew Wiles in 1995 (after a failed attempt a year before). (Full article...)
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