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 John Rolph was arrested while trying to solve Euclid's geometry problems?
- ... that Piper Harron's 2016 mathematics doctoral thesis has been described as "feminist", "unique", "honest", "generous", and "refreshing"?
- ... that the co-founder of Arkansas radio station KTOY, the first Black-owned radio station in the state, continued teaching math after starting it?
- ... that the Septet for trumpet, strings and piano was composed by Camille Saint-Saëns for a mathematician?
- ... that in the musical Fermat's Last Tango, mathematicians Euclid and Newton are played by women?
- ... 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 the 1914 Lubin vault fire in Philadelphia destroyed several thousand unique early silent films?
- ... that in 1593, French amateur mathematician François Viète found the first formula in European mathematics to represent an infinite process, a product of square roots that he used to compute π?
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- ... that the Herschel graph is the smallest possible polyhedral graph that does not have a Hamiltonian cycle?
- ... that the Life without Death cellular automaton, a mathematical model of pattern formation, is a variant of Conway's Game of Life in which cells, once brought to life, never die?
- ... that one can list every positive rational number without repetition by breadth-first traversal of the Calkin–Wilf tree?
- ... that the Hadwiger conjecture implies that the external surface of any three-dimensional convex body can be illuminated by only eight light sources, but the best proven bound is that 16 lights are sufficient?
- ... that an equitable coloring of a graph, in which the numbers of vertices of each color are as nearly equal as possible, may require far more colors than a graph coloring without this constraint?
- ... that no matter how biased a coin one uses, flipping a coin to determine whether each edge is present or absent in a countably infinite graph will always produce the same graph, the Rado graph?
- ...that it is possible to stack identical dominoes off the edge of a table to create an arbitrarily large overhang?
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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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