Portal:Mathematics
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At present, there are approximately 15472 mathematical articles in Wikipedia.
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| Problem II.8 in the Arithmetica by Diophantus, annotated with Fermat's comment, which became Fermat's Last Theorem |
- an + bn = cn has no solutions in non-zero integers a, b, and c when n 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).
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The circle map is a chaotic map showing a number of interesting chaotic behaviors. This figure shows the average Poincaré recurrence time for the iterated circle map modulo 1.
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- ... that the Gudermannian function relates the regular trigonometric functions and the hyperbolic trigonometric functions without the use of complex numbers?
- ... that a regular heptagon is the regular polygon with the least number of sides which is not constructible with a compass and straightedge?
- ... that the Catalan numbers solve a number of problems in combinatorics such as the number of ways to completely parenthesize an algebraic expression with n+1 factors?
- ... that a sphere can be cut up and reassembled into two spheres 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 Henri Poincaré is often described as the last "universalist" capable of understanding and contributing in virtually all parts of mathematics?
- ...that it is unknown whether π and e are algebraically independent?
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