Portal:Mathematics
The Mathematics Portal
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 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 Ukrainian baritone Danylo Matviienko, who holds a master's degree in mathematics, appeared as Demetrius in Britten's opera A Midsummer Night's Dream at the Oper Frankfurt?
- ... that people in Madagascar perform algebra on tree seeds in order to tell the future?
- ... that Fathimath Dheema Ali is the first Olympic qualifier from the Maldives?
- ... that circle packings in the form of a Doyle spiral were used to model plant growth long before their mathematical investigation by Doyle?
- ... that mathematician Mathias Metternich was one of the founders of the Jacobin club of the Republic of Mainz?
- ... 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?
- ... that after Archimedes first defined convex curves, mathematicians lost interest in their analysis until the 19th century, more than two millennia later?
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- ...that, for all prime numbers p, the pth Perrin number is divisible by p?
- ...that it is impossible to trisect a general angle using only a ruler and a compass?
- ...that in a group of 23 people, there is a more than 50% chance that two people share a birthday?
- ...that the 1966 publication disproving Euler's sum of powers conjecture, proposed nearly 200 years earlier, consisted of only two sentences?
- ...the hyperbolic trigonometric functions of the natural logarithm can be represented by rational algebraic fractions?
- ... that economists blame market failures on non-convexity?
- ... that, according to the pizza theorem, a circular pizza that is sliced off-center into eight equal-angled wedges can still be divided equally between two people?
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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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