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 Hong Wang's latest paper claims to have resolved the Kakeya conjecture, described as "one of the most sought-after open problems in geometric measure theory", in three dimensions?
- ... that despite a mathematical model deeming the ice cream bar flavour Goody Goody Gum Drops impossible, it was still created?
- ... that in 1940 Xu Ruiyun became the first Chinese woman to receive a PhD in mathematics?
- ... that in 1967 two mathematicians published PhD dissertations independently disproving the same thirteen-year-old conjecture?
- ... that Green Day's "Wake Me Up When September Ends" became closely associated with the aftermath of Hurricane Katrina?
- ... that the discovery of Descartes' theorem in geometry came from a too-difficult mathematics problem posed to a princess?
- ... 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 multiple mathematics competitions have made use of Sophie Germain's identity?
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- … that the Riemann Hypothesis, one of the Millennium Problems, depends on the asymptotic growth of the Mertens Function?
- … that every positive integer can be written as the sum of three palindromic numbers in every number system with base 5 or greater?
- … that the best known lower bound for the length of the smallest superpermutation was first posted anonymously to the internet imageboard 4chan?
- ...that the mathematician Grigori Perelman was offered a Fields Medal in 2006, in part for his proof of the Poincaré conjecture, which he declined?
- ...that a regular heptagon is the regular polygon with the fewest sides which is not constructible with a compass and straightedge?
- ...that the regular trigonometric functions and the hyperbolic trigonometric functions can be related without using complex numbers through the Gudermannian function?
- ...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?
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The second Borel-Cantelli lemma implies that a chimpanzee like this one typing at random will almost surely produce the complete works of Shakespeare, given enough time. Image credit: User:Chris 73 |
The infinite monkey theorem states that a monkey hitting keys at random on a typewriter keyboard for an infinite amount of time will almost surely type or create a particular chosen text, such as the complete works of William Shakespeare. Note that "almost surely" in this context is a mathematical term with a specific meaning, and that the "monkey" is not an actual monkey; rather, it is a vivid metaphor for an abstract device that produces an unending, random sequence of letters.
The theorem graphically illustrates the perils of reasoning about infinity by imagining a vast but finite number. If every atom in the visible universe were a monkey producing a billion keystrokes a second from the Big Bang until today, it is still very unlikely that any monkey would get as far as "slings and arrows" in Hamlets most famous soliloquy. The infinite monkey theorem is straightforward to prove, even without appealing to more advanced results. ('Full article...)
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