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 circle packings in the form of a Doyle spiral were used to model plant growth long before their mathematical investigation by Doyle?
- ... that museum director Alena Aladava rebuilt the Belarusian national art collection in the aftermath of the Second World War?
- ... that the number of cannonballs in a square pyramid with cannonballs along each edge is ?
- ... that after Archimedes first defined convex curves, mathematicians lost interest in their analysis until the 19th century, more than two millennia later?
- ... that Latvian-Soviet artist Karlis Johansons exhibited a skeletal tensegrity form of the Schönhardt polyhedron seven years before Erich Schönhardt's 1928 paper on its mathematics?
- ... that the discovery of Descartes' theorem in geometry came from a too-difficult mathematics problem posed to a princess?
- ... that despite a mathematical model deeming the ice cream bar flavour Goody Goody Gum Drops impossible, it was still created?
- ... that multiple mathematics competitions have made use of Sophie Germain's identity?
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- ...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?
- ...that the largest known prime number is nearly 25 million digits long?
- ...that the set of rational numbers is equal in size to the set of integers; that is, they can be put in one-to-one correspondence?
- ...that there are precisely six convex regular polytopes in four dimensions? These are analogs of the five Platonic solids known to the ancient Greeks.
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The German Lorenz cipher machine, used in World War II for encryption of very high-level general staff messages Image credit: Matt Crypto |
Cryptography (or cryptology) is derived from Greek κρυπτός kryptós "hidden," and the verb γράφω gráfo "write". In modern times, it has become a branch of information theory, as the mathematical study of information and especially its transmission from place to place. The noted cryptographer Ron Rivest has observed that "cryptography is about communication in the presence of adversaries." It is a central contributor to several fields: information security and related issues, particularly, authentication, and access control. One of cryptography's primary purposes is hiding the meaning of messages, not usually the existence of such messages. In modern times, cryptography also contributes to computer science. Cryptography is central to the techniques used in computer and network security for such things as access control and information confidentiality. Cryptography is also used in many applications encountered in everyday life; the security of ATM cards, computer passwords, and electronic commerce all depend on cryptography. (Full article...)
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