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Mathematical Knowledge Management
Mathematical knowledge management (MKM) is the study of how society can effectively make use of the vast and growing literature on mathematics. It studies approaches such as databases of mathematical knowledge, automated processing of formulae and the use of semantic information, and artificial intelligence. Mathematics is particularly suited to a systematic study of automated knowledge processing due to the high degree of interconnectedness between different areas of mathematics. See also *OMDoc *QED manifesto *Areas of mathematics *MathML External links * www.nist.gov/mathematical-knowledge-management NIST's MKM pageThe MKM Interest Group(archived) a programme at the Isaac Newton Institute
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Mathematics
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics with the major subdisciplines of number theory, algebra, geometry, and analysis, respectively. There is no general consensus among mathematicians about a common definition for their academic discipline. Most mathematical activity involves the discovery of properties of abstract objects and the use of pure reason to prove them. These objects consist of either abstractions from nature orin modern mathematicsentities that are stipulated to have certain properties, called axioms. A ''proof'' consists of a succession of applications of deductive rules to already established results. These results include previously proved theorems, axioms, andin case of abstraction from naturesome basic properties that are considered true starting points of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Database
In computing, a database is an organized collection of data stored and accessed electronically. Small databases can be stored on a file system, while large databases are hosted on computer clusters or cloud storage. The design of databases spans formal techniques and practical considerations, including data modeling, efficient data representation and storage, query languages, security and privacy of sensitive data, and distributed computing issues, including supporting concurrent access and fault tolerance. A database management system (DBMS) is the software that interacts with end users, applications, and the database itself to capture and analyze the data. The DBMS software additionally encompasses the core facilities provided to administer the database. The sum total of the database, the DBMS and the associated applications can be referred to as a database system. Often the term "database" is also used loosely to refer to any of the DBMS, the database system or an appli ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Artificial Intelligence
Artificial intelligence (AI) is intelligence—perceiving, synthesizing, and inferring information—demonstrated by machines, as opposed to intelligence displayed by animals and humans. Example tasks in which this is done include speech recognition, computer vision, translation between (natural) languages, as well as other mappings of inputs. The ''Oxford English Dictionary'' of Oxford University Press defines artificial intelligence as: the theory and development of computer systems able to perform tasks that normally require human intelligence, such as visual perception, speech recognition, decision-making, and translation between languages. AI applications include advanced web search engines (e.g., Google), recommendation systems (used by YouTube, Amazon and Netflix), understanding human speech (such as Siri and Alexa), self-driving cars (e.g., Tesla), automated decision-making and competing at the highest level in strategic game systems (such as chess and Go). ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
OMDoc
OMDoc (Open Mathematical Documents) is a semantic markup format for mathematical documents. While MathML only covers mathematical formulae and the related OpenMath standard only supports formulae and “content dictionaries” containing definitions of the symbols used in formulae, OMDoc covers the whole range of written mathematics. Coverage OMDoc allows for mathematical expressions on three levels: ;Object level:Formulae, written in Content MathML (the non-presentational subset of MathML), OpenMath or languages for mathematical logic. ;Statement level:Definitions, theorems, proofs, examples and the relations between them (e.g. “this proof proves that theorem”). ;Theory level:A theory is a set of contextually related statements. Theories may import each other, thereby forming a graph. Seen as collections of symbol definitions, OMDoc theories are compatible to OpenMath content dictionaries. On each level, formal syntax and informal natural language can be used, depending on ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
QED Manifesto
The QED manifesto was a proposal for a computer-based database of all mathematical knowledge, strictly formalized and with all proofs having been checked automatically. ( Q.E.D. means in Latin, meaning "which was to be demonstrated.") Overview The idea for the project arose in 1993, mainly under the impetus of Robert Boyer. The goals of the project, tentatively named ''QED project'' or ''project QED'', were outlined in the QED manifesto, a document first published in 1994, with input from several researchers. Explicit authorship was deliberately avoided. A dedicated mailing list was created, and two scientific conferences on QED took place, the first one in 1994 at Argonne National Laboratories and the second in 1995 in Warsaw organized by the Mizar group. The project seems to have dissolved by 1996, never having produced more than discussions and plans. In a 2007 paper, Freek Wiedijk identifies two reasons for the failure of the project. In order of importance: * Very few peopl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Areas Of Mathematics
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics with the major subdisciplines of number theory, algebra, geometry, and analysis, respectively. There is no general consensus among mathematicians about a common definition for their academic discipline. Most mathematical activity involves the discovery of properties of abstract objects and the use of pure reason to prove them. These objects consist of either abstractions from nature orin modern mathematicsentities that are stipulated to have certain properties, called axioms. A ''proof'' consists of a succession of applications of deductive rules to already established results. These results include previously proved theorems, axioms, andin case of abstraction from naturesome basic properties that are considered true starting points of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
MathML
Mathematical Markup Language (MathML) is a mathematical markup language, an application of XML for describing mathematical notations and capturing both its structure and content. It aims at integrating mathematical formulae into World Wide Web pages and other documents. It is part of HTML5 and is a ISO/IEC standarISO/IEC 40314since 2015. History MathML 1 was released as a W3C recommendation in April 1998 as the first XML language to be recommended by the W3C. Version 1.01 of the format was released in July 1999 and version 2.0 appeared in February 2001. In October 2003, the second edition of MathML Version 2.0 was published as the final release by the W3C Math Working Group. MathML was originally designed before the finalization of XML namespaces. However, it was assigned a namespace immediately after the Namespace Recommendation was completed, and for XML use, the elements should be in the namespace with namespace URL http://www.w3.org/1998/Math/MathML. When MathML is used i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
NIST
The National Institute of Standards and Technology (NIST) is an agency of the United States Department of Commerce whose mission is to promote American innovation and industrial competitiveness. NIST's activities are organized into physical science laboratory programs that include nanoscale science and technology, engineering, information technology, neutron research, material measurement, and physical measurement. From 1901 to 1988, the agency was named the National Bureau of Standards. History Background The Articles of Confederation, ratified by the colonies in 1781, provided: The United States in Congress assembled shall also have the sole and exclusive right and power of regulating the alloy and value of coin struck by their own authority, or by that of the respective states—fixing the standards of weights and measures throughout the United States. Article 1, section 8, of the Constitution of the United States, ratified in 1789, granted these powers to the new Congre ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Isaac Newton Institute
The Isaac Newton Institute for Mathematical Sciences is an international research institute for mathematics and its many applications at the University of Cambridge. It is named after one of the university's most illustrious figures, the mathematician and natural philosopher Sir Isaac Newton and occupies one of the buildings in the Cambridge Centre for Mathematical Sciences. History After a national competition run by SERC, the Science and Engineering Research Council (now known as EPSRC Engineering and Physical Sciences Research Council), this institute was chosen to be the national research institute for mathematical sciences in the UK. It opened in 1992 with support from St John's College and Trinity College. St. John's provided the land and a purpose-built building, Trinity provided running costs for the first five years and the London Mathematical Society provided other support. Shortly afterwards at the institute, the British mathematician Andrew Wiles announced hi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics And Culture
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics with the major subdisciplines of number theory, algebra, geometry, and analysis, respectively. There is no general consensus among mathematicians about a common definition for their academic discipline. Most mathematical activity involves the discovery of properties of abstract objects and the use of pure reason to prove them. These objects consist of either abstractions from nature orin modern mathematicsentities that are stipulated to have certain properties, called axioms. A ''proof'' consists of a succession of applications of deductive rules to already established results. These results include previously proved theorems, axioms, andin case of abstraction from naturesome basic properties that are considered true starting points of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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