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Identifying the borders of mathematical knowledge
Abstract Based on a divide and conquer approach, knBased on a divide and conquer approach, knowledge about nature has been organized into a set of interrelated facts, allowing a natural representation in terms of graphs: each `chunk' of knowledge corresponds to a node, while relationships between such chunks are expressed as edges. This organization becomes particularly clear in the case of mathematical theorems, with their intense cross-implications and relationships. We have derived a web of mathematical theorems from Wikipedia and, thanks to the powerful concept of entropy, identified its more central and frontier elements. Our results also suggest that the central nodes are the oldest theorems, while the frontier nodes are those recently added to the network. The network communities have also been identified, allowing further insights about the organization of this network, such as its highly modular structure.ork, such as its highly modular structure.
Abstractsub Based on a divide and conquer approach, knBased on a divide and conquer approach, knowledge about nature has been organized into a set of interrelated facts, allowing a natural representation in terms of graphs: each `chunk' of knowledge corresponds to a node, while relationships between such chunks are expressed as edges. This organization becomes particularly clear in the case of mathematical theorems, with their intense cross-implications and relationships. We have derived a web of mathematical theorems from Wikipedia and, thanks to the powerful concept of entropy, identified its more central and frontier elements. Our results also suggest that the central nodes are the oldest theorems, while the frontier nodes are those recently added to the network. The network communities have also been identified, allowing further insights about the organization of this network, such as its highly modular structure.ork, such as its highly modular structure.
Bibtextype article  +
Has author F.N. Silva + , B.A.N. Travencolo + , M.P. Viana + , L. da Fontoura Costa +
Has remote mirror http://dx.doi.org/10.1088/1751-8113/43/32/325202  +
Number of citations by publication 0  +
Number of references by publication 0  +
Peer-reviewed Yes  +
Published in Journal of Physics A: Mathematical and Theoretical +
Title Identifying the borders of mathematical knowledge +
Type journal article  +
Volume 43  +
Year 2010 +
Creation dateThis property is a special property in this wiki. 20 September 2014 17:45:39  +
Categories Publications without keywords parameter  + , Publications without language parameter  + , Publications without license parameter  + , Publications without DOI parameter  + , Publications without archive mirror parameter  + , Publications without paywall mirror parameter  + , Journal articles  + , Publications without references parameter  + , Publications  +
Modification dateThis property is a special property in this wiki. 20 September 2014 17:45:39  +
DateThis property is a special property in this wiki. 2010  +
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