Identifying the borders of mathematical knowledge

Based 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.

FAPESP[07/02938-5]

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

FAPESP[07/50882-9]

FAPESP[05/00587-5]

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

CNPq[133256/2007-3]

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

CNPq[301303/06-1]

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

CNPq[573583/2008-0]

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)