Mapping connections between topics covered in academic papers - does such a tool exist?
ScienceWISE is one of the attempts:

The ScienceWISE project aims to develop a scientist-generated on-line knowledge base fully integrated into the physics ArXiv.org
The ScienceWISE system allows scientists, in the course of their daily work to

dynamically generate professional-field-specific ontologies: add concepts and logical relations between them; provide expertly-written, community-ranked definition articles and links to other existing resources;
to create an interactive semantic environment, annotating scientific research papers, uploaded to ArXiv.org, and linking them to the ScienceWISE ontology, thus expanding content of their papers with supporting material in the form of encyclopedia-like articles.


(See also info on the arXiv: http://arxiv.org/help/sciencewise)