Full Idea
Successful competing founding disciplines in mathematics include: the various set theories, type theory, category theory, model theory and topology.
Gist of Idea
Is mathematics based on sets, types, categories, models or topology?
Source
Michèle Friend (Introducing the Philosophy of Mathematics [2007], 2.3)
Book Reference
Friend,Michèle: 'Introducing the Philosophy of Mathematics' [Acumen 2007], p.29
A Reaction
Or none of the above? Set theories are very popular. Type theory is, apparently, discredited. Shapiro has a version of structuralism based on model theory (which sound promising). Topology is the one that intrigues me...