Full Idea
Three views of mathematics: 'pure' mathematics, where it doesn't matter if it could ever have any application; 'real' mathematics, where every concept must be physically grounded; and 'applied' mathematics, using the non-real if the results are real.
Gist of Idea
Mathematics can be 'pure' (unapplied), 'real' (physically grounded); or 'applied' (just applicable)
Source
Brian Clegg (Infinity: Quest to Think the Unthinkable [2003], Ch.17)
Book Reference
Clegg,Brian: 'Infinity' [Robinson 2003], p.218
A Reaction
Very helpful. No one can deny the activities of 'pure' mathematics, but I think it is undeniable that the origins of the subject are 'real' (rather than platonic). We do economics by pretending there are concepts like the 'average family'.