I don't see a problem in splitting all these domains to an "applied" school, that focuses research into evolving solutions that currently seem effective in appr

I don't see a problem in splitting all these domains to an "applied" school, that focuses research into evolving solutions that currently seem effective in approximating answers for certain engineering problems, and a more theoretical school that has the potential to carve new revolutionary paths while pursuing some (abstract?) ideal such as mathematical elegance. One shouldn't exclude the other and apparently there are enough scientists around that are attracted to either one of the two approaches.