FOM: Natural examples/evolution of subjects

[John Baldwin]

Shipman wrote:

>2) I agree that the four traditional branches of
mathematical logic,
> >considered as individual subjects, are not at stage six yet; but can
you
> >provide an example of a mathematical field which is?  (Even better
would
> >be two examples, one where the stage six status is deserved and one
> >where it is undeserved.)
Harvey replied:
> Without commenting on deserved/undeserved, there is general topology and
> (general) category theory.
Maclane once told me that general topology was alway beyond the pale -
investigating notions that were not really central.

Here are some  examples that I think were once more accepted in
mainstream mathematics than general
topology and general category theory ever were:  non-associative algebras
(Lie, Engel, Dickson, Jacobson) ; noncommutative rings (Herrstein,
Jacobson, Wedderburn)
lattice
theory (Ore, Birkhoff, Van Neuman).