> >If every mathematician spent as much time dealing with foundations as > >you seem to want, no other math would ever get done. > > > >Is that what you want? > > What I want is to avoid extravagantly stupid claims that transfinite > arithmetic and set theory encompass all of mathematics
There are some notable areas of mathematics not encompassed IN set theory (for example some versions of category theory). But as far as I am aware, there are none which do not have some basis of assumptions which collectively can be called the axioms of that area.
> so we can > properly examine the basis of axiomatic assumptions regarding > definitions of things such as curves, straight lines, transcendental > numbers, angular momentum, and quantum effects on a sound unassuming > analytical foundation.
Analysis cannot be done on an "unassuming foundation" as without some foundation of assumptions, there is nothing to work with .
> It might be too much to ask of professional > academics but not of real scientists.
As "real scientists" are, by definition not mathematicians, at least to the extent that they are only "real scientists", Zick is implying the "real scientist" fallacy that no mathematics has any existence or validity outside of its scientific usage.