> But however this may work as a classification, it isn't the structure > that I'm looking for. Foundations (math. logic, set theory, etc.) > couldn't possibly be a branch at the same level as these others. And a > branch couldn't be a conjunction for another thing. And, in general, > there is no saying from this just why this division should be > exhaustive. > > <snip>
> This is really an old-fashioned project. I had assumed that there must > have been some systematizers who had worked on this, even if one had to > go back a bit in time to find them. >
Yes, I wouldn't be surprised if the ancients did classify maths in the way you seek. But there is a danger that an old classification will not take into account recent work. The idea that "math. logic, set theory, etc." to quote you, provides a foundation for all of mathematics is as recent as the late nineteenth/early twentieth century. More recently still category theory has been proposed as a foundation for (or an encompassing of) "all" mathematics. If you do find or produce the classification you are looking for do let us know.