Mathematics about mathematics. A branch of

maths and

philosophy dealing with the

foundations of mathematics. Includes

formal systems,

logic,

mereology, much of

ontology, parts of

metaphysics, etc. Nowadays, many people would include

model theory,

category theory and

topos theory (the latter being a branch of category theory relating mathematical systems to certain kinds of categories called

topoi).

Russell and Whitehead's *Principia Mathematica* is metamathematics. Gödel's famous *On Formally Undecidable Propositions of Principia Mathematica and Related Systems* is metamathematics. Frege, Wittgenstein, and many others are famous for their metamathematics (among other things, of course).