Agrippas trilemma states that formal systems are either self-circular, infinitely regressive or axiomatic.
Its commonly taken that mathematics is axiomatic. However just as mathematicians can build ever more elaborate structures, they can painstakingly dig-down into foundations.
Does this mean that mathematics is actually infinitely regressive, it's just that the diggig is a bit slow?
After ymars comment, I emphasise I mean formalistically.
(From another perspective mathematics is what mathematicians trained at certain schools do; similarly to some contemporary description of art by critics, art is something that artists trained at certain schools do. But one could argue here, the critics have just thrown in the towel.)