Greg Egan’s short story Glory features a “xenomathematician” who discovers that an ancient civilization had produced a sort of grand unification of their various branches of mathematics.
It was not a matter of everything in mathematics collapsing in on itself, with one branch turning out to have been merely a recapitulation of another under a different guise. Rather, the principle was that every sufficiently beautiful mathematical system was rich enough to mirror in part — and sometimes in a complex and distorted fashion — every other sufficiently beautiful system. Nothing became sterile and redundant, nothing proved to have been a waste of time, but everything was shown to be magnificently intertwined.
One thought on “Grand unification of mathematics”
I think it it is appproximately true by Godel’s work – for every mathematical claim you can formulate an arithmetic statement which says that there is a proof for that claim. On the other hand, a complex enough structure will probably enable you to define the natural numbers.