(and no, I haven't read them 'cause I'm a coward XD)
@Blaergh If you would like to avoid the nowadays unusual notation of Principia Mathematica, you could give #Metamath a try. For instance, 2p2e4, link is below, is the proof for 2+2=4. It allows you to track thos down to the axioms of set theory. As there are so many people trying to convince me that 2+2=5, this is an invaluable resource, IMHO.
note that if you *really* want to go down the recreation of math rabbit hole read all three volumes of the #PrincipiaMathematica by #Russell and #Whitehead (which #Gödel didn't ruin *at all* with his #IncompletenessTheorem 😅)