>>16772315
The proof that
1+1=2
Just requires introduction to (1) the notion of formal proofs, (2) the axioms of Peano arithmetic, and (3) basic axiomatic set theory because Russell specifically wants to use a set theoetic model of the Peano axioms, due largely to philosophical/methodological reasons, since he saw set theory as the foundation for math as a whole. The set theory stuff takes a long time and isnt even strictly necessary. An introductikn to formal proofs, the Peano axioms, and a proof that 1+1=2 should only require a few dozen pages at most.

The whole story about Principia Mathematic taking 200+ pages to prove the statement, speaks more to the conceptual, logical, and theoretical background that Russell and Whitehead had to develop before even beginning to penetrate more practical mathematical questions, than the actually length of the proof itself. In Peano Arithmetic the proof should only be a few lines. Russell and Whitehead took so long to reach that point because they had to lay out their entire theory of logic and set theory, not because the proof itself was long.