Question: What did the incompleteness theorem of 1931 indicate regarding Principia Mathematica?
Sentence: It is generally accepted that Kurt Gödel's incompleteness theorem of 1931 definitively demonstrated that for any set of axioms and inference rules proposed to encapsulate mathematics, there would in fact be some truths of mathematics which could not be deduced from them, and hence that Principia Mathematica could never achieve its aims.
Answer in sentence: yes