the interesting bit is that this isn't wrong; PM follows directly from Gödelian incompleteness
his theorem states that a given logical system can't be both complete & consistent; meaning that it can either be capable of expressing every true statement, OR free of contradictions
some historical context: the proof came as a direct response to the culmination of high modernist mathematics, in the form of Russell & Whitehead's Principia Mathematica, which was an attempt to codify the ultimate axiomatic system, capable of consistent universal expression