[marchdown]

There's Whitehead, who co-authored "Principia Mathematica", and then there's Wittgenstein and Wiener, who offered a fairly thorough critique. Doubtful that they didn't understand it. I can't hunt down the exact quote right now, but AFAIK, when asked how many people have read and fully appreciated Principia, Russell's answer was "perhaps a dozen".

[mathwrap]

Are there any good examples of the critiques of Wittgenstein and Wiener of Principia Mathematica?

The Wikipedia article for PM only mentions Wittgenstein and separately a 'shortcut' from Wiener. I would like to know if there are longer writings somewhere.

[marchdown]

I don't remember reading anything specific by Wiener, so that might have been from one of his talks or /Cybernetics/ or something, as for Wittgenstein, I'd look in the blue book. If it's important I can try and track down the references later. The point was, inscrutability of Principia is largely a myth. Sure, it is both nigh-unreadable and nobody actually uses the logical language developed therein, but it can be understood, it's simply not useful enough to compensate for verbosity. For a modern-day example, look at Coq. It is painfully verbose even after many iterations of refactoring.

[mathwrap]

I'm an armchair mathematician currently but I have high aspirations for my math career so it's not really important but if you have free time for definite references it would be much appreciated.

Thanks for the references so far. I'll look into Cybernetics. I already know of Coq but haven't looked that close, I'll make a note to investigate.