Natalie mentions  the Newman &  Nagel's text "Gödel's  Proof," a
      (//the//?) 1958 classic on the subject. [[1]] Having left IBM in
      December 1990, I spent a month  with the text, dipping into mild
      insanity, taking to strange wines  to relieve myself of the fear
      that  my previous  years  long study  of  Whitehead &  Russell's
      "Principia Mathematica" [[2]] was not useless.
   
      I  really  appreciate  the  inclusion of  Alvir's  statement  on
      whether  or not  Gödel  thought he  proved  all logical  systems
      undecidable and incomplete.   About 80% into the  article is her
      quote:
   
      >> Often people will speak as if  the CH is the smoking gun that
      >> shows sometimes  mathematical questions have no  answer.  But
      >> in my  opinion, this situation provides  very little evidence
      >> that   there   are  “absolutely   undecidable”   mathematical
      >> problems, relative to any given permissible framework.
   
      Though I would have added  a reference to Infinitary Logic [[3]]
      after dropping the reference to L-omega-1-omega.  I suspect most
      readers would find discussion of higher-order and modern logic a
      bit confusing  without a pause  for further study.  But  a guide
      post pointing in the appropriate direction would be good.
   
      That this is  the only critique I have of  the article speaks to
      Wolchover's  skill  in communicating  complex  ideas  for a  lay
      audience.  I really  liked this article, so  thank you @baruchel
      for posting the reference to it.
   
   :: References
   
      1. https://search.worldcat.org/title/1543160023
   
      2. https://search.worldcat.org/title/933122838
   
      3. https://en.wikipedia.org/wiki/Infinitary_logic