Name: Gödel's proof
ISBN: 9780814758373

Gödel's proof

In 1931 Kurt Godel published his fundamental paper, "On Formally Undecidable Propositions of "Principia Mathematica" and Related Systems." This revolutionary paper challenged certain basic assumptions underlying much research in mathematics and logic. Godel received public recognition of his work in 1951 when he was awarded the first Albert Einstein Award for achievement in the natural sciences--perhaps the highest award of its kind in the United States. The award committee described his work in mathematical logic as "one of the greatest contributions to the sciences in recent times." However, few mathematicians of the time were equipped to understand the young scholar's complex proof. Ernest Nagel and James Newman provide a readable and accessible explanation to both scholars and non-specialists of the main ideas and broad implications of Godel's discovery. It offers every educated person with a taste for logic and philosophy the chance to understand a previously difficult and inaccessible subject. With a new introduction by Douglas R. Hofstadter, this book will appeal students, scholars, and professionals in the fields of mathematics, computer science, logic and philosophy, and science.

What Hacker News says

andyjohnson0Aug 2026

GEB is a great book, and I've probably read it at least 3.33333333... times over the years. As a late teen it blew my mind. But I'm not sure I'd recommend it as a route into Gödel's proofs [1]. The book covers a lot of other ground too, and is notoriously digressive and quirky (looking at you, dialogues).

Instead I'd recommend Gödel's Proof by Nagel and Newman for a conceptual intro.

[1] I'm not a mathematician, so my understanding is necessarily informal.

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trescenziAug 2026

“Godel’s Proof”[1] is also a great and shorter read if the scale of GEB is intimidating(I know it was for me at first).

https://nyupress.org/9780814758014/godels-proof/

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MathMonkeyManAug 2026

"Gödel's Proof" by Ernest Nagel and James R. Newman helped me to get it at some point.

On Amazon: <https://www.amazon.com/Godels-Proof-Ernest-Nagel-ebook/dp/B0...>

I might even pick up an ebook version if I can find it somewhere else. Been a while.

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retrocryptidMay 2026

      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 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

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remywangMay 2026

The best way to understand the theorems is to try to understand the proofs, and the short book “Gödel’s proof” by Nagel and Newman is excellent for that. Just like Douglas Hofstadter wrote in the foreword, I found the book an absolute page turner and finished in one afternoon.

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thereticentNov 2023

Nagel & Newman's Gödel's Proof is an excellent book on how the proof works. It doesn't have all the tie-ins and fun asides that GEB has, but it's stronger for it.

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