A revised edition of the classic Ernest Nagel and James Newman explanation of Gödel’s insights, and the book that inspired Douglas Hofstadter’s immensely popular Gödel Escher Bach.
From Hofstader’s Forward: We now understand that the human mind is fundamentally not a logic engine but an analogy engine, a learning engine, a guessing engine, an esthetics-driven engine, a self-correcting engine.
From the authors’ Concluding Reflections: “… what we understand by the process of mathematical proof does not coincide with the exploitation of a formalized axiomatic method. … no antecedent limits can be placed on the inventiveness of mathematicians in devising new methods of proof.
In between, Nagel and Newman tell us about the antecedents to, methods of, and number-theoretic machinery in Gödel’s proof and its insights.