Gödel’s Proof
by Ernest Nagel, James R. Newman · Ernest Nagel, James R. Newman
A short classic that walks non-specialists through the structure of Gödel's incompleteness proof: Hilbert's program, Gödel numbering, and the construction of a self-referential undecidable sentence. This revised edition includes a foreword by Douglas Hofstadter.
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More resources on Gödel’s Theorems
Wolfram MathWorld
MathWorld is an online mathematics encyclopedia from Wolfram Research offering detailed, browsable articles on topics across the math spectrum, including algebra, geometry, calculus, and number theory. Each entry includes definitions, theorems, formulas, diagrams, worked examples, and links to further reading.
plato.stanford.edu
The Stanford Encyclopedia of Philosophy is a peer‑reviewed online encyclopedia of philosophy featuring in‑depth, scholarly articles written and regularly updated by experts, including comprehensive coverage of logic topics.
Stanford Encyclopedia of Philosophy: Gödel’s Incompleteness Theorems
Peer-reviewed encyclopedia entry by Panu Raatikainen explaining Gödel's first and second incompleteness theorems: arithmetization, the diagonal lemma, the role of consistency, later strengthenings, and what the results do and do not imply for philosophy of mathematics.
Mathematical Logic
Recorded lectures from UCLA's graduate course Math 220A, taught by Artem Chernikov. Covers first-order languages, structures, formal proofs, the completeness and compactness theorems and basic model theory, the groundwork needed before studying Gödel's incompleteness results.
Gödel, Escher, Bach
Pulitzer Prize-winning book that uses dialogues, Escher's art and Bach's music to explain formal systems, recursion and self-reference. Readers come away with an intuitive grasp of how Gödel's incompleteness theorem works and why it matters for minds and machines.
Introduction to Logic
This course is an introduction to Logic from a computational perspective. It shows how to encode information in the form of logical sentences; it shows how to reason with information in this form; and it provides an overview of logic technology and its applications - in mathematics, science, engineering, business, law, and so forth.